text:
\section{Introduction}

 The dynamical Casimir effect (DCE) consists in the generation of quanta from the initial vacuum (or any other) state of some field due to time-dependent boundary conditions or varying material properties of some macroscopic system (see \cite{book,vdodonov,revdal,nori} for reviews).
In the majority of cases this corresponds to the generation of photons due to accelerated motion of a single mirror, a cavity wall or time-dependent dielectric permittivity/conductivity of the intracavity medium \cite{e1,e2,e3,e4,e5,e6,e7}, although phonon generation is also possible in such systems as Bose-Einstein condensates \cite{e8,e8a}, quantum fluids of light \cite{e9} or laser-cooled atomic gases \cite{e10}.
In recent years, it has been shown that a microscopic analogue of DCE can be achieved using a time-dependent quantum Rabi model \cite{r1,r2,r3} -- a quantized single-mode electromagnetic field coupled to a two-level atom (TLA) with time-dependent parameters.
The photon generation occurs as a result of time-variation of the transition frequency of the TLA or the atom-field coupling strength, while the macroscopic boundary conditions for the field remain stationary \cite{jpcs,liberato,jpa}.
Ultimately, the photon creation relies on the presence of the counter-rotating terms (CRT) in the Rabi Hamiltonian (RH) \cite{special}, usually neglected under the rotating wave approximation (RWA) \cite{jc1,jc2}.
The time-dependent Rabi model can be implemented experimentally in the current circuit Quantum Electrodynamics (circuit QED) architecture \cite{cir2,majer,ge,ger,ger1,v1,v2,v3,blais-exp,simmonds} with artificial superconducting atoms coupled to microwave resonators, where DCE analogues were already observed both in a single-mirror and a cavity configurations \cite{dce1,dce2}.
However, the DCE is not the only relevant effect that arises from the combination of the CRT and the temporal modulation of the system parameters.
It was predicted in  Refs. \cite{igor,diego,lucas} that by properly adjusting the modulation frequency one can induce a coherent photon annihilation from non-vacuum states, in what became known as the {\em anti-dynamical Casimir effect} (ADCE).
Moreover, by letting the modulation frequency to slowly change with time, effective {\em Landau-Zener} transitions may occur between the dressed states of the time-independent Rabi Hamiltonian \cite{palermo}.

The DCE and the ADCE involve, respectively, creation and annihilation of excitations from some initial state of the atom-field system.
In order to implement these physical processes an external agent is required to supply or withdraw energy from the system by means of appropriate modulation of parameters.
However, till now there has been no clear relationship between the creation (annihilation) of excitations and the amount of energy supplied (withdrawn) by the external agent.
In this scenario, the following question can be stated: {\em is it possible to use the ADCE to extract work from the atom-field system}?
In order to address this issue, one can use the framework of quantum thermodynamics \cite{Mahler04,Horodecki13,goold15,XuerebNJP} - a field of physics seeking to establish a quantum version for thermodynamic principles and processes.
Studies in quantum thermodynamics aim to introduce appropriate definitions of work and heat \cite{HanggiPRE,Mahler08,Aberg,popescu14,HanggiPRE16,deffner16,diogo}, the development of quantum thermal machines \cite{alicki79,liden10,abah,Goswami,Bergenfeldt,RoPRL14,lutzPRL15,Ro16}, the analysis of the heat transport \cite{roukes,segal11,tanase,werlangPRE14,werlangPRE15,JoulainPRL16} and the validity of the second law at the microscopic level \cite{brandao08,esposito11,lacoste12,kosloff14,BrandaoPNAS,Oppenheim15,camati16},  the study of the stochastic thermodynamics \cite{SeifertRP,cyril15} and the fluctuation theorems \cite{Jarzynski,campisi11,batalhao14,an14,brito,TalknerNatPhys}, just to name a few.
An interesting result involving the Rabi model in the context of the quantum thermodynamics was presented in Ref. \cite{benenti}.
The authors have shown that the CRT prevent the atom-field system from reaching the absolute zero temperature, even in the limit of an infinite number of cycles.

In this paper we investigate the relationship between quantum work and the creation or annihilation of excitations in the Rabi model.
Work extraction has already been investigated in the stationary regime of the Rabi model \cite{altintas}, requiring ultra-strong couplings and huge atom-field detunings.
In our case, the time-dependent Rabi model is shown to allow for finite-time work extraction even for perturbative modulation amplitudes and moderate atom-field detunings, without demanding ultra-strong couplings.
Work can be extracted either periodically or steadily, depending on whether the modulation frequency is itself constant or time-varying.

This paper is organized as follows.
The theoretical framework is presented in Sec. \ref{II}.
In Sec. \ref{IIA} the time-dependent RH is introduced, and the system dynamics under parametric modulation is elucidated. In Sec. \ref{IIB} the definitions of work and heat are delineated.
Our main result is described in Sec. \ref{III}: ADCE can be a resource for work extraction.
In Sec. \ref{IIIA} we evidence how work extraction is related to annihilation of system excitations driven by an out-of-equilibrium finite-time protocol,  implemented as a perturbative modulation of the atomic frequency.
In Sec. \ref{IIIB} we extend the method for multi-tone modulations, which are useful for realistic initial states of the system. In Sec. \ref{IIIC} we employ a time-dependent modulation frequency in order to solve two issues, namely, the need for an asymptotic finite work extraction and the challenge of finding a very fine-tuned modulation frequency. Finally, in section \ref{IIID} we investigate how the presence of dissipation may reduce the amount of extracted work in actual implementations.
Conclusions are presented in Sec. \ref{IV}, and some formal analytical derivations are summarized in the appendix \ref{append}.

\section{Model} \label{II}

\subsection{Atom-Field Interaction}\label{IIA}

The atom-field interaction is described by the time-dependent Rabi Hamiltonian (we set $\hbar=1$) \cite{jpcs,liberato,red1,red2,jpa}
\begin{equation}\label{hrabi}
H=\omega a^\dagger a +\frac{\Omega(t)}{2}\sigma_z + g(a+a^\dagger)(\sigma_+ + \sigma_-),
\end{equation}
where $a$ ($a^\dagger$) is the cavity annihilation (creation) operator, and $\sigma_+=\ket{e}\bra{g}$ and $\sigma_-=\sigma_+^\dagger$ are the atomic ladder operators.
Here $\ket{g}(\ket{e})$ denotes the atomic ground (excited) state and $\sigma_z=\ket{e}\bra{e}-\ket{g}\bra{g}$.
The field number states are denoted by $\ket{n}$, such that $a^\dagger a\ket{n}=n\ket{n}$.
$\omega$ is the cavity frequency, $g$ is the atom-field coupling strength and
$\Omega(t)$ is the time-dependent atomic transition frequency.
The total average number of excitations is given by $N=\mbox{Tr}\left(\rho a^\dagger a\right)+ \mbox{Tr}\left(\rho\ket{e}\bra{e}\right)$, where $\rho$ denotes the atom-field density operator.

