text:
\section{Introduction}
\par
In cold Fermi gas physics, there are two ways to tune pairing fluctuations. One is to use a Feshbach resonance\cite{Timmermans,Chin}, where pairing fluctuations are enhanced by increasing the strength of a pairing interaction associated with a Feshbach resonance. The other is lowering the system dimension by introducing an optical lattice\cite{Morsch,Bloch} to a three-dimensional Fermi gas. The latter approach uses the fact that pairing fluctuations are enhanced by the low-dimensionality of the system. In condensed matter physics, it is not so easy to tune the interaction strength, as well as the system dimension. Thus, having these techniques is an advantage of cold Fermi gas physics, especially in systematically studying strong-coupling physics.
\par
In this paper, we theoretically investigate the pseudogap phenomenon in an ultracold Fermi gas, when pairing fluctuations are enhanced by lowering the system dimension down to two. Pseudogap is a typical many-body phenomenon associated with strong pairing fluctuations\cite{Perali,Levin,Tsuchiya,Watanabe1}, and is characterized by the appearance of a dip in the single-particle density of states $\rho(\omega)$ (DOS) around the Fermi level in the normal state. When one simply describes pairing fluctuations as the repeat of the formation and dissociation of preformed Cooper pairs, the pseudogap is physically interpreted as a result of the ``binding energy" of preformed Cooper pairs. In this paper, we calculate the pseudogapped DOS in a two-dimensional uniform Fermi gas using a strong-coupling theory (which we specify soon later). From the temperature dependence of the pseudogap, we determine the pseudogap temperature $T^*$ as the temperature below which a dip appears in $\rho(\omega)$. Using $T^*$, we identify the pseudogap regime (where the pseudogap appears in $\rho(\omega)$) in the phase diagram of a two-dimensional Fermi gas with respect to the temperature and the interaction strength. We briefly note that a two-dimensional Fermi gas has recently attracted much attention both theoretically\cite{Botelho,Tempere,Pietilla,Watanabe,Bauer,Mulkerin,Marsiglio,Matsumoto1,Salasnich,Mulkerin1} and experimentally\cite{Martiyanov,Feld,Frohlich,Sommer,Makhalov,Fenech,Ries,Murthy2}, especially since the observation of the Berezinskii-Kosterlitz-Thouless(BKT) transition\cite{Berezinskii,Berezinskii1,Kosterlitz,Kosterlitz1} in a $^6$Li Fermi gas\cite{Ries,Murthy2}.
\par
The importance of studying two-dimensional pseudogap phenomena is related to the current debate for this phenomenon in a three-dimensional Fermi gas. In the three-dimensional case, the ``Feshbach-resonance approach" has extensively been used to study the BCS (Bardeen-Cooper-Schrieffer)-BEC (Bose-Einstein condensation) crossover phenomenon\cite{Chin,Regal,Zwierlein,Kinast,Bartenstein,Bloch,Ketterle,Zwerger}, where the character of a Fermi superfluid gradually deviates from the weak-coupling BCS-type with increasing the strength of a pairing interaction\cite{Eagles,Leggett,NSR,Melo,Randeria,Ohashi2002,Levin2005,Gurarie,Giorgini}. In the intermediate coupling regime (BCS-BEC crossover region), system properties are dominated by strong pairing fluctuations, where the pseudogap has been expected\cite{Tsuchiya,Watanabe1,Chen,Hu,Mueller,Bulgac,Jarrell,Bulgac2,Ota}. However, while the recent photoemission-type experiments on $^{40}$K Fermi gases\cite{Jin1,Jin2,Jin3,Jin4} agree with the pseudogap scenario\cite{Tsuchiya,Watanabe,Chen,Hu,Mueller,Bulgac,Jarrell,Bulgac2,Ota}, it has been shown that the observed pressure\cite{Salomon1}, as well as spin polarization rate\cite{Salomon2}, can be explained by the normal Fermi liquid theory {\it without} assuming the pseudogap. Thus, further studies are necessary to clarify whether or not pairing fluctuations really cause the pseudogap phenomenon. The mechanism of the pseudogap originating from strong pairing fluctuations is sometimes referred to as the preformed pair scenario\cite{Perali,Randeria1992,Singer,Rohe,Yanase}, and has been discussed as a candidate for the origin of the pseudogap in the under-doped regime of high-$T_{\rm c}$ cuprates\cite{Kadowaki,Shen,Fischer}. Thus, once the validity of this scenario is confirmed in cold Fermi gas physics, it would also make an impact on condensed matter physics.
\par
At a glance, using a Feshbach resonance seems more effective than the optical-lattice method for the study of pseudogap phenomenon, because the former can directly adjust the interaction strength. However, we recall that pairing fluctuations in one- and two-dimensional systems are very strong, to {\it completely} destroy the superfluid long-range order (Hohenberg-Mermin-Wagner's theorem)\cite{Hohenberg,Mermin}. In the three-dimensional case, on the other hand, although the superfluid phase transition temperature $T_{\rm c}$ is suppressed by pairing fluctuations (compared to the mean-field $T_{\rm c}$)\cite{NSR,Melo,Randeria}, the superfluid long-range order itself is always realized in the whole BCS-BEC crossover region. In this sense, lowering the system dimension is more effective than simply increasing the interaction strength, in order to enhance pairing fluctuations. Since the above-mentioned controversial situation implies that three-dimensional pairing fluctuations may not be strong enough to clearly observe the pseudogap phenomenon even in the BCS-BEC crossover region, the further enhancement of  pairing fluctuations by lowering the system dimension is a promising idea to resolve this debate. We briefly note that, even in the two-dimensional case, one can still use a Feshbach resonance\cite{Martiyanov,Feld,Frohlich,Sommer,Makhalov,Fenech,Ries,Murthy2}.
\par
Besides the pseudogap problem, the detailed pseudogap structure in $\rho(\omega)$ may also provide useful information about how to theoretically deal with the BKT transition in a two-dimensional Fermi gas. It is known that some strong coupling theories, such as the Gaussian fluctuation theory\cite{NSR,Melo,Randeria,Ohashi2002}, non-selfconsistent $T$-matrix approximation (TMA)\cite{Perali,Tsuchiya}, as well as their extended versions\cite{Haussmann,Haussmann2}, that have extensively been used to successfully explain the BCS-BEC crossover phenomenon in a three-dimensional Fermi gas, cannot describe the BKT transition, when simply applied to the two-dimensional case. To overcome this problem, a useful approach has been proposed\cite{Botelho,Tempere}, where phase fluctuations of the superfluid order parameter $\Delta$ are only taken into account, under the assumption that amplitude fluctuations of $\Delta$ can be ignored, to give a fixed value of $|\Delta|$. In this theory, with help of the KT-Nelson formula\cite{Nelson}, the BKT transition temperature $T^{\rm th}_{\rm BKT}$ can be evaluated in the wide interaction regime. This approaches uses the fact that the BKT transition belongs to the 2D-XY universality class, that is, the amplitude and phase of $\Delta$ correspond to the length and the direction of spin in the ordinary 2D-XY model, respectively. However, it is still unclear whether or not the assumption of the fixed $|\Delta|$ (or ignoring amplitude fluctuations) is always valid for the whole interaction regime. Indeed, while the calculated $T^{\rm th}_{\rm BKT}$\cite{Botelho,Tempere} agrees with the recent experiment on a two-dimensional $^6$Li Fermi gas\cite{Ries,Murthy2} in the strong-coupling regime, one clearly sees discrepancy between the two in the weak-coupling regime, implying the necessity of improving this theory. Since the fixed $|\Delta|$ gives a BCS-state-like fully gapped DOS, one can check the validity of this assumption from the detailed pseudogap structure near $T^{\rm th}_{\rm BKT}$.
\par
In this paper, we employ a self-consistent $T$-matrix approximation (SCTMA)\cite{Haussmann,Haussmann2}, to include two-dimensional pairing fluctuations. Although a non-selfconsistent $T$-matrix approximation (TMA) has extensively been used to study the pseudogap phenomenon in the three-dimensional case, we do not take this approach, because TMA is known to unphysically give large pseudogap size at low temperatures, when applied to a two-dimensional Fermi gas, even in the weak-coupling regime\cite{Marsiglio,MatsumotoJLTP}. We briefly note that SCTMA has recently been applied to the weak-coupling regime of a two-dimensional Fermi gas\cite{Bauer,Mulkerin}.
\par
So far, DOS has not been measured in a two-dimensional Fermi gas, so that we cannot completely assess the validity of our SCTMA approach, by directly comparing the calculated DOS with experimental data. However, as an alternative strategy, we show that the pseudogap size in SCTMA does not contradict with the {\it observed} Tan's contact $C$\cite{Tan} in a two-dimensional $^6$Li Fermi gas\cite{2DTan40K}.
\par
This paper is organized as follows. In Sec. 2, we explain our formulation. In Sec. 3, we show the density of states $\rho(\omega)$, as well as the spectral weight $A({\bm p},\omega)$. From the temperature dependence of the pseudogap in $\rho(\omega)$, we determine the pseudogap temperature $T^*$, to identify the pseudogap regime in the phase diagram with respect to the temperature and the interaction strength. We also examine the detailed pseudogap structure near $T_{\rm BKT}$ which has been evaluated by a previous theory assuming a fixed $|\Delta|$, to discuss the importance of amplitude fluctuations of the superfluid order parameter there. In Sec. 4, we assess our SCTMA results by using the Tan's contact. Throughout this paper, we take $\hbar=k_{\rm B}=1$, and the two-dimensional system area is taken to be unity, for simplicity.
\par
\par
\section{Formulation}
\par
We consider a two-dimensional uniform Fermi gas, described by the Hamiltonian,
\begin{eqnarray}
H
&=&
\sum_{{\bm p},\sigma}\xi_{\bm p}c^\dagger_{{\bm p},\sigma}c_{{\bm p},\sigma}
\nonumber
\\
&-&
U\sum_{{\bm p},{\bm p}',{\bm q}}
c^\dagger_{{\bm p}+{\bm q}/2,\uparrow}
c^\dagger_{-{\bm p}+{\bm q}/2,\downarrow}
c_{-{\bm p}'+{\bm q}/2,\downarrow}
c_{{\bm p}'+{\bm q}/2,\uparrow},
\label{eq1}
\end{eqnarray}
where $c^\dagger_{{\bm p},\sigma}$ is the creation operator of a Fermi atom with the two-dimensional momentum ${\bm p}=(p_x, p_y)$ and pseudospin $\sigma=\uparrow,\downarrow$, describing two atomic hyperfine states. $\xi_{\bm p}=\varepsilon_{\bm p}-\mu={\bm p}^2/(2m)-\mu$ is the kinetic energy, measured from the Fermi chemical potential $\mu$, where $m$ is an atomic mass. $-U~(<0)$ is a tunable pairing interaction associated with a Feshbach resonance. As usual, we measure the interacting strength in terms of the $s$-wave scattering length $a_{2{\rm D}}$, which is related to the bare interaction $-U$ as\cite{Morgan},
\begin{equation}
{2\pi \over m}
\left[\ln(k_{\rm F}a_{2{\rm D}})\right]^{-1}
=
{U \over 1-U\sum_{p\ge k_{\rm F}}{1 \over 2\varepsilon_{\bm p}}}.
\label{eq2}
\end{equation}
Here, $k_{\rm F}=\sqrt{2\pi N}$ is the Fermi momentum, where $N$ is the total number of Fermi atoms. In this scale, the weak- and strong-coupling regime are, respectively, characterized as $\ln{(k_{\rm F}a_{2{\rm D}})} \gesim 1$ and $\ln{(k_{\rm F}a_{2{\rm D}})} \lesssim -1$. The region between the two ($-1\lesssim \ln{(k_{\rm F}a_{2{\rm D}})} \lesssim 1$) is the intermediate coupling regime.