 We assume that the atomic frequency undergoes an external multi-tone modulation as
\begin{equation}
\Omega(t) = \Omega_0 + \sum_k \epsilon_\Omega^{(k)}\sin(\eta^{(k)}(t)t+\phi^{(k)}),
\end{equation}
where $\eta^{(k)}(t)$ is the $k$-$th$ modulation frequency  and $\epsilon_\Omega^{(k)}$ is the $k$-$th$ modulation amplitude.
It is worth noting that this particular choice for the modulation does not restrict the generality of our results, since for the regime considered here ($g\ll\omega,\Omega$) a weak modulation of any system parameter produces similar results \cite{jpa,igor,tom}.
We suppose that the modulation frequency $\eta^{(k)}(t)$ may also slowly change as function of time.
To uncover the effects of temporal modulation on the system dynamics, we assume a perturbative regime characterized by $\epsilon_\Omega^{(k)}\ll\Omega_0$ and $\epsilon_\Omega^{(k)}\lesssim g$. Besides, for the validity of the single-mode approximation we require the inequality $|\Delta_-|\ll\omega$, where $\Delta_-=\omega-\Omega_0$ is the average field-atom detuning.
In the following we restrict our attention to the dispersive regime, $g\sqrt{n_{max}}\ll|\Delta_-|/2$, where $n_{max}$ is the maximum number of system excitations.

The time-dependent RH can be implemented in the circuit QED architecture -- area of research that investigates the interaction between the quantized Electromagnetic field confined in microwave resonators and superconducting artificial atoms composed of Josephson junctions. Originally proposed in 2004 with the target of implementing the Jaynes-Cummings model in a highly controllable environment \cite{pra-blais}, this field has expanded enormously over the past ten years, and now it embraces a plenty of experimental architectures with different kinds of multi-level artificial atoms and sophisticated assemblies of
interconnected resonators and waveguides \cite{cir2,transmon,majer,ge,ger,majer,paik,APL}. However, all the setups have in common the attribute of strong atom-field coupling and the ability to control {\it in situ} the system parameters (e.g., the atomic transition frequency or the coupling strength). The typical parameters in current circuit QED architectures read \cite{ger1,par1,par2,par3,simmonds}: $\omega/2\pi\sim5-10$\,GHz, $g/\omega\sim 10^{-2}-10^{-1}$, $|\Delta_-|/g\sim 0-20$, $\kappa/\omega\sim\gamma/\omega\sim5\times 10^{-7} - 5\times 10^{-6}$, $T_r\sim 10-50$ mK, where $\kappa$ ($\lambda$) denotes de cavity (atom) damping rate and $T_r$ is the temperature. As will be shown in the following, these values are sufficient for the realization of the protocol proposed in this paper.

For $g/\omega,\epsilon_\Omega/\Omega_0\ll 1$ the dynamics of the time-dependent Rabi model presents qualitatively different behaviors depending on the choice of the modulation frequency $\eta(t)$ \cite{jpcs,liberato,jpa,igor,diego,lucas,tom,red2}. By properly adjusting $\eta(t)$, which depends on the initial state of the system, one can resonantly couple a specific set of the dressed states (eigenstates) of the bare RH (see Appendix \ref{append} for details).
Below we resume three qualitatively different phenomena that alter the total number of excitations: the DCE, the anti-Jaynes-Cummings behavior (AJC) and  the ADCE.

The DCE regime is characterized by the creation of photon pairs from the vacuum and occurs for the modulation frequency $\eta_{\mbox{\tiny{DCE}}}\approx2\omega$. For the initial zero-excitation state $\ket{g,0}$ the number of excitations increases through the induced transitions between the states $\ket{g,0}$, $\ket{g,2}$, $\ket{g,4}$, $\ldots$, $\ket{g,2k}$, where $k$ depends on the values of $\Delta_-$, $g$ and $\epsilon_\Omega$ \cite{igor}.
The population of the atomic excited state remains approximately unchanged in this scenario. (In reality, the transitions occur between the atom-field dressed states, which in the dispersive regime can be approximated as $\ket{g,n}$ -- see appendix \ref{append}).
On the other hand, using the same initial state and $\eta_{\mbox{\tiny{AJC}}}\approx \omega+\Omega_0$, the dynamics consists of periodic transitions between the approximate states $\ket{g,0}$ and $\ket{e,1}$. So the increase in the number of quanta occurs due to the excitation of both the atom and the cavity field. Such behavior is known as AJC regime \cite{jpcs,roberto,igor,diego} or the blue-sideband transition \cite{red1,red2}.

Both regimes presented so far are responsible for the increase in the number of excitations.
However, in Refs. \cite{igor,diego,lucas,tom} the authors showed that the number of excitations can be reduced instead, in what they called ADCE.
This effect consists of coherent annihilation of two system excitations due to the approximate transition $\ket{g,n}\longleftrightarrow\ket{e,n-3}$ (for $n\ge 3$), and takes place for the modulation frequency
$\eta_{\mbox{\tiny{ADCE}}}\approx 3\omega-\Omega_0$. For constant $\eta$ the total number of system excitations presents a periodic behavior, with the typical period of oscillation on the order of $\sim 10^{-4}g^{-1}$ for realistic experimental parameters.
One way to get a reduction in the total number of excitations without a subsequent return to its initial value is to use a time-dependent modulation frequency, $\eta(t)$, swept across the expected resonance associated with the ADCE \cite{palermo}.
A steep decrease in the number of excitations is observed when $\eta(t)\approx\eta_{\mbox{\tiny{ADCE}}}$, and as $\eta(t)$ moves away from $\eta_{\mbox{\tiny{ADCE}}}$ the resonance condition is forfeit. As shown in appendix \ref{append} this process can be viewed as an effective Landau-Zener-Stueckelberg-Majorana problem \cite{landau,zener,stuck,majo}, which asserts that the asymptotic transition between the two involved states will be complete for sufficiently small $|\dot{\eta}|$.
Hence, it is possible to deterministically induce a steady decrease in the number of excitations.

\subsection{Quantum Thermodynamics}\label{IIB}

In the context of quantum thermodynamics, the internal energy of a quantum system is the average energy $U(t)=\left\langle H(t)\right\rangle=\mbox{Tr}\left(\rho(t)H(t)\right)$, where $H(t)$ is the system's Hamiltonian and $\rho(t)$ -- its density operator.
The quantum version of the first law of thermodynamics reads \cite{alicki79,goold15}
\begin{equation}\label{ienergy}
\Delta U=W+Q,
\end{equation}
where $W$ is the work performed by an external agent and $Q$ is the heat supplied to the system by its thermal environment.
The quantum work $W$ computed from time $t_i$ up to $t_f$ is related to the time variation of the system's Hamiltonian,
\begin{equation}\label{work}
W=\int_{t_i}^{t_f}\mbox{Tr}\left(\rho(t)\partial_tH(t)\right)dt,
\end{equation}
while the heat $Q$ is related to the time variation of the density operator $Q=\int_{t_i}^{t_f}\mbox{Tr}\left(\partial_t\rho(t)H(t)\right)dt$.
For an isolated quantum system there is no heat exchange between the system and its environment, $Q=0$. Therefore, the variation of the internal energy coincides with the work done on the system ($W>0$) or extracted from the system ($W<0$).

It is important to note that the work performance crucially depends on the time variation of the system's Hamiltonian.
For example, for an isolated system described by the time-independent Rabi model, Eq. (\ref{hrabi}) with $\Omega(t)=\Omega_0$, the quantum work will always be equal to zero, even with the increase in the number of excitations caused by the counter-rotating terms.
This result shows that in order to extract work from the atom-field system it is necessary that the system's Hamiltonian itself evolves over time, driven by an external agent.

\section{Results and Discussions}\label{III}

In this section we discuss the relationship between the creation or annihilation of excitations and quantum work in the Rabi model. We shall show that generation of a finite number of excitations is accompanied by positive work performed on the system, while the coherent annihilation of quanta is accompanied by negative work of the order $\sim (-2\hbar\omega)$, i.e., the energy is withdrawn by the external agent. We shall also demonstrate that energy can be added or withdrawn from the system without changing the total number of excitation (with only infinitesimal changes in $N$), however, the net amount of work is $|W|<\hbar\omega$ in this case.

\subsection{Single-tone modulations}\label{IIIA}

We begin our analysis by investigating how the creation of excitations from the zero-excitation state $\ket{g,0}$ affects the quantum work.
The dynamics of the system was obtained through the numerical solution of the Liouville-von Neumann equation, $\dot{\rho}=-i\left[H(t),\rho(t)\right]$, where $H(t)$ is the time-dependent RH, Eq. (\ref{hrabi}).
In Fig.\ref{f1} we plot the dynamics of the quantum work
\begin{equation}
W(t)=(1/2)\int_0^t dt' \dot{\Omega}(t')\langle \sigma_z(t') \rangle\label{megadeth}
\end{equation}
 and the total number of excitations $N$ for the parameters $g/\omega=5\times10^{-2}$, $\Delta_-=8g=0.4\omega$, $\phi=0$ and $\epsilon_\Omega=0.05\Omega_0=0.03\omega$.
The DCE regime (Fig.\ref{f1} - a1 and a2) was obtained using a single-tone modulation with $\eta=2.0089\omega$.
The AJC regime (Fig.\ref{f1} - b1 and b2) was obtained using $\eta=0.9943\Delta_+$, where $\Delta_+=\omega+\Omega_0$.
In both regimes, the quantum work is predominantly positive (it may take small negative values when $N\approx 0$) and presents an oscillatory behavior, which is periodic for AJC and quasi-periodic for DCE.
This behavior resembles the dynamics of the average number of excitations in the atom-field system.
As a positive amount of work means that an external agent does work on the system, the creation of excitations in the DCE and AJC comes from the energy supplied to the system, following the relation $W = N \hbar \omega-\hbar\Delta_-P_e$, where $P_e=\mbox{Tr}\left(\rho\ket{e}\bra{e}\right)$ is the atomic excitation probability.

Work can also be realized on the system without variation of $N$. As the simplest example, consider the Jaynes-Cummings Hamiltonian (JCH) \cite{jc1,jc2}, obtained from Eq. (\ref{hrabi}) by neglecting the counter-rotating terms. This approximate model describes well the dynamics provided $g\ll\omega,\Omega_0$ and the modulation frequency is low, $\eta\ll\omega$. For JCH the total number of excitations is a constant of motion, and for the initial state $|\varphi_{n,\pm}\rangle$, which is the eigenstate of JCH with $n$ excitations (see appendix \ref{append}), the work reads
\begin{equation}
W_{\mathrm{JC}|\eta/\omega\rightarrow0} = \pm \frac{1}{2}%
\varepsilon _{\Omega }\cos 2\theta _{n}\left[ \sin \left( \eta t+\phi
\right) -\sin \left( \phi \right) \right] .
\label{WJCsmallEta}
\end{equation}
Therefore the work of magnitude $|W_{\mathrm{JC}|\eta/\omega\rightarrow0}|\le \hbar\epsilon_\Omega$ can be performed on or by the system without any change in $N$.

Still under JCH, one can obtain a finite work, either positive or negative, by setting the modulation frequency to $\eta\approx |\Delta_-|$, thereby promoting the coupling between approximate states $|g,n\rangle$ and $|e,n-1\rangle$ in the dispersive regime. This behavior is known as Jaynes-Cummings or red-sideband regime \cite{jpcs,roberto,red1,red2}, and has recently been implemented experimentally in circuit QED \cite{blais-exp,simmonds}. For instance, for the initial state $|g,n\rangle$ a straightforward energetic
reasoning predicts for the extremum amount of work $W_{\mathrm{JC}} \approx-\hbar\Delta_-$, so energy can be added or withdrawn from the system depending on the sign of $\Delta_-$. This result holds under RH as well, as illustrated in Fig. \ref{f1} - c1 and c2 for the initial state $|g,3\rangle$ and the modulation frequency $\eta=1.07\Delta_-$ (all other parameters are as previously). We see that work is indeed extracted from the system, while the total number of excitations undergoes only infinitesimal changes due to the off-resonant contribution of CRT.