\par
We briefly note that the present two-dimensional system always has a bound state in the two-particle limit, irrespective of the interaction strength. The two-body binding energy is given by\cite{Petrov,Levinsen,noteEb},
\begin{equation}
E_{\rm bind}={1 \over ma_{\rm 2D}^2}.
\label{eq2b}
\end{equation}
This is different from the three-dimensional case, where a two-body bound molecule is only formed in the strong-coupling regime where the three-dimensional $s$-wave scattering length $a_s$ is positive\cite{Randeria}.
\par
\begin{figure}
\begin{center}
\includegraphics[width=7.5cm]{fig1.eps}
\caption{Self-energy $\Sigma({\bm p},i\omega_n)$ in the self-consistent $T$-matrix approximation (SCTMA). The solid line and the dashed line denote the dressed single-particle thermal Green's function $G$ in Eq. (\ref{eq3}), and the pairing interaction $-U$, respectively.}
\label{fig1}
\end{center}
\end{figure}
\par
In the self-consistent $T$-matrix approximation (SCTMA)\cite{Haussmann,Bauer, Mulkerin}, strong-coupling corrections to single-particle excitations are described by the self-energy $\Sigma({\bm p},i\omega_n)$ in the single-particle thermal Green's function,
\begin{equation}
G({\bm p},i\omega_n)=
{1 \over i\omega_n-\xi_{\bm p}-\Sigma({\bm p},i\omega_n)},
\label{eq3}
\end{equation}
where $\omega_n$ is the fermion Matsubara frequency. The SCTMA self-energy $\Sigma(\bm{p},i\omega_{n})$ is diagrammatically described as Fig. \ref{fig1}, which gives
\begin{equation}
\Sigma({\bm p},i\omega_n)
=T\sum_{{\bm q},i\nu_n}
\Gamma({\bm q},i\nu_n)G({\bm q}-{\bm p},i\nu_n-i\omega_n).
\label{eq4}
\end{equation}
Here, $\nu_n$ is the boson Matsubara frequency, and
\begin{equation}
\Gamma({\bm q},i\nu_n)=-{U \over 1-U\Pi({\bm q},i\nu_n)}
\label{eq5}
\end{equation}
is the particle-particle scattering matrix, where
\begin{equation}
\Pi({\bm q},i\nu_n)=T\sum_{{\bm p},i\omega_n}
G({\bm p}+{\bm q}/2,i\omega_{n}+i\nu_n)
G(-{\bm p}+{\bm q}/2,-i\omega_{n})
\label{eq6}
\end{equation}
is a pair-correlation function, describing fluctuations in the Cooper channel.
\par
\begin{figure}
\begin{center}
\includegraphics[width=7.5cm]{fig2.eps}
\caption{(Color online) Calculated Fermi chemical potential $\mu(T)$, as well as the renormalized chemical potential ${\tilde \mu}(T)$ in Eq. (\ref{eq12}), in a two-dimensional Fermi gas. At each interaction strength, ${\tilde \mu}(T)$ is larger than $\mu(T)$. The interaction strength is measured in terms of $\ln(k_{\rm F}a_{\rm 2D})$, where $a_{\rm 2D}$ is the $s$-wave scattering length in Eq. (\ref{eq2}) and $k_{\rm F}$ is the Fermi momentum. $T_{\rm F}$ and $\varepsilon_{\rm F}$ are the Fermi temperature and the Fermi energy, respectively.  Because of computational problems, we could not calculate $\mu$ down to $T=0$. The lowest temperature at each interaction strength is nothing to do with the BKT transition temperature.
}
\label{fig2}
\end{center}
\end{figure}
\par
The Fermi chemical potential $\mu$ is determined from the equation for the total number $N$ of Fermi atoms,
\begin{equation}
N=2T\sum_{{\bm p},i\omega_n}G({\bm p},i\omega_n).
\label{eq7}
\end{equation}
We show the calculated $\mu$ in Fig. \ref{fig2}.
\par
Using $\mu$ in Fig. \ref{fig2}, we calculate the single-particle spectral weight,
\begin{equation}
A({\bm p},\omega)=-{1 \over \pi}
{\rm Im}G({\bm p},i\omega_n\to \omega+i\delta),
\label{eq8}
\end{equation}
as well as the single-particle density of states (DOS),
\begin{equation}
\rho(\omega)=\sum_{\bm p}A({\bm p},\omega),
\label{eq.8b}
\end{equation}
where $\delta$ is an infinitesimally small positive number. In this paper, we employ the Pad\'e approximation\cite{Vidberg}, to numerically carry out the analytic continuation ($i\omega_n\to\omega+i\delta$) in Eq. (\ref{eq8}).
\par
For later convenience, we briefly note that the non-self-consistent $T$-matrix approximation (TMA) is given by simply replacing the {\it dressed} Green's function $G({\bm p},i\omega_n)$ in Eqs. (\ref{eq4}) and (\ref{eq6}) with the {\it bare} one,
\begin{equation}
G_0({\bm p},i\omega_n)=
{1 \over i\omega_n-\xi_{\bm p}}.
\label{eq6b}
\end{equation}
\par
As mentioned previously, SCTMA and TMA cannot describe the superfluid (BKT) phase below $T_{\rm BKT}$. These strong-coupling theories determine the superfluid instability from the Thouless criterion\cite{Thouless}, stating the appearance of gapless Goldstone collective mode associated with the broken $U(1)$ gauge symmetry. This condition is achieved, when the particle-particle scattering matrix in Eq. (\ref{eq5}) has a pole at ${\bm q}=\nu_n=0$, that is,
\begin{equation}
\Gamma^{-1}(0,0)=0.
\label{eq8c}
\end{equation}
However, in the two-dimensional case, Eq. (\ref{eq8c}) cannot simultaneously be satisfied with the required number equation (\ref{eq7}), because the latter diverges when the former condition is satisfied. This is a direct consequence of the Hohenberg's theorem\cite{Hohenberg}, stating the vanishing superfluid long-range order in one- and two-dimensional systems, due to the enhanced superfluid fluctuations by the low-dimensionality. In the context of two-dimensional BCS-BEC crossover physics, this problem has also been discussed within the framework of the Gaussian fluctuation theory\cite{Varma,Tokumitu}.
\par
\begin{figure}[t!]
\begin{center}
\includegraphics[width=7cm]{fig3.eps}
\caption{(Color online) SCTMA single-particle density of states $\rho(\omega)$ in the normal state of a two-dimensional Fermi gas. $\rho_0=m/(2\pi)$ is DOS in a free Fermi gas. (a) Weak-coupling case ($\ln{(k_{\rm F}a_{2{\rm D}})}=1$). (b) Intermediate coupling case ($\ln{(k_{\rm F}a_{2{\rm D}})}=0$). (c) Strong-coupling case ($\ln{(k_{\rm F}a_{2{\rm D}})}=-1$). Panel (d) shows the position of each result in the phase diagram with respect to the temperature and the interaction strength (where $T_{\rm F}$ is the Fermi temperature). In this figure, $T_{\rm BKT}^{\rm th}$ is the calculated BKT transition temperature by a BKT theory assuming a fixed $|\Delta|$\cite{Botelho,Tempere}. $T_{\rm BKT}^{\rm exp}$ is the observed one in a two-dimensional $^6$Li Fermi gas\cite{Ries}.
}
\label{fig3}
\end{center}
\end{figure}
\par
\begin{figure}[t!]
\begin{center}
\includegraphics[width=7.5cm]{fig4.eps}
\caption{ (Color online) Phase diagram of a two-dimensional uniform Fermi gas in terms of the temperature and the interaction strength. The pseudogap temperature $T^*$ is determined as the temperature below which a dip appears in $\rho(\omega\sim 0)$. The two BKT transition temperatures, $T_{\rm BKT}^{\rm exp}$\cite{Ries} and $T_{\rm BKT}^{\rm th}$\cite{Botelho,Tempere}, are the same as those in Fig. \ref{fig3}(d). The region between $T^*$ and $T_{\rm BKT}^{\rm th}$ is the pseudogap regime (PG). The region above $T^*$ is the ``normal Fermi-gas regime (NF)" with no pseudogap. On the left side of the dotted line (MB), the renormalized chemical potential ${\tilde \mu}$ in Eq. (\ref{eq12}) is negative, so that the system properties is close to those of a Bose gas of two-body bound molecules. We briefly note that the phase transition only occurs at $T_{\rm BKT}^{\rm th}$ and $T_{\rm BKT}^{\rm exp}$. The other boundaries, such as $T^*$, are crossover temperatures without being accompanied by any phase transition.}
\label{fig4}
\end{center}
\end{figure}
\par
\section{Pseudogap regime in a two-dimensional Fermi gas}
\par
Figure \ref{fig3} shows DOS $\rho(\omega)$ in a two-dimensional uniform Fermi gas. In the weak-coupling case (panel (a)), $\rho(\omega)$ at the Fermi temperature $T_{\rm F}$ monotonically increases with increasing $\omega$, to approach the  value $\rho_0=m/(2\pi)$ in the high-energy region. Since DOS in a two-dimensional free Fermi gas has the step-functional energy dependence as
\begin{equation}
\rho_0(\omega)={m \over 2\pi}\Theta(\omega+\mu)
\label{eq8d}
\end{equation}
(where $\Theta(x)$ is the step function), the broadening of this step structure seen in Fig. \ref{fig3}(a) at $T=T_{\rm F}$ is due to particle-particle scatterings (giving finite lifetime of Fermi quasi-particles). Indeed, this broadening at $T=T_{\rm F}$ becomes more remarkable in the intermediate coupling case shown in Fig. \ref{fig3}(b).
\par
In addition to this broadening effect, Figs. \ref{fig3}(a) and (b) also show that the pairing interaction (which induces pairing fluctuations) also causes the expected pseudogap phenomenon at low temperatures ($T\lesssim 0.3T_{\rm F}$). When we introduce the pseudogap temperature $T^*$ as the temperature below which a dip appears in $\rho(\omega)$ around $\omega=0$, we can conveniently identify the region where the pseudogap appears, in the phase diagram of a two-dimensional Fermi gas, as shown in Fig. \ref{fig4}. In this figure, since SCTMA cannot describe the BKT transition, we draw $T^{\rm th}_{\rm BKT}$ which has been evaluated by the recent BKT theory assuming a fixed $|\Delta|$\cite{Botelho,Tempere}. In this phase diagram, the region between $T^*$ and $T^{\rm th}_{\rm BKT}$ is regarded as the pseudogap regime (PG). We emphasize that, while $T^{\rm th}_{\rm BKT}$ is a phase transition temperature, the pseudogap temperature $T^*$ is a crossover temperature, without being accompanied by any phase transition.
\par
In the strong-coupling regime shown in Fig. \ref{fig3}(c), a dip structure is already seen at $T=T_{\rm F}$. In addition, DOS exhibits an almost fully gapped structure, when $T\lesssim 0.5T_{\rm F}$. In this regime, the {\it renormalized} chemical potential ${\tilde \mu}$ involving many-body corrections, which is determined from the equation,
\begin{equation}
-{\tilde \mu}= -\mu+{\rm{Re}}[\Sigma({\bm p}=0, \omega_{+}
=-{\tilde \mu}+i\delta)],
\label{eq12}
\end{equation}
is negative (see Fig. \ref{fig2}). Thus, as well known in BCS-BEC crossover physics\cite{Eagles,Leggett,NSR,Melo,Randeria,Ohashi2002}, system properties in this regime would be close to those of a Bose gas of two-body bound molecules, rather than an atomic Fermi gas\cite{note}. To emphasize this, we identify the region with ${\tilde \mu}\le 0$ as the ``molecular Bose gas regime" (MB) in Fig. \ref{fig4}. In this strong-coupling regime, the pseudogap temperature $T^*$, as well as the pseudogap width, are considered to be directly related to the binding energy $E_{\rm bind}$ of a two-body bound molecule in Eq (\ref{eq2b}). Indeed, Fig. \ref{fig4} shows that $T^*$ rapidly increases with increasing the interaction strength in this regime, reflecting the rapid increase of $E_{\rm bind}$.
\par
\begin{figure}[t!]
\begin{center}
\includegraphics[width=7.5cm]{fig5.eps}
\caption{(Color online) Evaluated pseudogap size $E_{\rm PG}$ in the weak-coupling side ($\ln(k_{\rm F}a_{\rm 2D})\ge 0$) of a two-dimensional Fermi gas at $T/T_{\rm F}=0.15$. $E_{\rm PG}$ is defined as the energy difference between the dip position and the lower peak position in $\rho(\omega)$ in the pseudogap regime.}
\label{fig5}
\end{center}
\end{figure}
\par
Figure \ref{fig4} also shows that the pseudogap regime widely exists in the weak-coupling regime ($\ln(k_{\rm F}a_{\rm 2D})\gesim 1)$, compared to the three-dimensional case, where the pseudogap regime is almost absent in the BCS regime (($k_{\rm F}a_s)^{-1}\lesssim -1$)\cite{Tsuchiya}. This is because the two-dimensionality of the system enhances pairing fluctuations, as well as the pseudogap phenomenon, as expected.
\par
However, we also see in Fig. \ref{fig4} that $T^*$ is rather insensitive to the interaction strength, when $0\lesssim \ln(k_{\rm F}a_{\rm 2D})\lesssim 2$, in spite of the fact that pairing fluctuations become strong with increasing the interaction strength there. In addition, defining the pseudogap size $E_{\rm PG}$ as the energy difference between the dip position and the lower peak position in the pseudogapped DOS\cite{noteZ}, we find in Fig. \ref{fig5} that $E_{\rm PG}$ at $T=0.15T_{\rm F}$ only weakly depends on the interaction strength. These indicate that the increase of the interaction strength does not necessarily promote the pseudogap phenomenon.
\par
\begin{figure}[t!]
\begin{center}
\includegraphics[width=7.5cm]{fig6.eps}
\caption{The same plots as in Fig. \ref{fig3}, in the non-self-consistent $T$-matrix approximation (TMA).}
\label{fig6}
\end{center}
\end{figure}
\par
To explain this in more detail, we point out that the non-selfconsistent $T$-matrix approximation (TMA) gives a clearer pseudogap than SCTMA, as shown in Fig. \ref{fig6}. In addition, the growth of the TMA pseudogap size $E_{\rm PG}$ with increasing the interaction strength is also more remarkable than the SCTMA case (see Fig. \ref{fig5}). Thus, in TMA, the pairing interaction simply contribute to the pseudogap phenomenon in a positive manner. In this regard, we note that TMA is given by replacing the SCTMA dressed Green's function $G({\bm p},i\omega_n)$ in the self-energy $\Sigma({\bm p},i\omega_n)$ in Eq. (\ref{eq4}) with the bare one $G_0({\bm p},i\omega_n)$ in Eq. (\ref{eq6b}). The resulting TMA particle-particle scattering matrix $\Gamma({\bm q},i\nu_n)$ (which physically describes pairing fluctuations) only consists of {\it stable} Fermi atoms with infinite lifetime. On the other hand, $\Gamma({\bm q}i\nu_n)$ in SCTMA uses the dressed Green's function $G({\bm p},i\omega_n)$, which takes into account finite quasi-particle lifetime by particle-particle scatterings. Indeed, as shown in Figs. \ref{fig7}(a1)-(c1), the SCTMA spectral weight $A({\bm p},\omega)$ exhibits {\it broad} single-particle dispersion along $\omega=\varepsilon_{\bm p}-{\tilde \mu}$ in the pseudogap regime. (Note that the bare Green's function gives a $\delta$-functional peak line along $\omega=\varepsilon_{\bm p}-\mu$ in $A({\bm p},\omega)$.) As a result, SCTMA includes the situation that one of two Fermi atoms that are repeating the formation and dissociation of a preformed Cooper pair is scattered into another state, causing the suppression of pairing fluctuations compared to the TMA case\cite{noteW}. This explains the difference between Figs. \ref{fig3} (SCTMA) and \ref{fig6}(TMA).
\par
In addition, the quasi-particle lifetime would be shorter for a stronger interaction, which tends to weaken the enhancement of pairing fluctuations by the same pairing interaction. This also explains the weaker interaction dependence of the pseudogap size $E_{\rm PG}$ in SCTMA than that in TMA, seen in Fig. \ref{fig5}.
\par
\begin{figure}[t!]
\begin{center}
\includegraphics[width=8cm]{fig7.eps}
\caption{(Color online) Calculated intensity of single-particle spectral weight $A({\bm p},\omega)$ in SCTMA (left panels), as well as in TMA (right panels). (a1) and (a2): $\ln(k_{\rm F}a_{\rm 2D})=1$ at $T/T_{\rm F}=0.122$ (``E" in Fig. \ref{fig3}(d)). (b1) and (b2): $\ln(k_{\rm F}a_{\rm 2D})=0$ at $T/T_{\rm F}=0.14$ (``D" in Fig. \ref{fig3}(d)). (c1) and (c2): $\ln(k_{\rm F}a_{\rm 2D})=-1$ at $T/T_{\rm F}=0.3$ (``C" in Fig. \ref{fig3}(d)). In the left figures, the dashed and dotted lines show the particle dispersion ($\omega=\varepsilon_{\bm p}-{\tilde \mu}$) and the hole dispersion ($\omega=-[\varepsilon_{\bm p}-{\tilde \mu}]$), respectively. The intensity is normalized by $\varepsilon_{\rm F}^{-1}$.
}
\label{fig7}
\end{center}
\end{figure}
\par
Since DOS $\rho(\omega)$ is given by the momentum-summation of the spectral weight $A({\bm p},\omega)$ (see Eq. (\ref{eq.8b})), the spectral intensity around $\omega=0$ seems also to be suppressed in the pseudogap regime. However, Figs. \ref{fig7}(a1) and (b1) actually show that, although one can slightly see the coupling of particle ($\omega=\varepsilon_{\bm p}-{\tilde \mu}$) and hole ($\omega=-[\varepsilon_{\bm p}-{\tilde \mu}]$) branches (which is also characteristic of the pseudogap phenomenon associated with pairing fluctuations\cite{Tsuchiya}), such suppression around $\omega=0$ is not clearly seen, because of broad particle and hole dispersions. While this is consistent with the relatively large value of $\rho(\omega=0)$ even in the pseudogap regime, it might become an obstacle in observing the pseudogap by using the photoemission-type experiment\cite{Jin1,Jin2,Jin3,Jin4}. We briefly note that the suppression of the spectral weight around $\omega=0$ is clearly seen in the strong-coupling regime when ${\tilde \mu}<0$, as shown in Fig. \ref{fig7}(c1).
\par
On the other hand, Figs. \ref{fig7}(a2)-(c2) shows that TMA gives the BCS-state-like spectral weight, where the two sharp peak lines are similar to the Bogoliubov single-particle dispersions in the mean-field BCS state,
\begin{equation}
E_\pm({\bm p})=\pm \sqrt{(\varepsilon_{\bm p}-\mu)^2+|\Delta|^2},
\label{eq12d}
\end{equation}
although the system is in the normal state.
\par
From the viewpoint of the recent BKT theory for a two-dimensional Fermi gas which assumes a fixed $|\Delta|$\cite{Botelho,Tempere}, Figs. \ref{fig6} and \ref{fig7}(a2)-(c2) shows that this assumption is justified in TMA, because the (almost) {\it fully-gapped} DOS is indeed realized near $T_{\rm BKT}^{\rm th}$. However, as discussed previously, this gapped structure in TMA is actually filled up to some extent by the quasi-particle lifetime effect in SCTMA (except in the strong-coupling regime where ${\tilde \mu}<0$). This SCTMA result physically means that, not only phase fluctuations, but also {\it amplitude fluctuations} of the superfluid order parameter $\Delta$, are important near $T_{\rm BKT}^{\rm th}$. We also see in Fig. \ref{fig8} that the pseudogap at $T_{\rm BKT}^{\rm th}$ becomes less remarkable, as one approaches the weak-coupling regime.
\par
At present, we have no idea about how to extend the recent BKT theory\cite{Botelho,Tempere} to include amplitude fluctuations. However, since the difference between $T_{\rm BKT}^{\exp}$\cite{Ries} and $T_{\rm BKT}^{\rm th}$\cite{Botelho,Tempere} becomes remarkable in the weak-coupling regime (see Fig. \ref{fig4}), this improvement might be a key to resolve this discrepancy, which remains as our future challenge.
\par
\begin{figure}[t!]
\begin{center}
\includegraphics[width=7.5cm]{fig8.eps}
\caption{(Color online) Calculated DOS $\rho(\omega)$ in SCTMA, in the weak-coupling regime of a two-dimensional Fermi gas at $T_{\rm BKT}^{\rm th}$\cite{Botelho,Tempere}.
}
\label{fig8}
\end{center}
\end{figure}
\par
\section{Assessment of calculated pseudogap from the viewpoint of observed Tan's contact}
\par
In the current stage of cold Fermi gas physics, DOS has not been measured, so that we cannot assess the SCTMA scheme by directly comparing the calculated DOS with experimental data. In this section, however, we demonstrate that we can still do this assessment to some extent, by using the Tan's contact\cite{Tan}, which has recently been measured in a two-dimensional $^{40}$K Fermi gas\cite{2DTan40K},
\par
To simply grasp our idea, we first deal with the TMA case, to clarify that it really overestimates the pseudogap size $E_{\rm PG}$. When low-energy pairing fluctuations are strong, the TMA self-energy $\Sigma_{\rm TMA}({\bm p},i\omega_n)$ may be approximated to\cite{Tsuchiya,Chen,note20}
\begin{eqnarray}
\Sigma_{\rm TMA}({\bm p},i\omega_n)
&=&
T\sum_{{\bm q}\nu_n}\Gamma({\bm q},i\nu_n)
G_0({\bm q}-{\bm p},i\nu_n-i\omega_n)
\nonumber
\\
&\simeq&
-\Delta_{\rm PG}^2
G_0(-{\bm p},-i\omega_n).
\label{eq20}
\end{eqnarray}
Here, the particle-particle scattering matrix $\Gamma({\bm q},i\nu_n)$ in TMA is given in Eq. (\ref{eq5}) where the dressed Green's function $G$ in the pair correlation function $\Pi({\bm q},i\nu_n)$ is replaced by the bare one $G_0$. In Eq. (\ref{eq20}),
\begin{equation}
\Delta_{\rm PG}=\sqrt{-T\sum_{{\bm q},i\nu_n}\Gamma({\bm q},i\nu_n)}
\label{eq21}
\end{equation}
is the pseudogap parameter\cite{Chen}. In this so-called static approximation for pairing fluctuations, the TMA single-particle Green's function $G_{\rm TMA}^{\rm static}({\bm p},i\omega_n)$ formally has the same form as the diagonal component of the mean-field BCS Green's function as\cite{Tsuchiya,Schrieffer},
\begin{eqnarray}
G_{\rm TMA}^{\rm static}({\bm p},i\omega_n)=-
{i\omega_n+\xi_{\bm p}
\over
\omega_n^2+\xi_{\bm p}^2+\Delta_{\rm PG}^2}.