\begin{figure}[!htb]
\centering
\includegraphics[width=0.99\linewidth]{fig1}
\caption{(color online) Quantum work and average total number of excitations as a function of dimensionless time $t/\tau$ for the regimes: DCE (panels a1-a2), AJC (panels b1-b2), JC (panels c1-c2) and ADCE (panels d1-d2).
Here $\tau^{-1}=g\epsilon_\Omega/2\Delta_+$ with $\Delta_\pm=\omega\pm\Omega_0$.
For the DCE and AJC regimes the initial state is $\ket{g,0}$; for the JC and ADCE regimes it is $\ket{g,3}$.
Parameters: $g/\omega=5\times10^{-2}$, $\Delta_-=8g$, $\epsilon_\Omega=0.05\Omega_0$, $\phi=0$. The modulation frequencies are $\eta_{\mathrm{DCE}}=2.0089\omega$, $\eta_{\mathrm{AJC}}=0.9943\Delta_+$, $\eta_{\mathrm{JC}}=1.07\Delta_-$ and $\eta_{\mathrm{ADCE}}=1.0076(3\omega-\Omega_0)$. Panels e1 and e2 show the dynamics of $\langle \sigma_z\rangle$ over short timescales, exhibiting fast oscillations synchronized with $\dot{\Omega}$. In the DCE regime (panel e1) the oscillations are nonsinusoidal, but the characteristic period is still $\approx 2\pi/\eta$.
}
\label{f1}
\end{figure}

Because in the DCE and AJC regimes the maximal extracted work is $W_{\mathrm{max}} > |W_{\mathrm{JC}}|$, one can see that the counter-rotating terms crucially contribute to the quantum work. Since the creation of excitations is related to the performance of work on the system, the annihilation of excitations is expected to play a role in the extraction of work.
To investigate this point, we evaluate the dynamics of $W(t)$ in the ADCE regime.
For this, we adopted $\eta=1.0076(3\omega-\Omega_0)$ and the initial state $\ket{g,3}$.
Fig. \ref{f1}- d1 and d2 show that the quantum work becomes negative indeed, proving that the ADCE can be used to extract work from the atom-field system.
Maximal work extraction occurs at times when the population of the state $\ket{g,3}$ attain its minimum value due to the transfer of population to the state $\ket{e,0}$, that is, when $N$ reaches its lowest value. We also see that in the ADCE regime one can extract the energy $\approx 2\hbar\omega$ from the system, compared to $\approx \hbar\omega/2$ under the JC resonance.

The main contribution of this paper to the field of quantum thermodynamics is that it shows a finite-time, out-of-equilibrium realistic resource for work extraction from systems suitably described by the Rabi model.
The Rabi model itself has already been investigated in the context of heat engines \cite{altintas}.
In that case, the so called adiabatic regime was addressed, which restricts the rate of change in any system's parameter to an infinitely slow pace, in order to keep it in equilibrium at all points of the cycle.
As a consequence, the exchanged work is directly proportional to the variation of the system's energy gap, since populations of the eigenstates remain constant during the work exchange protocol for an isolated atom-field system.
Therefore, a fair amount of work extraction requires huge variations of the gap, that means equally huge changes in the atom-field detuning, as well as an ultra-strong coupling regime, $g\sim \omega$.
The out-of-equilibrium process we present here conveys a conceptually different origin for work extraction: it comes from the time-dependent gap variation that under resonance conditions induces the amplification of oscillations between the eigenstates of the non-modulated system, thereby allowing the system to be driven to a lower-energy state.

The quantum thermodynamics approach also leaves clear the interference nature associated with the generation or annihilation of excitations in our protocol. As is clear from Eq. (\ref{megadeth}), the work averaged over a few periods of oscillation of $\Omega$ would be zero unless $\langle \sigma _{z}(t)\rangle $ also exhibits fast oscillations with frequencies of the order of $\eta$. This is precisely what one observes by making a zoom of $\langle\sigma_z (t)\rangle$ corresponding to data in Figs. \ref{f1} - a1 and b1, as shown in Figs. \ref{f1} - e1 and e2. This confirms that a finite average amount of work can only be obtained when the oscillations of $\langle \sigma _{z}(t)\rangle $ become synchronized with $\dot{\Omega}(t)$, meaning that energy can be added or withdrawn from the system only under resonance conditions. Since the modulation frequency must also match the energy gap associated to the transition between two system eigenstates, modulation frequencies of the order $\sim 2\omega$ lead to larger amount of added or extracted work than modulation frequencies of the order $\sim|\Delta_-|$.

\subsection{ADCE under multi-tone modulation}\label{IIIB}

The initial state influences the maximum amount of work that can be extracted from the system by means of ADCE.
As a realistic example, we consider the scenario where the field is initially in a thermal state and
the atom is in the ground state, $\rho(0)=\ket{g}\bra{g}\otimes\rho^f_T$. We recall that the thermal state is given by $\rho^f_T=\sum_np_n\ket{n}\bra{n}$, where $p_n=\bar{n}^n/(\bar{n}+1)^{n+1}$ is the  population of the state $\ket{n}$ and $\bar{n}$ is the average photon number related to temperature as $T^{-1}=k_B\omega^{-1}\ln(\frac{1+\bar{n}}{\bar{n}})$ ($k_B$ is the Boltzmann constant).

\begin{figure}[!htb]
\centering
\includegraphics[width=0.99\linewidth]{fig2}
\caption{(color online) {\it Panel a}: Quantum work as a function of dimensionless time $t/\tau$ for single-tone modulations with $\{\eta^{(1)}=1.0076(3\omega-\Omega_0),\epsilon_\Omega^{(1)}=0.05\Omega_0\}$ (black curve), $\{\eta^{(2)}=1.0113(3\omega-\Omega_0), \epsilon_\Omega^{(2)}=0.025\Omega_0\}$ (red curve), and for the two-tone modulation with the above frequencies and modulation amplitudes (blue curve). All curves correspond to the ADCE regime and $\phi^{(1,2)}=0$.
We used the initial state $\rho(0)=\ket{g}\bra{g}\otimes\rho^f_T$, where $\rho^f_T=\sum_np_n\ket{n}\bra{n}$ is a field thermal state with $p_n=\bar{n}^n/(\bar{n}+1)^{n+1}$ and $\bar{n}=1.5$ (other parameters are as in Fig. \ref{f1}).
$\tau_m$ denotes the instant of time when the extracted work is maximum.
{\it Panel b:} Dynamics of quantum work around the instant of time $\tau_m$ for a single-tone modulation with frequency $\eta^{(1)}$.
{\it Panel c:} Level diagram related to the modulation-induced transitions between the approximate eigenstates of the time-independent RH for frequencies $\eta^{(1)}$ and $\eta^{(2)}$.{\it Panel d:} Quantum work for single-tone modulation $\eta^{(1)}$ in the presence of Markovian dissipation. The cavity and atom damping rates are $\kappa=\gamma=2\times 10^{-5}g$, and the reservoirs' temperature is $k_B T_r/\omega=0.33$. {\it Panel e:} Behavior of $N$ under unitary and dissipative dynamics.}
\label{f2}
\end{figure}

\begin{figure}[!htb]
\centering
\includegraphics[width=0.99\linewidth]{fig3}
\caption{(color online) {\it Panels a-b}: Quantum work and $N$ under unitary (black curves) and dissipative (green curves) evolution for aperiodic modulation with frequency $\eta(t)=\eta^{(1)}-10\lambda + \lambda^2t$, where
$\eta^{(1)}=1.0076(3\omega-\Omega_0)$, $\phi=0$ and $\lambda=1.67\times10^{-5}\omega$.
The initial state and other parameters are as in Fig. \ref{f2}. The dynamics resembles the typical Landau-Zener behavior for an effective TLA undergoing adiabatic frequency sweep.  {\it Panel c}: Quantum work under dissipative dynamics for two different choices of the modulation frequency: $\eta(t)=\eta^{(1)}-10\lambda + \lambda^2t$ (red curve) and $\eta(t)=\eta^{(1)}-6\lambda + \lambda^2t$ (blue curve). One can see that for the blue curve the work extraction is larger and faster, hence there is room for further optimization of our protocol.
}
\label{f3}
\end{figure}