\label{eq23G}
\end{eqnarray}
Thus, the resulting density of state has the same form as that in the ordinary BCS state with the gap size $E_{\rm PG}=\Delta_{\rm PG}$.
\par
\begin{figure}[t!]
\begin{center}
\includegraphics[width=7.5cm]{fig9.eps}
\caption{(Color online) Calculated DOS in TMA (a), and SCTMA (b). In each figure, the solid line shows the full TMA and SCTMA result, and the dashed line shows the result in the static approximation. We take $\ln(k_{\rm F}a_{\rm 2D})=0.853$ and $T/T_{\rm F}=0.27$ in order to compare our results with the recent experiment on a two-dimensional $^{40}$K Fermi gas\cite{2DTan40K}. In this experiment, the Tan's contact is measured as $C/k^4_{\rm F}=0.223$. TMA and SCTMA give $C/k^4_{\rm F}=0.766$ ($\Delta_{\rm PG}/\varepsilon_{\rm F}=1.75$) and $C/k^4_{\rm F}=0.238$ ($\Delta_{\rm PG}/\varepsilon_{\rm F}=0.975$), respectively.}
\label{fig9}
\end{center}
\end{figure}
\par
Figure \ref{fig9}(a) compares the ``BCS density of states" obtained from Eq. (\ref{eq23G}) with the full TMA result, where the static approximation is found to well describe the TMA result. Then, noting that the pseudogap parameter $\Delta_{\rm PG}$ in Eq. (\ref{eq21}) is related to the Tan's contact as\cite{Pieri,Houcke}
\begin{equation}
C=m^2\Delta_{\rm PG}^2,
\label{eq22}
\end{equation}
we find that the observable Tan's contact can be used to assess the TMA pseudogap size $E_{\rm PG}$ in Fig. \ref{fig9}(a). Evaluating Eq. (\ref{eq21}) in TMA, we have $\Delta_{\rm PG}/\varepsilon_{\rm F}=1.75$. Although this is consistent with $E_{\rm PG}/\varepsilon_{\rm F}=1.686$ evaluated from the TMA result in Fig. \ref{fig9}(a), it gives $C_{\rm TMA}/k^4_{\rm F}=0.766$, which is much larger than the recent experimental result $C/k^4_{\rm F}=0.223$\cite{2DTan40K} in the same situation as Fig. \ref{fig9}. This disagreement clearly means the overestimation of the pseudogap size in TMA, at least in the case of Fig. \ref{fig9}.
\par
We now proceed to the SCTMA case. In the case of Fig. \ref{fig9}(b), SCTMA gives $\Delta_{\rm PG}/\varepsilon_{\rm F}=0.975$. Substituting this into Eq. (\ref{eq22}), we obtain
\begin{equation}
C_{\rm SCTMA}/k^4_{\rm F}=0.238.
\label{eq23}
\end{equation}
While these values ($\Delta_{\rm PG}$ and $C_{\rm SCTMA}$) are smaller than the TMA results, Eq. (\ref{eq23}) agrees well with the observed value $C/k^4_{\rm F}=0.223$\cite{2DTan40K} in a two-dimensional $^{40}$K Fermi gas. Although one cannot simply relate $\Delta_{\rm PG}$ to the pseudogap size $E_{\rm PG}$ in the case of SCTMA, the smaller pseudogap gap size ($E_{\rm PG}/\varepsilon_{\rm F}=0.46$) in SCTMA (Fig. \ref{fig9}(b)) than that in TMA (Fig. \ref{fig9}(a)) is considered to come from the smaller value $\Delta_{\rm PG}/\varepsilon_{\rm F}=0.975 $ in the former approximation than in the latter ($\Delta_{\rm PG}/\varepsilon_{\rm F}=1.75$). Thus, although we need further analyses to check the validity of SCTMA for the study of the pseudogap phenomenon in a two-dimensional Fermi gas, at least, the calculated pseudogap size in SCTMA does not contradict with the observed value of the Tan's contact $C$. We briefly note that it has recently been shown\cite{Bauer} that SCTMA well explains the observed Tan's contact $C$ in a two-dimensional Fermi gas\cite{2DTan40K} at various interaction strengths.
\par
Before ending this section, we briefly note that the SCTMA single-particle Green's function $G_{\rm SCTMA}^{\rm static}({\bm p},i\omega_n)$ in the static approximation has the form (For the derivation, see the Appendix.),
\begin{equation}
G^{\rm static}_{\rm SCTMA}({\bm p},i\omega_n)=-
{i\omega_n+{\tilde \xi}_{\bm p} \over
\omega_n^2+{\tilde \xi}_{\bm p}^2
+{\tilde \Delta}^2_{\rm PG}({\bm p},i\omega_n)}.
\label{eq24}
\end{equation}
Here, ${\tilde \xi}_{\bm p}=\varepsilon_{\bm p}-{\tilde \mu}$, and
\begin{equation}
{\tilde \Delta}_{\rm PG}({\bm p},i\omega_n)=\Delta_{\rm PG}
\sqrt{
2
\over
1+\sqrt{1+{4\Delta^2_{\rm PG} \over \omega_n^2+{\tilde \xi}_{\bm p}^2}}
},
\label{eq25}
\end{equation}
where the pseudogap parameter $\Delta_{\rm PG}$ is also given in Eq. (\ref{eq21}), but the SCTMA particle-particle scattering matrix $\Gamma({\bm q},i\nu_n)$ in Eq. (\ref{eq5}) is now used.
\par
Comparing Eq. (\ref{eq24}) with Eq. (\ref{eq23G}), one finds that the pseudogap parameter $\Delta_{\rm PG}$ in TMA is replaced by the momentum- and energy-dependent parameter ${\tilde \Delta}_{\rm PG}({\bm p},i\omega_n)$ in Eq. (\ref{eq25}). In this regard, we note that this (${\bm p},\omega_n$)-dependence comes from the self-energy corrections in the dressed Green's function $G$ in the outer loop of the SCTMA self-energy in Fig. \ref{fig1}. In this sense, effects of quasi-particle lifetime are still partially taken into account in this static approximation for SCTMA. Indeed, this $({\bm p},\omega_n)$-dependent pseudogap parameter ${\tilde \Delta}_{\rm PG}({\bm p},i\omega_n)$ gives the partially-filled pseudogap structure (except at $\omega=0$), as shown in Fig. \ref{fig9}(b). However, Fig. \ref{fig9}(b) also shows that this static approximation overestimates the pseudogap size, indicating that it underestimates effects of quasi-particle lifetime on pairing fluctuations described by the particle-particle scattering matrix $\Gamma({\bm q},i\nu_n)$.
\par
\par
\section{Summary}
\par
To summarize, we have discussed pseudogap phenomena in a two-dimensional Fermi gas. Including pairing fluctuations within the framework of the self-consistent $T$-matrix approximation (SCTMA), we have calculated single-particle density of states $\rho(\omega)$ (DOS), as well as the single-particle spectral weight $A({\bm p},\omega)$, in the normal state. Determining the pseudogap temperature below which a dip appears in $\rho(\omega\sim 0)$, we have identify the region where the pseudogap appears (pseudogap regime) in the phase diagram with respect to the interaction strength and the temperature. We have also examined the detailed pseudogap structure near the BKT transition temperature $T_{\rm BKT}^{\rm th}$ which has been obtained by the recent BKT theory\cite{Botelho,Tempere} assuming a fixed magnitude of the superfluid order parameter $|\Delta|$, to assess the validity of this assumption.
\par
We showed that the pseudogap regime widely exists in the weak-coupling regime of a two-dimensional Fermi gas, compared to the three-dimensional case. This is an expected result, because the two-dimensionality of the system should enhance pairing fluctuations. However, we also found that the pseudogap temperature $T^*$, as well as the pseudogap size $E_{\rm PG}$, are not so sensitive to the interaction strength in the weak and intermediate coupling regime. This is because the increase of the pairing interaction shortens the lifetime of Fermi quasi-particles, which tends to suppress the enhancement of pairing fluctuations by the same pairing interaction. Indeed, when the quasi-particle lifetime effects on pairing fluctuations are completely ignored in the non-selfconsistent $T$-matrix approximation (TMA), the pseudogap size $E_{\rm PG}$ grows more remarkably with increasing the interaction strength than the SCTMA result.
\par
For the assessment of the recent BKT theory assuming a fixed amplitude $|\Delta|$ of the superfluid order parameter\cite{Botelho,Tempere}, our results show the importance of amplitude fluctuations near the BKT transition temperature $T_{\rm BKT}^{\rm th}$ which is obtained by this BKT theory. That is, the calculated pseudogapped DOS at $T_{\rm BKT}^{\rm th}$ in SCTMA still has sizable intensity around $\omega=0$, especially in the weak-coupling regime. Since TMA gives the BCS-state-like almost fully gapped DOS at $T_{\rm BKT}^{\rm th}$ (which justifies the assumption of fixed $|\Delta|$), the above-mentioned quasi-particle lifetime is found to also play an important role in this problem. Since $T_{\rm BKT}^{\rm th}$ is known to deviate from the observed BKT transition temperature $T_{\rm BKT}^{\rm exp}$\cite{Ries} in the weak-coupling regime, it is an interesting future challenge to improve this BKT theory to include amplitude fluctuations, to see to what extent this improvement can resolve this discrepancy.
\par
At present, DOS has not been measured in an ultracold Fermi gas, so that we cannot directly compare our results with experimental data. However, we pointed out that the Tan's contact (which has recently been observed in a two-dimensional Fermi gas\cite{2DTan40K}) can be used to assess our theoretical results to some extent. Using this approach, we showed that, while the TMA overestimates the pseudogap size, the pseudogap size in SCTMA does not contradict with the observed value of the Tan's contact $C$. Of course, we need further analyses for the validity of SCTMA for the study of pseudogap phenomena in a two-dimensional Fermi gas.
\par
While the wide pseudogap regime is an advantage of a two-dimensional Fermi gas in studying the pseudogap phenomenon, we still need to overcome the smearing of pseudogap structure in $\rho(\omega)$ and $A({\bm p},\omega)$ by quasi-particle lifetime, which also comes from the pairing interaction. In the current stage of cold Fermi gas physics, the photoemission-type experiment would be the most effective to directly measure single-particle properties of an ultracold Fermi gas. Thus, it is also an interesting future problem to theoretically evaluate the photoemission spectrum in the pseudogap regime of a two-dimensional Fermi gas, by using the present SCTMA formalism. Since the pseudogap is a key phenomenon in understanding strong-coupling properties of an ultracold Fermi gas, as well as in constructing BKT theory for a two-dimensional Fermi gas, our results would be useful for the studies of these crucial current topics in cold Fermi gas physics.
\par

\begin{acknowledgment}

\par
 We thank H. Tajima, P. van Wyk, D. Kharga, and D. Kagamihara for discussions. This work was supported by the KiPAS project in Keio university. M.M. was supported by a KLL Ph.D. Program Research Grant. D.I. was supported by Grant-in-Aid for Young Scientists (B) (No. JP16K17773) from JSPS. R.H. was supported by Grant-in-Aid for JSPS fellows. Y.O. was supported by Grand-in-Aid for Scientific Research from MEXT and JSPS in Japan (No. JP15K00178, No. JP15H00840, No. JP16K05503).
\par
\end{acknowledgment}
\par

redpajama_set_name: RedPajamaArXiv


text:
West London Orbital Railway
The Mayor of London has accepted the compelling case put forward by Barnet Council and its neighbouring west London boroughs for the development of a West London Orbital Railway.
Hendon Area Committee postponed
The meeting of Hendon Area Committee scheduled for tonight, Wednesday 28 February, has been postponed due to the adverse weather conditions.
Last updated: 28 February, 2018
Tenancy fraudster jailed
A local authority housing officer who illegally sublet the council property she had never lived in, has been jailed following an investigation by Barnet Council's anti-fraud team.
Suspected loan shark arrested in Barnet
A 47 year-old woman was arrested this morning (20 February 2018) on suspicion of illegal money lending and money laundering, following an operation in Barnet.
Helping looked after children follow their dreams
Barnet has become the first local authority in London to launch its own charity to help looked after children fulfil their dreams and aspirations.
Care leavers to receive Council Tax exemptions
Barnet Council is set to introduce a policy which will offer council tax relief to care leavers up to the age of 25.
Zero tolerance to FGM
Barnet Council is today (6 February) supporting this year's International Day of Zero Tolerance for Female Genital Mutilation (FGM).
Last updated: 6 February, 2018
Residents love living in Barnet
Barnet residents love where they live according to the latest Residents' Perception Survey.
Views sought on early help services
The council is seeking residents' views to help shape early help services in the borough.

redpajama_set_name: RedPajamaCommonCrawl


text:
Euro, Yen and British Pound Futures Lift DGCX Volumes in October 2017
Recently, DGCX announced its plan to launch the region's first Sharia-compliant Spot Gold contract.
Aziz Abdel-Qader | Exchanges ( Institutional FX ) | Friday, 03/11/2017 | 17:27 GMT+1 2019-05-29 14:15:40
Photo: Bloomberg
The Dubai Gold & Commodities Exchange (DGCX) has witnessed an uptick in trading volumes for the month ending October 2017, driven by increased investor interest in euro, Japanese yen and sterling futures, per a company statement.
As market participants digested the implications of geo-political tensions in key markets, which led investors to increasingly turn to derivatives to hedge and mitigate the impact of volatility, the monthly turnover of DGCX's G6 Currency portfolio touched a strong milestone in October 2017, recording a 225 percent year-on-year increase.
The exchange said in a statement that euro and pound sterling futures showed their highest monthly Average Open Interest (AOI) at 2077 and 1275 contracts respectively. Taking a year-to-date (YTD) prospective, trading volumes in the two currency pairs registered impressive growth of 112 percent and 36 percent compared to the comparable period in 2016.
Japanese yen futures witnessed strong growth too, with volumes expanding by 205 percent year-on-year compared to the same period last year. With investors looking for protection after a period of low volatility, the Swiss franc, Canadian dollar, and Australian dollar surged, leading the major currencies to mark year-on-year growth of 438 percent, 458 percent and 95 percent respectively.
Meanwhile, the exchange's Indian Single Stock Futures (SSF) grew by ten-fold compared to the same period last year, having traded an aggregate 877,218 contracts this year and crossing over 17,959 contracts on October 25th. In addition, the bourse recorded its highest ever daily volume in AOI for the BSE Sensex Index Futures.
Commenting on the exchange's performance, Gaurang Desai, CEO of DGCX, said: "As the largest and most diversified bourse in the Middle East, we are committed to providing our traders and members with a range of trading options across different asset classes to manage their risk effectively in times when they most need it. We are pleased to see our G6 currency portfolio achieve stronger trading volumes this month, as this demonstrates that DGCX currency derivatives products are increasingly used by traders for hedging and risk management purposes. We will continue to push forward with our efforts to provide our market participants with a diverse array of products and tools so that they are in a better position to take advantage and protect themselves during volatility spikes."
Recently, DGCX, the only regulated gold exchange in the Middle East, announced its plan to launch the region's first Sharia-compliant Spot Gold contract.
Tags: dgcx / dubai / trading volumes
CME Group Reports Record International Volumes in Q2 2019
DGCX Signs MoU with MDX to Enhance Commodity Trading
SGX Launches New Multi-Matching Trading Engine from Nasdaq


By the time an individual learns about vaccinations it's too late. Someone else will have made the decision that we must have one. Most likely a parent or guardian. As such, the deed will have been done years ago, evidenced by a tell-tale mark that was left on one shoulder.
Today it's possible to have had immunization shots before you were born. Still without your consent.
There are other signs of evidence that one has been vaccinated, and it's not in the form of good health. It could be autism spectrum disorder and its variations. It could be seizures. It could be sudden infant death. Few are willing to acknowledge that there might be a connection, but many will "defend" the system that doesn't take careful measures to monitor and question its practices. They tend to be ones who either make their living from these practices, or defend the "$cience" behind them. The quote below by Dr. Mayer Eisenstein isn't one of them.
Believe it or not, evidence exists which suggests that the wisdom of vaccine policies and practices may not only be questionable, but may be an unacknowledged contributor to a long list of chronic and degenerative diseases. Critics were not lay people like myself who might be quickly dismissed, but highly respected medical doctors, some of whom were ostracized for speaking out.
Without benefit of informed consent or a second opinion, a vaccinated individual is left only with the option to hope that it did indeed help strengthen the immune system, or at the very least, did no harm. It could take anywhere from a few days to many years before we know for sure.
Oddly, there is no second opinion about vaccinations, no safe haven where nature's ways are remembered, understood, and respected. We've become so convinced in the story that has been passed down through the decades – of virulent and dastardly diseases vanquished with needle and serum – that the only way to combat the growing rash of new pathologies that persist in raining on our health parade, is by pressing the pedal of the vaccination rescue wagon ever harder to the metal.
Perhaps we're going too fast for our own good.
Despite its relative youth, since the time of Edward Jenner, vaccination has controlled the following 12 major diseases, at least in parts of the world: smallpox, diphtheria, tetanus, poliomyelitis, measles, mumps, rubella, typhoid and rabies.
In the case of smallpox, the dream of eradication has been fulfilled, because this disease – at least naturally occurring disease – has disappeared from the world. Cases of poliomyelitis have been reduced by 99% thanks to vaccination, and this disease also is targeted by the World Health Organization for eradication.
The impact of vaccination on the health of the world's peoples is hard to exaggerate. With the exception of safe water, no other modality, not even antibiotics, has had such a major effect on mortality reduction and population growth.
Please pay close attention to the last paragraph, we will revisit it later.
For a few weeks after they are born, babies will have some protection, which was passed from their mother through the placenta before birth. After a short period of time, this natural protection goes away.
"Natural protection goes away?" It's in the New York Times, so it must be true, right? That's certainly what a young parent may very well think.
For these and many other reasons, any question as to the efficacy or wisdom of administering vaccines is tantamount to heresy. But that's not all. Emboldened, and not satisfied by their success in raising vaccinations to unquestionable status, proponents have pushed to make the practice mandatory, even including prenatal cases. In other words, to force them, early and often, on young and old alike.
With the question of efficacy no longer being asked or assessed, the true effects of vaccinating wouldn't be acknowledged if it hit us upside the head. The "disease" is conveniently available to take the blame instead.
The idea behind vaccinations is to affect an immune response to a particular potential disease by insinuating what is, in essence, a foreign agent carrier. An overload condition of the variola virus, the disease known as smallpox is attributed to several major population reductions that have occurred throughout history.
Why look at vaccinations now?
Increasingly, the evidence is showing that vaccinations are not doing the great good that we've accepted to be true, and for those willing to look, history reveals that they never have.
The above graphic, which was posted on the blog Ascension with Mother Earth and Current State of Affairs, speaks for itself. Yet, a commenter who chose to remain "anonymous," is dismissive, suggesting in one breath that the drug companies are to blame and not the vaccines, and that it is conjecture, not science.
If there is even a shred of truth to the graphic, then this is cause for concern. Both of my children received vaccinations as they were coming up; my son in 1977 and daughter in 1985 as a requirement for enrollment in California public schools. Yet, if vaccinations themselves are not really helpful… to put it another way, if vaccinations are really dangerous to the human, then requiring a parent to submit the child to vaccination is nothing less than extortion, and contributes to a greater conspiracy.
This subject was brought to my attention by the man who, a couple years ago, appeared out of the blue to answer naysayers who have posted their responses to this video excerpt of Dr. John Humiston from my documentary on Jim Humble's Miracle Mineral Supplement titled, Understanding MMS: Conversations with Jim Humble.
Dr. John Humiston weighed in on MMS in my documentary.
Writing under the screen name of frootloopsian, he has demonstrated a depth of knowledge of the molecular dynamics of MMS that exceeds any that I've heard, including Jim Humble. In addition, the focus of his attention is not MMS. He has no bias for, or against it. As such, in explaining how it works and why it is important, he points to other effective products that share the same chemistry.
In our mutual desire to learn, compile and share that knowledge, we have begun a collaboration on a new book that I'll tell you more about soon. I'll say this, vaccinations are only part of a larger problem that we should understand, and MMS is one of a number of solutions that should also be understood.
At the most fundamental level, however, we have before us an opportunity and responsibility to discover, and then exercise, that immeasurable element that is within.
Ending the practice of administering vaccines is one thing that the medical industry can do to demonstrate that it truly cares for the health and well-being of humanity. I'm not holding my breath on that. Refusing to permit our children to be given vaccinations is something we can do as well.
First off….WOW….I love the amount of knowledge on your site! It is amazing! I stumbled upon it while researching magnesium. 🙂 Just made my own homemade magnesium spray today. I digress. I had a question about vaccinating my 5-year-old. I am a little late the my understanding of vaccines. Sadly, she has already had most of the vaccines "recommended," and her doctor is saying she needs 5 more to be current. I'm really struggling with this. My question is this: since she has already had all of the vaccines up to this point, should I go ahead and finish them out, or not give her anymore? I know that sounds silly, but I have no idea what has already been done to her body and if I am going to leave something "unfinished", I guess is what I'm getting at. I totally disagree with vaccinating children, so my question probably sounds silly…..Please advise! 🙂 Thank you!!!
Hi Andrea… I would suggest that you request a specific list of the five more vaccines that your doctor is advising you that your daughter "needs." Once you get that list, there are sites that you can consult that will tell you the actual ingredients of each.
When you KNOW what is in the vaccine, you have a better idea of gauging how it might impact her metabolically. You can then better determine the risk that she may be under, because the chemical compounds that these serums represent are not metabolized by the body; they are stored, and the alterations that they cause remain in effect if they are not neutralized.
It's time to get beyond disagreeing with vaccinating, and KNOWING why. Also, knowing how to neutralize the effects of vaccines already taken.
I want to strongly suggest that you do this with CONFIDENCE, not fear. Nothing has been done that can't be corrected. However, you don't want to knowingly do additional harm, if harm is evident.
THANK YOU! Yes, that is the big thing, isn't it? FEAR. The mainstream medical society wants you to live in fear of NOT vaccinating! People who go against mainstream are considered freaks and fanatics! I have never heard about being able to neutralize the effects of vaccines! I have a lot of research to do!
Andrea, there are countless advocates for ZERO vaccination. Few are as well trained and informed as the man presenting the Youtube video titled… CDC's Vaccination Genocide.flv.
As you research the vaccines, you will note much reference to the Thimerosol MERCURY used in the vaccines. Of course, you will also research mercury's effect upon the human.
The true danger in vaccine is well hidden within the contagious simian cancers such as SV40, the contagious animal and human viruses, and the contagious Human Papilloma (herpes). The HeLa cell, first mentioned during 1953, carries herpes and is responsible for placing the above-listed mess into your child's DNA, via the process "lateral gene transfer". Any non-human DNA present in the vaccines also is placed in that DNA.