Since the modulation frequency depends on the initial state, we can adjust the value of $\eta$ to select a particular transition $\ket{g,n}\longleftrightarrow\ket{e,n-3}$ for a given value of $n$.
Therefore, the amount of work extracted from the system depends on the initial populations of the states $\ket{g,n}$ and $\ket{e,n-3}$. As shown in the appendix \ref{append}, one is able to extract work from any initial state of the form $\ket{g}\bra{g}\otimes\rho^f$  provided the initial population $P_{\ket{g,n}}$ is larger than $P_{\ket{e,n-3}}$.
To illustrate this point we plot in Fig. \ref{f2} - a the quantum work $W$ as a function of dimensionless time $t/\tau$ for two different modulation frequencies: $\eta^{(1)}=1.0076(3\omega-\Omega_0)$ (black curve) and $\eta^{(2)}=1.0113(3\omega-\Omega_0)$ (red curve).
We use the same parameters as previously, $\bar{n}=1.5$ and $\phi^{(1,2)}=0$.
As discussed in section \ref{IIIA}, the dynamics of the quantum work in the ADCE regime presents a periodic behavior on large timescales.
In Fig. \ref{f2} - a we adopt a time interval that corresponds to a single oscillation period.
Frequency $\eta^{(1)}$ drives the transition $\ket{g,3}\longleftrightarrow\ket{e,0}$, whereas frequency $\eta^{(2)}$ drives the transition $\ket{g,4}\longleftrightarrow\ket{e,1}$.
Since the initial population of state $\ket{g,3}$ is larger than the initial population of state $\ket{g,4}$, $p_3\approx0.086>p_4\approx0.052$, it is possible to extract a larger amount of work using the modulation frequency $\eta^{(1)}$ rather than the frequency $\eta^{(2)}$~\cite{foot}.
The instant of time $\tau_m$ at which the work extraction is maximum depends on both the number of photons in the state $\ket{g,n}$ and the modulation amplitude $\epsilon_\Omega$: $\tau_m^{-1}\propto\sqrt{n(n-1)(n-2)}\epsilon_\Omega^{(k)}$ (see Appendix \ref{append} for details).
Fig. \ref{f2} - b shows the dynamics of quantum work around the instant of time $\tau_m$.
The quantum work rapidly oscillates at time scale $1/\eta^{(1)}$ due to the fast oscillations of $\langle \sigma_z\rangle$, which are necessary to withdraw a finite amount of energy from the system (as discussed in section \ref{IIIA}).

In order to adjust the same $\tau_m$ for both modulation frequencies, $\eta^{(1)}$ and $\eta^{(2)}$, the modulation amplitude associated with frequency $\eta^{(2)}$ was set as $\epsilon^{(2)}_\Omega=\epsilon^{(1)}_\Omega/2$, where $\epsilon^{(1)}_\Omega=0.05\Omega_0$ is the modulation amplitude associated with frequency $\eta^{(1)}$.
This choice of modulation amplitudes is particularly convenient for employing multi-tone modulations.
The blue curve in Fig. \ref{f2} - a describes the dynamics of the quantum work for a two-tone modulation characterized by the atomic frequency $\Omega(t) = \Omega_0 + \sum_{k=1,2} \epsilon_\Omega^{(k)}\sin(\eta^{(k)}t)$.
In this case, the amount of work extracted is effectively affected by both transitions: $\ket{g,3}\longleftrightarrow\ket{e,0}$ and $\ket{g,4}\longleftrightarrow\ket{e,1}$.
Hence, according to expression (\ref{megadeth}), the total amount of work extracted from the system is equal to the sum of the works extracted by each single-tone modulation individually.
Therefore, in order to maximize the extracted work, one needs to adjust the amplitudes $\epsilon_\Omega^{(k)}$ in such a way that all the induced transitions have the same $\tau_m$.

\subsection{Effective Landau-Zener transitions}\label{IIIC}

In the cases studied so far, we observed two features that can possibly be regarded as issues.
Firstly, the dynamics of the quantum work in the ADCE regime presents a periodic behavior.
The amount of work extracted from the system will, then, be maximal around specific instants of time ($t=n\tau_m$ with $n=1,2,\ldots$), after which it will return to zero.
Secondly, the ADCE regime is obtained for a very fine-tuned modulation frequency $\eta$, which must be ultimately found either numerically or experimentally.

We overcome these possible limitations by using a time-dependent modulation frequency $\eta(t)$ \cite{palermo}.
As discussed in section \ref{IIA}, when the modulation frequency varies over time, it can assume values close to the resonance frequency $\eta_{\mbox{\tiny{ADCE}}}$, that corresponds to the ADCE regime for a given initial state.
When $\eta(t)$ is close to $\eta_{\mbox{\tiny{ADCE}}}$, the energy of the atom-field system will decrease due to the work extraction.
But, as $\eta(t)$ moves away from $\eta_{\mbox{\tiny{ADCE}}}$, the resonance condition $\eta(t)\approx\eta_{\mbox{\tiny{ADCE}}}$ is lost.
Therefore, the external agent responsible for the atomic frequency modulation will not be able to give back energy to the system.
To illustrate this point we choose $\eta(t)=\eta^{(1)}-10\lambda + \lambda^2t$, where $\lambda$ is the transition rate between the states $\ket{g,3}$ and $\ket{e,0}$.
The initial state is the local thermal state $\rho(0)=\sum_np_n\ket{g,n}\bra{g,n}$, and all other parameters are as in section \ref{IIIB}.
In this case, $\eta^{(1)}=1.0076(3\omega-\Omega_0)$ and $\lambda=1.67\times10^{-5}\omega$.

In Fig. \ref{f3} - a  we plot the quantum work as a function of dimensionless time $t/\tau$.
The transition $|g,3\rangle \longrightarrow |e,0\rangle$ begins at $t_b\approx5/\lambda\approx 140\tau$, corresponding to $\eta(t_b)=\eta^{(1)}-5\lambda$, instead of $\eta(t_b)=\eta^{(1)}$ one would expect naively. Such discrepancy can be explained after rigorous derivation of the effective Hamiltonian, which reads $H_{\mathrm{eff}}=V(t)(\ket{g,3}\bra{g,3}-\ket{e,0}\bra{e,0})/2+(\lambda\ket{g,3}\bra{e,0}+h.c.)$, where $V(t)=2\lambda^2t-10\lambda$ (see appendix \ref{append}).
Indeed, for $t\approx t_b$ one obtains $V(t_b)\approx 0$, corresponding to the expected resonance condition. Fortunately, we do not have to solve analytically the time evolution according to the Hamiltonian $H_{\mathrm{eff}}$, since this was made independently in 1932 by \emph{Landau, Zener,  Stueckelberg and Majorana}, in what became known as Landau-Zener problem \cite{landau, zener,stuck,majo}. As shown in the appendix \ref{append}, for sufficiently slow $\dot{\eta}$ the transition from $|g,3\rangle$ to $|e,0\rangle$ is almost complete, even for finite duration of the process \cite{palermo}.
Therefore, the work extracted from the system tends to a steady value $W\approx-0.2\hbar\omega$.
Note that this steady value is practically equal to the maximum extracted work using the time-independent modulation frequency $\eta=\eta^{(1)}$, shown in Fig. \ref{f2} - a (black curve).

\subsection{Account of dissipation}\label{IIID}

For actual experimental implementation of our proposal it is necessary to take into account the interaction between the system and its environments. For the quantum Rabi model with moderate coupling rates, $g/\omega \lesssim 10^{-1}$, one can use the Markovian master equation in the dressed picture, which was rigorously deduced from the first principles in \cite{red1}. We did solve it numerically and verified that for the parameters of Figs. \ref{f1} and \ref{f2} the results are almost indistinguishable from the predictions of a much simpler \lq standard master equation\rq\ of Quantum Optics: $\dot{\rho}=-i\left[H(t),\rho(t)\right]+\mathcal{L}(\rho)$.
The Liouvillian superoperator $\mathcal{L}(\rho)$ reads \cite{pra-blais,red1,diego,palermo}
\begin{eqnarray}
\mathcal{L}(\rho)&=&\gamma(1+n_a)\mathcal{D}[\sigma_-]\rho+\gamma n_a\mathcal{D}[\sigma_+]\rho\nonumber\\
&+& \kappa(1+n_c)\mathcal{D}[a]\rho+\kappa n_c\mathcal{D}[a^\dagger]\rho,
\end{eqnarray}
where $\mathcal{D}[c]\rho\equiv\frac{1}{2}(2c\rho c^\dagger-c^\dagger c\rho-\rho c^\dagger c)$, $\kappa$ ($\gamma$) is the decay rate of the cavity (atom) and $n_c=[\exp(\beta\hbar\omega)-1]^{-1}$ ($n_a=[\exp(\beta\hbar\Omega_0)-1]^{-1}$) is the mean number of thermal excitations in the cavity (atom). Here $\beta=k_B T_r$ and $T_r$ is the common temperature of both reservoirs, adjusted so that $n_c=0.05$. We use the same parameters as previously, which give $n_a=0.19$ for the positive detuning adopted in this paper. For the dissipative rates we assume the state-of-the-art values in circuit QED: $\kappa=\gamma=2\times10^{-5}g$.

We studied the influence of dissipation on the quantum work and average number of excitations in the ADCE regime for the initial state $\rho(0)=|g\rangle\langle g|\otimes\rho_T^f$ with $\bar{n}=1.5$. In Fig. \ref{f2} - d and e we show the behavior of $W$ and $N$ for a single-tone modulation that drives the transition $|g,3\rangle \longleftrightarrow |e,0\rangle$. For initial times the amount of extracted work is approximately equal to the one obtained in the lossless case, although its absolute value decreases as time goes on. The average number of excitations decreases with exponential envelope superposed with small oscillations due to the periodic transitions between $|g,3\rangle$ and $|e,0\rangle$, which are resolvable for initial times.

The aperiodic regime with time-dependent $\eta$ is also feasible in the presence of dissipation, as illustrated in Fig. \ref{f3}. The behavior of $W$ and $N$ for the modulation frequency $\eta(t)=\eta^{(1)}-10\lambda + \lambda^2t$ is illustrated in Fig. \ref{f3} - a and b. The qualitative behavior of quantum work is similar in the unitary and dissipative cases, although the amount of extracted work is roughly $50\%$ smaller due to the losses. The behavior of $N$ is also affected by the ADCE: instead of an exponential decay expected for pure damping, $N$ exhibits an accentuated decrease around $t\sim 130\tau$, which is precisely where the LZ transition takes place.

We finally note that in the presence of dissipation it is advantageous to decrease the duration of the frequency sweep in the effective LZ process, so that the transition occurs at earlier times while the population of the state $|g,3\rangle$ is as high as possible. The downside of such a drastic measure is that the probability of complete population transfer from $|g,3\rangle$ to $|e,0\rangle$ is lowered and the Landau-Zener formula (\ref{Dau}) loses its validity. Yet a compromise can be found in order to optimize the work extraction. An example is shown in Fig. \ref{f3} - c for the modulation frequency $\eta(t)=\eta^{(1)}-6\lambda + \lambda^2t$ (blue curve): the LZ transition takes place earlier than in the previous case, and the amount of extracted works is slightly higher. This results demonstrate that our protocol can be optimized for maximum work extraction in realistic scenarios.

\section{Conclusions}\label{IV}
We have established for the first time the direct relationship between the quantum work and generation or annihilation of excitations in the quantum Rabi model with time-modulated atomic frequency. Our results are valid in the dispersive regime of light-matter interaction ($|\Delta_-|\sim 10g$), moderate coupling strengths ($g/\omega\sim 0.05$) and perturbative modulation amplitude ($\epsilon_\Omega/\Omega_0 \sim 0.05$), and can be easily extended for the modulation of other parameters. We showed that the \lq rotating\rq\ (or \lq Jaynes-Cummings\rq ) terms in the Rabi Hamiltonian can be used both do add and extract energy from the system while maintaining the total number of excitations approximately constant.
However, the maximum value of the work is limited by $|W_{\mathrm{max}}|\lesssim\hbar|\Delta_{-} |<\hbar\omega$ in this case.
Even in this number-conserving scenario, the out-of-equilibrium protocol we propose outperforms the very slow adiabatic modulations, i.e., $|W_{\mathrm{max}}| \sim 0.5 \hbar\omega  > \hbar \epsilon_\Omega = 0.03 \hbar\omega$.