Arrow. Your statement couldn't be more inaccurate. In fact, the reading of one paper or text doesn't educate anyone. You must read and research EVERYTHING printed from 1717 to 1866.
I read everything printed on smallpox from 4 continents, involving 3350 years.
The Constantinople comment should be about variolation, which used HUMAN smallpox scab material in a relatively safe manner. The vaccination (VACA means COW) used in England and France, was Jenner's stolen copycat effort originally used by an English farmer.
Lady Montagu of France, and her friend Queen Consort Caroline of England, were responsible for not only bringing (1721) Variolation to their countries, but also for the changing of the method of application. The scab material remained from human smallpox. Neither the Ottoman Empire, France, or England gave free Variolation or vaccination. The Ottoman Empire record showed scab material as a trade good. English Vaccination LAWS stated that the Vaccine controllers were ORDERED to charge NO LESS THAN 18 Pence per treatment.
Both Variolation and Vaccination quickly transferred smallpox to untreated populations, especially those populations living under poor conditions. The vaccinated public were highly contagious, and the above-mentioned text stated that smallpox epidemics were most evident among the greatest percentage vaccinated public.
There are six text written by Doctors and/or Ph.D's during that time which are important, in that their Authors ALL formed Anti-Vaccination Leagues. Two of those text were used as sworn testimony during Royal Commissions investigating Vaccine.
One of those text produced evidence which caused England to ban use of Vaccine.
I suggest that folks read the history of smallpox. It is not a disese that is spread by poor hygine. It is a contageous viral infection clearly transmitted from person to person regardless of hygine and not to someone who had already had smallpox or the cowpox. In the Ottoman empire, Constanople,they vaccinated for small pox for likely centuries before this vaccine made its way to Europe and they suffered very little small pox there. It was given freely to even the poorest of people. Constanople was not known for great advances in hygine. Communal bathing was common. They had nearly erradicated small pox in their area of the world.
One needs discernment with the vaccines. Small pox was not erradicated due to improved hygine.
Thank you for adding your powerful voice and gift for incisive communication to exposing the truth about vaccines. Your work is greatly appreciated.
Greetings, I want to first say Thank You for all the information you share.
Are you familiar with the book, Poisoned Needle : Suppressed Facts about Vaccinations by Eleanor McBean published in 1957 ? I happened upon it while searching Google for more information about Vaccination injury to the Elderly.


text:
Johannes Heesters
Dutch actor, singer and entertainer
Heesters in 1964
(1903-12-05)5 December 1903
Amersfoort, Netherlands
24 December 2011(2011-12-24) (aged 108)
Starnberg, Germany
Nordfriedhof, Munich, Germany
Louisa Ghijs
(m. 1930; died 1985)
Simone Rethel
Wiesje Heesters (born 1931)
Nicole Heesters (born 1937)
www.johannes-heesters.de
Johan Marius Nicolaas Heesters (5 December 1903 – 24 December 2011) professionally known as Johannes Heesters, was a Dutch actor of stage, television and film, as well as a vocalist of numerous recordings and performer on the concert stage with a career dating back to the 1920s. Heesters worked as an actor until his death and was one of the oldest performing entertainers in history, performing shortly before his death at the age of 108. Heesters was almost exclusively active in the German-speaking world from the mid-1930s and became a film star in Nazi Germany, which later led to controversy in his native country.[1] He was able to maintain his popularity in Germany in the decades until his death.
2 Nazi Germany
3 After the war
6 Honours, decorations, awards
7.1 Television
Record of Heesters' birth
Heesters was born in Amersfoort, Netherlands, the youngest of four sons. His father Jacobus Heesters (1865–1946) was a salesman and his mother Geertruida Jacoba van den Heuvel (1866–1951), a homemaker.
Heesters was fluent in German from a very early age having lived for several years in the household of a German great uncle from Bavaria.[2] Heesters decided to become an actor and a singer at the age of sixteen and began vocal training. Heesters specialized in Viennese operetta very early in his career, and made his Viennese stage debut in 1934 in Carl Millöcker's Der Bettelstudent (The Beggar Student).
Nazi Germany[edit]
Aged 31, Heesters permanently moved to Germany with his wife and daughters in 1935. His signature role was Count Danilo Danilovich in Franz Lehár's Die Lustige Witwe (The Merry Widow). His version of Count Danilo's entrance song, "Da geh' ich ins Maxim", was well known. During his time in Germany, he performed for Adolf Hitler and visited the Dachau concentration camp, which made him a controversial figure for many Dutch.[3] Joseph Goebbels placed Heesters on the Gottbegnadeten list as an artist considered crucial to Nazi culture.[4]
Heesters funded the German war machine by donating money to the weapons industry.[5] This helped to make Heesters a very controversial figure in the late 1970s. Heesters always denied these accusations despite reliable evidence.[6]
Heesters befriended several high-ranking Nazi-officials and SS-officers.[7] Hitler is known to have been an avid admirer of his acting skills.[8][9]
At the same time, he was idolized by the Swingboy subculture, who admired his pale face and combed long black hair and tried to copy his attire. His style contrasted that promoted by the Hitlerjugend.[10]
Heesters met Hitler several times,[11] especially in the role of Count Danilo.[12] Throughout the war Heesters continued to perform for German soldiers in camps and barracks. According to German author Volker Kühn, Heesters performed for the SS at the Dachau concentration camp. Kühn cites as evidence the testimony of a Dachau inmate, Viktor Matejka, who worked for the SS and told Kühn he pulled the curtain when Heesters performed in 1941.[13][14] According to German writer Jürgen Trimborn [de] however, the interview with Matejka may not be reliable as it occurred some fifty years after the performance was said to have taken place.[15]
In December 2009, Heesters lost his libel suit against Kühn.[16] While acknowledging having visited the camp, he denied having performed as entertainment for the SS troops. In its ruling, the German court did not find whether Kühn's allegations were true, but rather that too much time had passed for an accurate determination of fact to be made.[17]
After the war[edit]
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Heesters with his future wife, Louisa Ghijs, in 1928
Heesters worked extensively for UFA until almost the end of the Second World War (his last wartime movie being Die Fledermaus, produced in 1945) and easily made the transition from the Nazi-controlled cultural scene to post-war Germany and Austria, appearing again in a number of films. These included Die Jungfrau auf dem Dach and the 1957 version of Viktor und Viktoria. He stopped making movies around 1960 to concentrate on stage and television appearances and on producing records.
In later years, Heesters spoke fondly of Hitler as a person, but condemned his political stance.[18] In the 1990s, he and his wife toured Germany and Austria with Curth Flatow's play Ein gesegnetes Alter (A Blessed Age), which was also televised in 1996. On 5 December 2003, he celebrated his 100th birthday with a television special Eine Legende wird 100 (A legend turns 100) on the ARD television channel. He received the title "Kammersänger". In December 2004, at the age of 101, Heesters appeared in Stuttgart at the Komödie im Marquardt theatre in a show commissioned on the occasion of his 100th birthday, Heesters – eine musikalische Hommage. In 2005, at the age of 102, he was featured as a soloist in a major concert tour with the Deutsches Filmorchester Babelsberg under the direction of Scott Lawton. On 5 December 2006, Heesters celebrated his 103rd birthday with a concert at the Wiener Konzerthaus. On 5 December 2007, he celebrated his 104th birthday with a concert at the Admiralspalast, Berlin. Then in February 2008, he performed in his home country for the first time in four decades amidst protests against his Nazi associations.[citation needed]
On 13 December 2008, at the age of 105, Heesters apologised for calling Adolf Hitler a "good chap" on the popular German TV show Wetten, dass..?. He stated that he had said something stupid and horrible and asked for forgiveness.[19] German media suggested that he had failed to understand the show's satirical nature.[20]
Heesters played smaller roles in his last years, as he began to lose his eyesight due to macular degeneration and could not perform on stage for long periods of times. Unable to read a teleprompter, he had to memorize his lines before a show. He played in the 2011 short film Ten as Simon Petrus and made his last stage appearance on 31 October 2011 in Munich.[21]
Personal life[edit]
Heesters' second wife Simone Rethel
My secret to a long, healthy life is love and passion; age differences do not matter.
—  Johannes Heesters, December 2010[22]
Heesters had two daughters by his first wife Louisa Ghijs, whom he married in 1930. After her death in 1985, he remarried in 1992. His second wife, Simone Rethel (born 1949), was a German actress, painter, and photographer. His younger daughter Nicole Heesters is a well-known actress in the German-speaking world, as well as his granddaughter Saskia Fischer.