Much greater amount of energy can be transferred between the system and the external agent by harnessing the \lq counter-rotating\rq\ (or \lq anti-Jaynes-Cummings\rq ) terms. We showed that the generation of excitations is accompanied by positive work, as in the dynamical Casimir and anti-Jaynes-Cummings effects. On the other hand, the work becomes negative in the so called anti-dynamical Casimir effect (ADCE), when one pair of excitations is coherently annihilated under appropriate modulation frequency. For ADCE the maximum amount of extracted work is $|W_{\mathrm{ADCE}}| \sim 2\hbar\omega \gg \hbar \epsilon_\Omega = 0.03\hbar\omega$, and strongly depends on the initial state. We also explained why the generation and annihilation of excitations are always accompanied by fast low-amplitude oscillations of the atomic population inversion: the attainment of a finite amount of work requires the synchronization of oscillations of $\langle \sigma_z(t)\rangle$ and the atomic transition frequency $\Omega(t)$.

We extended our results to realistic initial states in circuit QED, arguing that multi-tone modulations are more effective in extracting energy from the system when the field is prepared in a thermal equilibrium state. Additionally, we have shown how effective Landau-Zener transitions between the system dressed-states may be employed for obtaining aperiodic work extraction, which also solves the problem of an extremely fine-tuned adjustment of the modulation frequency. Lastly, we carried out numerical simulations to assess the feasibility of our proposal in realistic circuit QED setup subject to atomic and cavity dampings, demonstrating that periodic and aperiodic work extraction is still possible, although in a smaller amount compared to the lossless case. We hope these results will find applications in out-of-equilibrium quantum thermal machines of finite-time cycles.

redpajama_set_name: RedPajamaArXiv


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Are conservatives 'misunderestimating' Harry Reid?
His supposedly "mild-mannered" replacement, Nevada Sen. Harry Reid, could become a bigger headache for Republicans and conservatives than Daschle ever was. He's misunderstood by the opposition, and the political machine he built in Nevada provides great insight into what may happen nationally.
I know from experience: I've been on his bad side and lived to tell about it only because of a lucky career break.
In 1996, after a stint as a radio talk-show host in California, I was hired to host the afternoon drive program at Reno's primary news/talk radio station, KOH-AM. Its news anchors, rare longtime locals in a transient state, were quick to help acquaint me with Nevada's quirky political culture.
I drove all over the area to meet various political leaders, but found most had little idea why they should spend time with the new kid on talk radio. The medium's nationwide impact just hadn't registered despite the 1994 election results.
Before I even got started, though, I encountered Sen. Harry Reid. Steps ahead of the others in understanding talk radio's impact, he visited the station regularly to tape on-air commentaries. Listeners would complain the Democrat was getting free airtime without Republican responses, but the feature continued. It wasn't a case of media bias, as ours was a rare news operation almost free of known liberals. Rather, it was a testament to Reid's power in the state: Don't mess with me if you know what's good for you.
My first crime apparently was not to have him as a regular guest on my show, lobbing softball questions Larry King-style, as had been done previously. It was like refusing to pay protection money to local goons in a tough neighborhood.
Worse, I went after him on the air, attacking positions, votes, his partisan nature and most of all ties to southern Nevada's fat-cat special interests. Since he was one of many I criticized, including Republicans, I didn't realize the severity of the transgression. Some of the other targets didn't seem to be paying attention. Why would a U.S. senator? I was na?ve; he certainly was keeping tabs.
After spending a program lambasting Reid over a front-page Wall Street Journal story connecting him to a controversial land exchange involving Del Webb Corp., Reid and his staff finally took the gloves off. They demanded tapes of the show, threatened litigation and personally attacked me in a Las Vegas Review-Journal story. Station management publicly downplayed the pressure placed by Reid and his staff to get me off the air, but what was going on behind the scenes was less clear.
As luck would have it, at the same time, I was grabbed by a Seattle station for a similar position and left just as the kitchen got too hot. Had that not come through, he might have succeeded in yanking an opponent from the airwaves. I'm glad I didn't stick around to find out.
Let's shatter some myths: One, he isn't the bipartisan-division-healer the press has made him out to be. His recent mean-spirited slam against Supreme Court Justice Clarence Thomas on "Meet the Press" ought to shatter this faulty perception.
Two, the low-key image he's created is exactly how he wants to be seen. It's to disguise a very experienced operative in the art of political hardball, a skill developed across years of getting Nevada's good ol' boys to do exactly what he needed.
Most of all, he isn't a moderate (or laughingly, a "conservative" as the New York Times labeled him recently). Aside from some pro-life positions held until recently, due to his Mormon faith, his voting record is liberal.
This hasn't wavered: In 1996, Americans for Democratic Action, a leftist group, gave Reid a solid 85 out of 100 approval rating based on his votes. The American Conservative Union consistently rates him in the single or low double digits on a scale where 100 reflects full agreement on bills. He's not far from Ted Kennedy territory. National Journal has given him liberal marks especially on economic and foreign policy issues. Waffling on the abortion issue to appease the party base is the one recent change.
Reid doesn't give a strong first impression and you wouldn't notice him walking toward you in even the lightest of pedestrian traffic. But I think that's just the way he wants it. Harry's busy consolidating power and working on media control at the same time he's characterized as unassuming. If he attempts to reinstate the FCC's former Fairness Doctrine to muzzle talk radio once and for all, I will be the least surprised person in the country.
So, just in case this hasn't yet happened, it's time to clean up the paper plates and leftover cake from the Adios Daschle party and take his replacement seriously before he has a chance to do nationally what he did with ease in his home state.
Brian Maloney, a longtime radio talk-show host and writer, has hosted programs in Washington state, Nevada, California and as a frequent substitute in Dallas-Fort Worth, Kansas City and around the country. A resident of Cape Cod, Mass., he can be reached at [email protected] and maintains a blog at http://radioequalizer.blogspot.com.