In December 2010, the 107-year-old Heesters announced that he had quit smoking for his then 61-year-old wife: "She should have me as long as possible."[23]
On 1 January 2008, he fell down some stairs in his holiday home in Tyrol and broke two ribs.[24]
On 31 October 2011, Heesters gave his last public performance at the Bayrischer Hof in Munich.[25] Four weeks later, on 29 November 2011, he developed a fever, and was rushed into the hospital.[26] On 4 December, he was fitted with a heart pacemaker following a good recovery. He was allowed to go home less than a week later, just in time to spend his 108th birthday the next day with family. He did not feel strong enough to make the planned stage appearance to sing in celebration of his birthday and also had missed the premiere of his last film, Ten. Due to a relapse in his condition, on 17 December he was readmitted to the hospital where he subsequently suffered a stroke,[27] dying on Christmas Eve in 2011.[28][29][30]
Discography[edit]
Johannes Heesters in 2006
1965: Jetzt geh' ich ins Maxim
2003: Ich werde 100 Jahre alt
1937: "Ich werde jede Nacht von ihnen träumen"
1939: "Musik, Musik, Musik" (featuring Marika Rökk)
1941: "Liebling, was wird nun aus uns beiden"
1941: "Man müßte Klavier spielen können"
1949: "Das kommt mir spanisch vor"
1949: "Tausendmal möchte' ich dich küssen"
1998: "Ich werde 100 Jahre alt"
2007: "Generationen" (featuring Claus Eisenmann [de])
Honours, decorations, awards[edit]
1984: Bavarian Order of Merit
1993: Berlinian Order of Merit
2000: Ring of Honour of the City of Vienna
Bambi in 1967, 1987, 1990, 1997, 2003, 2007, 2008, 2009, 2010, 2011
2001: Platinum Romy (TV award)
2003: Goldene Kamera
2004: Kammersänger
Filmography[edit]
Johannes Heesters as Franz Joseph I of Austria (2008)
1924: Cirque hollandais
1934: Bleeke Bet - Ko Monje
1935: De Vier Mullers - Otto Muller, hun zoon
1935: Alles für die Firma
1936: The Emperor's Candlesticks - Grossfürst Peter Alexandrowitsch
1936: The Beggar Student - Simon Rymanowics
1936: The Court Concert - Lt. Walter van Arnegg
1936: Die Weltmeisterin
1937: When Women Keep Silent - Curt van Doeren
1937: Gasparone - Erminio Bondo
1938: Nanon - Marquis Charles d'Aubigne
1938: Immer wenn ich glücklich bin
1939: Das Abenteuer geht weiter [de] - Heinz van Zeelen
1939: Hello Janine! - Count Rene
1939: My Aunt, Your Aunt - Peter Larisch
1940: Liebesschule [de] - Enrico Villanova, Tenor
1940: Die lustigen Vagabunden - Werner Schratt, Schauspieler
1940: Roses in Tyrol - Graf Herbert von Waldendorf
1941: Immer nur Du [de] - Will Hollers
1941: Jenny und der Herr im Frack [de] - Peter Holm
1941: Illusion [de] - Stefan von Holtenau
1943: Karneval der Liebe [de] - Tenor Peter Hansen
1943: Melody of a Great City - Spielt sich selbst in einer Revue (cameo)
1944: Es lebe die Liebe [de] - Manfred
1944: Glück bei Frauen - Stefan Hell
1944: Es fing so harmlos an - Clemens Verné
1944: Axel an der Himmelstür - Axel
1946: Die Fledermaus - Herbert Eisenstein
1946: Renee XIV - (unfinished film)
1947: Wiener Melodien - Ferry van der Heuvels
1948: Insolent and in Love - Dr. Peter Schild, Ingenieur
1949: Dear Friend - Adrian van der Steer
1950: Wenn eine Frau liebt [de] - Martin Pratt
1950: Wedding Night In Paradise - Pieter van Goos
1951: Professor Nachtfalter - Professor Dr. Joachim Wendler
1951: Tanz ins Glück - Pedro Domingo
1951: The Csardas Princess - Edwin von Weylersheim
1952: The White Horse Inn - Dr. Siedler
1953: The Moon Is Blue - Tourist (uncredited)
1953: Die Jungfrau auf dem Dach - David Slader
1953: A Musical War of Love - Ralph Beyron
1953: The Divorcée - Karel
1953: Hit Parade - Singer
1953: Hab' ich nur Deine Liebe [de] - Franz von Suppé
1955: Hello, My Name is Cox - Paul Cox
1955: The Star of Rio - Don Felipe
1955: Bel Ami - Georges Duroy genannt Bel Ami
1956: Ein Herz und eine Seele / …und wer küßt mich - Johannes Heesters
1956: Opera Ball - Georg Dannhauser
1956: My Husband's Getting Married Today - Robert Petersen
1957: Victor and Victoria - Jean Perrot
1957: Von allen geliebt - Rudolf Avenarius
1958: Bühne frei für Marika [de] - Michael Norman
1958: Frau im besten Mannesalter [de] - Bernhard Hauff
1958: Besuch aus heiterem Himmel [de] - John Underhower
1959: Die unvollkommene Ehe - Professor Paul Lert
1961: Junge Leute brauchen Liebe [de] - Charles Fürst
1985: Otto – Der Film - Clochard
1994: Silent Love (Short) - Geigensolist
2008: 1½ Knights – In Search of the Ravishing Princess Herzelinde - Wissenschaftler
2011: Ten (short) - Mr. Peterson (final film role)
1956: Meine Schwester und ich (TV film) - Dr. Roger Fleuriot
1960: Am grünen Strand der Spree (TV miniseries) - Graf Chiaroscuro
1968: Unsere liebste Freundin (TV film) - Christian Bach-Nielsen
1973: Paganini [de] (TV film) - Prince Felice Baciocchi
1973: Hallo – Hotel Sacher … Portier!: Opernball (TV series episode) - Marinus de Ryder
1974: Hochzeitsnacht im Paradies (TV film) - Dr. Hansen
1980: Liebe bleibt nicht ohne Schmerzen (TV film) - Narrator
1982: Sonny Boys (TV film) - Al Lewis
1984: Beautiful Wilhelmine (TV miniseries) - Marschall Keith
1991: Altes Herz wird nochmal jung (TV film)
1991-1993: Zwei Münchner in Hamburg (TV series, 33 episodes) - Konsul Thaddäus van Daalen
1995: Zwei alte Hasen: Grandhotel (TV series episode) - Jan van Houten
1996: Ein gesegnetes Alter (TV film)
1999: Theater: Momo (TV film) - Meister Hora
2001: Otto – Mein Ostfriesland und mehr
2003: In aller Freundschaft: Zurück ins Leben (TV series episode) - Prof. Dr. Junghans
2008: Wege zum Glück (TV series episode) - Arbeitgeber Johannes Heesters
^ 'Heesters was Methusalem van Nederlandse podiumkunsten' (in Dutch)
^ Peter Czada/Günter Große: Comedian Harmonists. Ein Vokalensemble erobert die Welt, p. 15, Edition Hentrich, Berlin 1993; ISBN 978-3-89468-082-4
^ "Nazi-era singer returns to stage". BBC News. 17 February 2008. Retrieved 17 February 2008.
^ "Goebbels' Gottbegnadeter" by Alfred Wagner, Jüdische Allgemeine [de], 11 December 2008. (in German)
^ Ross, Beatrix (2003). Johannes Heesters, Beatrix Ross: Johannes Heesters. Auch hundert Jahre sind zu kurz. Germany: Langen/Müller. p. 234. ISBN 3-7844-2934-3.
^ Trimborn, Jürgen (2005). Der Herr im Frack – Johannes Heesters. Germany: Aufbau-Taschenbuchverlag. p. 326. ISBN 3-7466-2153-4.
^ Jürgen Trimborn Der Herr im Frack, Johannes Heesters: Biographie, p.?
^ "De favoriet van Hitler", Metro (Netherlands), quoted at Koelman.com (14 February 2008) (in Dutch)]
^ Hanna Inber Win, "Johannes Heesters: Singer Known As Hitler's Favorite Has Libel Case Thrown Out", The Huffington Post, 21 December 2008
^ »Neger, Neger, Schornsteinfeger!«: Meine Kindheit in Deutschland, page 155, Hans J. Massaquoi, S. Fischer Verlag, ISBN 3104002991.
^ Thissen, Torsten (30 November 2008). "Nie sexy, immer galant". Die Welt (in German). Retrieved 19 July 2011.
^ "Johannes Heesters – Auf den Spuren eines Phänomens" (in German). Akademie der Künste. 22 October 2006. Retrieved 19 July 2011.
^ "Der Sänger will nur geredet haben", Süddeutsche Zeitung (27 November 2008) (in German)
^ "Schlagabtausch um Heesters' KZ-Auftritt" Mitteldeutsche Zeitung, 27 November 2008. (in German)
^ "Experte sieht keine Beweise für Heesters-Auftritt im KZ Dachau" Neue Musikzeitung, 24 October 2008. (in German)
^ "Nazi-era singer loses libel suit". BBC News. 16 December 2008. Retrieved 6 May 2010.
^ Case citation: Kammergericht Berlin 10 U 6/09
^ "Historiker darf weiter von Heesters' SS-Auftritt sprechen", Der Spiegel (16 December 2008) (in German)
^ Silke Burmester, "Mr. Sexy meets Ministerin", Der Spiegel, 14 December 2008. (in German)]
^ Thomas Burmeister, "Hitler war ein guter Kerl", Stern, 4 December 2008. (in German)
^ Heesters last appearance was a unique experience for all, abendblatt.de; accessed 27 January 2016.
^ "Johannes Heesters (106): Seine zehn Geheimnisse für ein langes Leben" by Frank Gerdes, Das Neue Blatt, quoted at Wunderweib.de; accessed 27 January 2016. (in German)
^ Eric Kelsey, "Actor Johannes Heesters Quits Smoking – at age 107", Reuters, 3 December 2010.
^ "Johannes Heesters geht es besser", Der Spiegel, 2 January 2008.
^ http://m.fnp.de/nachrichten/politik/tagesthema/Heesters-letzter-Auftritt-Einmaliges-Erlebnis-fuer-alle;art742,442251
^ "Johannes Heesters muss Zwangspause einlegen", Berliner Morgenpost, 30 November 2011
^ A legend leaves the stage: Johannes Heesters, 1903–2011 Archived 2013-04-23 at the Wayback Machine
^ "Johannes Heesters ist Tot", Berliner Morgenpost, 24 December 2011.(in German)
^ Gayathri, Amrutha (26 December 2011). "Hitler's Favorite Actor Dead at 108". International Business Times; accessed 27 January 2016.
^ "Johannes Heesters". The Daily Telegraph. London, UK. 14 February 2012. Retrieved 21 February 2012.
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2011 NFL Draft: 1st Round Winners and Losers…
April 29, 2011 DrKronner	1 Comment
The focus so far has been the 4 QBs taken in the Top 12 picks, but what jumps out at me is the amount of Linemen selected in the first round of the Draft Friday. 20 of the 32 players taken are will be either attacking or protecting the QB. A lot of teams reached for needs, which allowed a lot of other teams to get great value in their position.
The Cleveland Browns – The Browns have potential to be the biggest winner in the draft here, as they traded their #6 overall pick to Atlanta for the #27 along with this years 2nd and 4th rounds picks, and next year's 1st and 4th round picks. Now I wasn't crazy about them jumping back up later in the first from 27 to 21. They selected Phil Taylor, a DT from Baylor which isn't a bad pick, but I'm not convinced they couldn't have stayed put and still gotten him with the 27. We'll have to see what else Holmgren does in the next few rounds, but so far you gotta be happy in Cleveland.
The Jacksonville Jaguars – The Jags had to trade up to get him, but with the 10th pick they got a Top 5 Projected QB in Blaine Gabbert. I've never been a Garrard fan, so to me this is a great value for them, even if they did lose a pick to jump up from 16 to 10, they got their guy. And while Gabbert can't be happy falling to 10, this seems like a good fit to me.
The Detroit Lions – My beloved Lions. After years of ineptitude by the Millen Regime they seem to finally know what they are doing. DT Nick Fairley out of Auburn was projected as a Top 3 pick a month ago, but fell out of favor because of work ethic questions, much like Ex-Lion Shaun Rodgers. The difference here is, this Lion's team has guys like Vanden Bosch and Suh, leaders on the D who will push those around them. The first organized player workouts in the NFL, after the lockout started, were those put together by Vanden Bosch. This is a great value at #13 and I think we have the guys to motivate Fairley into becoming a star. The Lions should now have the best D-Line in football.
Continue reading 2011 NFL Draft: 1st Round Winners and Losers… →
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NFL Draft: 11 Players to Look for in the 2011 Draft
April 10, 2011 Rev. Kaiser	Leave a comment
The NFL draft, to most football fans is just a little event for their teams to restock the stables with fresh rookie talent, that will end up buried on their team's depth charts just learning the ropes. Then, within a few years those fans will say: "Hey didn't we draft that guy a couple of years back?" Not really caring where the talent came from, but just sitting back and enjoying the luxury of their team's front office doing everything right and loading their teams with quality players. Ah, to be a fan of teams like that…
Well, I have no idea what that's like because I'm a Detroit Lions fan, scratch that… Detroit Lions MEGA FAN!!! And over the past decade the NFL draft has become Lions fans Super Bowl, mainly because it always seems like we're picking in the top 5, but also because it's that time of year where that magical thing starts to creep into our heads, and that thing is called Hope.
Hope that next year will be better; maybe we'll have a winning record, or even make the play-offs, or maybe even… oh sorry, I got lost in my own fantasy again.
Anyways, over the past decade I have really paid attention to who's coming out of college that could help my beloved Lions reach the top of the mountain, only to sit by and watch them blow almost all our draft picks.
I always like trying to pick guys that the casual fan hasn't really seen play, or sometimes even heard of. So without further ado – Here is my list of 11 players you should keep an eye on during this years NFL draft.
Casey Matthews LB (Oregon)
For 2010 Matthews was a 2nd Team All-American, 1st Team All-Pac 10, a semifinalist for the Butkus Award, and lead the Oregon Ducks in tackles for the 2010 season. He also had a very good showing in the National Championship Game and the Senior Bowl. Matthews is a very instinctive, tough linebacker with a high football I.Q., who isn't quite as athletic as his older brother Clay, but is a very hard-working football player who brings with him the right mentality. Matthews will be most likely taken in the 3rd or 4th round of the draft and will be a very solid starter either on the inside (4-3 or 3-4) or at the strong side (4-3) position during his NFL career.
Mark Herzlich LB (Boston College)
I have two words for this guy, TACKLING MACHINE!! Herzlich has had a very impressive career at Boston College; in 2006 he was named to the Freshman All-American Team. He finished the 2007 season with 97 tackles and led his team in tackles for a loss, which surely got him national recognition for 2008 where he won the ACC Defensive Player of the Year, 1st Team All-American, and a Butkus Award Finalist; He also had the most interceptions in the country for a linebacker that year with 6. After his Junior season he was considered a 1st round draft pick if he would've entered the NFL draft, but Herzlich decided to stay for his Senior year where, in the off-season, he was diagnosed with Ewing's Sarcoma, which is a rare form of bone cancer. Herzlich had to have surgery on his left leg to remove a tumor from his femur where doctors inserted a metal rod to help repair his leg. After the surgery the doctors told him he would never run again, but after a long rehab and a season off from football Herzlich played his last season at Boston College where he started all 13 games, and finished third on the team with 65 tackles and 50 solo stops. He tied for first on the team with two forced fumbles, and was second on the team with four interceptions. He is the definition of tough, and its players like him that make me and probably most fans love the game of football. It will probably take him another season to get his speed back fully, but he is an extremely instinctive player with good range and good coverage skills, and he heavily relies on his best attribute, which is tackling. Herzlich has a 4th to 6th round grade on him but I hope he goes no later than the 3rd round because this guy deserves it.
Marcus Cannon OT/OG (TCU)
Cannon is an absolute beast; this guy is 6-5 and weighs 358 lbs. He hang cleans 520 lbs. (A record at TCU) and he squats 720 lbs for 2 reps. He will be among the very strongest players in the NFL, not only is he strong, but he is also very athletic (for a guy his size) he ran the 40 in 5.2 sceonds and was very fluid in all of his drills he performed at his Pro Day. Cannon has been dominant as a starter at TCU as a Right Tackle for 2010 Cannon was a three-time All-Mountain West Conference selection, a 3rd Team All-American in 2010, and anchored an offensive line that led TCU to single-season records in touchdowns (70) and points scored (520). Cannon was also instrumental in TCU tying for seventh nationally, allowing just 0.75 sacks per game. Cannon played Right Tackle at TCU but is projected to play either Right Tackle or one of the Guard positions. Cannon is a down right nasty run blocker and was great as a pass blocker at the college level, but a lot of NFL Analysts think that he doesn't have the footwork to pan out as an elite Tackle at the NFL level (we'll see). Cannon will most likely go in the 2nd round, but I wouldn't be surprised if he got picked up at the end of the 1st.
Phil Taylor DT/NT (Baylor)
This guy is a load to handle on the inside, and he is a true Nose Tackle at 334 lbs. Taylor was very dominant against the "elite" Big 12 Offensive lines and he consistently beat double teams all season long. He has long arms, a huge frame, and is very strong which allows him to stack and shed his blocks, making him perfect for any 3-4 defenses looking for an anchor at the Nose Tackle position. Taylor earned 2nd Team All-Big 12 for 2010, and had the most tackles by a Baylor interior lineman (62) since Ethan Kelley in 2002. Taylor ran the 40 in 5.18 and has a good amount of pass rush moves and athleticism which will help him at the next level. After the Combine and his Pro Day Taylor is projected to be a late 1st or early 2nd round draft pick this year, especially since there are a lot of teams running a 3-4 defense in today's NFL.
Colin Kaepernick QB (Nevada)
Kaepernick is possibly the next Ben Roethlisberger. Their style of play is very similar; Kaepernick is 6-5 233 lbs, is very mobile and can throw with strength and accuracy down the field while in the pocket, or on the move. Kaepernick is also the only quarterback in college football history to have passed for over 10,000 yards and rushed for over 4,000 yards in a collegiate career, and also as the only QB to have passed for over 2,000 yards and rushed for over 1,000 yards in a single season three times in a career (consecutively).
Kaepernick is the type of Quarterback that on 3rd and long can hit a receiver down field or run for the first down. He doesn't have blazing speed, but he's fast enough. His throwing accuracy is inconsistent and he has the instinct to run instead of stay in the pocket in some situations. Kaepernick is most likely a year or 2 away from being ready to start in the NFL, but when he does I think he will be a very good NFL Quarterback. Kaepernick is projected as a 2nd-3rd round draft pick, but I would not be surprised if a team reaches for him late in the 1st round.
Kendall Hunter RB (Oklahoma State)
Hunter had a great Senior Bowl week and some considered him to be the best looking back overall. From his running ability to his blitz pickups, NFL analysts have made comparisons from Thurman Thomas to Maurice Jones-Drew. His stats are not that impressive over his career at Oklahoma State, but Hunter has a great understanding of his position and his assignments. His running ability is solid; he finds his gap and hits it hard while having good vision and cut back ability. Hunter is very impressive in picking up the blitz, at 5-7 200 lbs he is taking on much bigger and stronger players without fear or hesitation. Hunter is projected to go in the middle of the draft, but don't be shocked if he was picked up in the late 2nd round or early 3rd round.
Brooks Reed DE/OLB (Arizona)
Reed is an explosive player that is versatile enough to play either a Defensive End in a 4-3 alignment, or an Outside Linebacker in a 3-4 alignment. He was named 1st Team All-Pac 10 for his senior year at Arizona. A lot of teams have him at OLB in a 3-4 after his 4.65 40 time at the combine which was faster than 18 of the 24 linebackers there, but he's still considered a "tweener" and could work as a DE in a 4-3. Reed has a lot of experience with his hand in the dirt starting for 3 years as a DE. He has a very powerful bull rush and a quality speed rush, which he will have to add to at the next level. He has a great work ethic, a high football I.Q. and he is relentless in pursuit. When he arrives to the ball carrier he does so with power and burst. Reed is projected to go in the 2nd or 3rd round due to his skill and versatility.
Jordan Cameron TE (USC)
Cameron has really improved his stock after the Combine and his Pro day. Cameron is an athletic freak and posted great numbers for a player his size. He is 6-5, 250 lbs. and ran the 40 in 4.53 while registering a 37 ½ inch vertical leap. Cameron didn't put up impressive stats this past season, but he was very versatile for the Trojans. Cameron regularly split out from Tight End to a split receiver position resulting in a matchup problem for opposing defenses. Cameron moves extremely well for a TE, he catches the ball naturally and is very fluid in his route running. He also has the frame to only get bigger. Not to mention he also played for the USC basketball team, and we all know how teams like TE that where also basketball players. Cameron is projected to go anywhere from the 2nd round to the 4th round, but I believe he will be off the board sooner rather than later.
Davon House CB (New Mexico State)
At 6-1, 200 lbs and a 4.35 40 time at his Pro day what's not to like? Add to that great ball-hawking skills with 11 career interceptions and setting a record at NMS in interception return yardage (319) and you got a solid NFL quality Corner Back. House also has the ability of being a very dangerous return man, which will only make him more valuable to teams in need of such a player. House has the ideal size and athleticism to be a starting CB at the next level, he is also very physical and aggressive in run support which is always a plus. House is projected to be a 2nd to 4th round draft pick and considering the demand for quality CB, I would say he goes late in the 2nd round.
Stefen Wisniewski C/G (Penn State)
I just love Penn State, blue-collar, bring your lunch pail to work type players and that is exactly what Wisniewski is. Wisniewski made his first start during his freshman year at Penn State and has been a staple on the O-line ever since. A 1st Team All-American, Wisniewski is known for not only his toughness but his outstanding technical skills at his position, and extremely high football I.Q. Wisniewski has a ton of experience at both the guard and center positions against top competition throughout his career. He is very instinctive and aware of picking up blitzes, he finishes his blocks, and he is very quick and mobile with a great work ethic. In my opinion he should be the first Center off the board in the draft. Wisniewski is projected to go in the 2nd round.
Mason Foster LB (Washington)
Foster had a monster Senior year for the Huskies finishing the season with 162 tackles. Yeah, you read that right, 162 tackles in 13 games which comes out to 12.58 tackles per game. Take a minute to let it sink in…yeah it's ridiculous. Anyways, Foster was named a 1st Team All-American his Senior year and named to the All-Pac 10 team his Senior, Junior, and Sophomore year while also being named the Huskies team MVP in 2008. Foster is extremely instinctive and has good coverage skills to go along with his ability to dominate in run defense. This guy is the ideal Linebacker – He's tough, he's smart and he can play all 3 LB positions. If I had to pick just one player on this list who I thought was going to be a truly great player in the NFL, I would have to pick Foster. He not only has the experience and the skill, but he also has the right mentality and has a good head on his shoulders. I believe Foster will go in the 2nd round to a team that desperately needs LB help (hint, hint DETROIT LIONS). Anyways aside from wishful thinking Foster has a 2nd to 3rd round grade for this year's draft.
So that is my list, we'll just have to watch the draft to see where these guys go. And then, God willing, there will be a season and maybe we'll see them on the field.
Brooks ReedCasey MatthewsColin KaepernickDavon HouseDetroit LionsJordan CameronKendall HunterMarcus CannonMark HerzlichMason FosterNFLPhil TaylorStefen Wisniewski
Captain America, Christina Aguilera, and Detroit, all at the Super Bowl
February 7, 2011 DrKronner	Leave a comment
Last night was Super Bowl 45. As Vegas predicted the Packers won a close game despite some big injuries, and Ben Rapelesberger was denied his 3rd ring in 6 years. It was a good game, and as much as I hate the Lion's division rival, Green Bay has a loyal fan base and I'm happy for them.
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Dr. Ndamukong: or How I learned to stop worrying & love a rookie…
January 24, 2011 DrKronner	2 Comments
So the Lions appear to have finally done something right. Last year's 1st round pick, DT Ndamukong Suh exceeded even the loftiest of expectations. He plays old school, punch 'em in the mouth football. And the maturity he's shown so far in his early career has been impressive to say the least.
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TOPICS:Gabe AlbernozMontgomery County Council
Posted By: Ryan Miner December 11, 2017
Gabe Albornoz is the latest at-large candidate to announce he has qualified for public matching funds under the new Montgomery County public financing law.
Albornoz, who serves in the Leggett administration as the Director of the Montgomery County Recreation Department, sent an email blast yesterday announcing that his campaign has reached "250 contributors, totaling more than $20,000 from Montgomery County residents."
Ashley Bynum, Albornoz's campaign manager, forwarded A Miner Detail the following financials:
As of December 7th, we had 293 contributions totaling $29,734.44, which includes some non-County resident donors as well.
As of December 5th, we had $25,014.44 in qualifying Montgomery County contributions, and expect to receive an additional $80,399.00 in matching funds from those qualified contributions.
Montgomery County candidates must agree to raise money only from individuals and limit any single outside contribution to $150 to qualify for public financing.
In return, county executive candidates (currently four of the seven executive candidates are running under the county's public financing program) will be eligible to receive up to $750,000 in public money, with $250,000 apiece for at-large council candidates and $125,000 each for district council candidates.
Under the law, candidates cannot accept money from corporations or PACS.
According to most Montgomery County political insiders, Albornoz's name recognition and prominent senior-level position within the Leggett administration, as well as his alphabetical standing amid the crowded at-large field, is expected to give him a slight advantage in the June primary.
More than 40 candidates are expected to file for an at-large seat on the council before the February filing deadline.
The 2018 primaries are expected to see the most number of candidates in Montgomery County political history, largely as a result of the term limits ballot initiative that passed overwhelmingly in November 2016.
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