text:
Industrialists Ambani, Agarwal, Munjal Supports Coronavirus Fight
The current count of nearly 22 per cent population is below the poverty line. With these donations made by the industrialists is an addition to the Rs 1.7 lakh crore relief package announced by the government on March 26th.
1568801968_X13HHi_Mukesh_Ambani.jpg
Reliance Industries decides to double the salaries of their employees earning less than Rs 30,000, said Mukesh Ambani, CMD of the company. Apart from helping their employees, companies like Vedanta Resources, Hero Cycles and Microsoft are donating to fight against coronavirus.
Maharashtra Chief Minister's Relief Fund receives the support of Rs 5 crore from Reliance Industries along with a setup of the 100-bed centre at Seven Hills Hospitals and an isolation facility for COVID-19 patients. Whereas Vedanta Resources Chairman Anil Agarwal and Hero Cycles MD Pankaj Munjal commits Rs 100 crore each to fight against the pandemic. Telangana Chief Minister's Welfare Fund is helping the poor people with a donation of Rs 2 crore offered by Anupama Nadella, wife of Microsoft CEO Satya Nadella.
As per the news reports, India has registered the maximum number of deaths on March 26th. As of March 27th, over 730 people have been tested positive with the disease. Out of which, 66 has been recovered while 17 deaths have been reported.
mukesh ambani satya nadella anil agarwal

redpajama_set_name: RedPajamaCommonCrawl


text:
Keane confirmed for Thetford Forest
Published: 12:41 AM November 30, 2009
One of Britain's favourite bands was this week confirmed as the latest addition to Thetford Forest's summer concert line-up.
Keane will be performing at six forest locations in June, including the first leg of their Forestry Commission tour at High Lodge visitor centre, near Brandon, on Thursday June 10.
The three-piece band has sold more than 10 million albums with three consecutive chart toppers, including Hopes and Fears in 2004, Under the Iron Sea in 2006, and Perfect Symmetry in 2008.
Their collection of hits include Everybody's Changing, Is It Any Wonder?, Crystal Ball, Somewhere Only We Know and Spiralling and they have won a string of Brit, Grammy's and Ivor Novello awards.
Simply Red has already been confirmed as an act to play at High Lodge on Friday, June 11 and four more live performers will be announced in the coming months.
Money generated by Forestry Commission live music ticket sales is spent directly on the nation's woodlands, benefitting everything from butterflies to mountain bikers.
2 Homes with dedicated support for rough sleepers to be built in Thetford
3 Jess Glynne cancels summer show in Thetford Forest
4 Pair deny dangerous driving on the A11 in Suffolk
5 Council leader refuses to condemn Downing Street parties
6 Rescued Mariah and Carey recovering after A11 crash
8 How are England's Covid restrictions changing after Plan B?
9 These are the dog breeds given up most at a Norfolk rehoming centre
10 Driver sustains neck injuries in two-vehicle crash near Thetford
Tickets for the Keane concert at Thetford Forest will go on sale at 9am on Friday and will cost �32, subject to booking fee, from the ticket hotline on 01842 814612 or online at www.forestry.gov.uk/music and www.keanemusic.com.


text:
Moments from the past week.
playing with the big kids
carpenter's helper
swingin' cat
painting Swedish horses
Sunday, March 4th, 2018 at 5:00 am
kit-based artisanry
Friday there was practically a hurricane, so we were limited to indoor activities. That wasn't a problem—we always have plenty do, especially now that we've added the option of Pokemon TCG Online—but a stormy day seemed like the perfect opportunity to open a craft box we've been saving since Christmastime.
he is interested
For Christmas my brother and his family gave our boys a subscription from Tingomo, a company that makes kits highlighting traditional arts and crafts from around the world. As I understand it we're getting four kits; the first one—the winter edition—highlighted wooden Dala horses (Dalahäst!) from Sweden.
The only problem is that the kits are made for two kids, and the gift was for Harvey and Zion. That won't fly in our household. Good thing we own a jigsaw and plenty of scraps of pine board! I defy you to tell my horse from the two which were industrially mass-produced to simulate traditional Dalecarlian artisanry.
see? three!
Then we painted them. The kit came with not-totally-washable acrylic paint—great for turning out an attractive finished project, less-great for a three-year-old's painting style (that's why the kits are officially six and up). And then there were some tears when we didn't let Lijah use his usual technique of dipping his brush in each of the colors in succession. There were instructions for painting a horse in the traditional style, including some brush mixing techniques; we followed them to the extant of starting with a solid-color base layer, but from there creativity ran (relatively) wild.
accomplishment
All told, it was a fun craft with high-quality materials attractively presented in beautiful packaging. With our budget I'd never be able to justify buying a kit myself, but it was a fun gift to enjoy on a rainy day. Thanks, Tom!
Monday, March 5th, 2018 at 9:49 am
Elijah is 4
birthday (pan)cake
Today was Lijah's birthday. We celebrated by letting him choose the menu for breakfast and lunch; pancakes and chicken nuggets, respectively. He also wore a Pokemon party hat for part of the day. I dream of being a proper homeschool blogger and asking him some birthday questions, but we didn't get around to it today... maybe we'll manage later in the week, before his party on Saturday. Because we're making this a whole birthday week!
Happy Birthday Lijah!
Tuesday, March 6th, 2018 at 9:44 pm
still very lion-like
snow, man!
The weather continues to be wild. After a summer-like warm spell it's hard to feel ready for a blizzard, but it's still winter and we're in New England, so. It could have been worse; the front half of the storm, all day Wednesday, was all rain. But overnight Wednesday to Thursday brought plenty of snow—heavy, wet, solid snow, just right for epic snowmen. And for bringing trees down too, as it happens.
About a third of Bedford was still without electricity yesterday evening, and there are limbs and trees down all over our neighborhood. We didn't lose anything important; the neighbors' lilac breaking onto Leah's car wasn't really a problem.
pretty heavy
We had friends over for most of the day, in order to help their parents out with school being cancelled. After they left Harvey and I enjoyed some relaxing outside time. Even with dry wood from our newly-built woodpile shelter our fire wasn't totally successful—too much snow in the fireplace—but it made a nice smell and some cheery smoke. And nothing could be more successful than Harvey's snowmen. We can still enjoy winter!
with real home-made charcoal!
tagged with: snow, weather
Friday, March 9th, 2018 at 9:43 am
homeschool recess
Moments and images from Lijah's birthday week.
the party at Grandma and Grandpa's
snowman work
birthday sillies
birthday = celebrated!
As of a few days ago the garlic and rhubarb were up in the garden, and the daffodils and crocuses growing fast in the beds; I assume they're still growing, but it's hard to tell because yesterday we got like two feet of snow.
pretty good for one storm in March...
I measure it at 18 inches, actually, but I hear from neighbors with reliable information that we actually got over 20; either way, it was enough to close school for two days. So our schedule—never particularly rigorous to begin with—was thrown out the window so our kids could entertain their friends who were suddenly deprived of their usual weekday framework. I missed school today too: I'm taking part in a class at work, and it was cancelled today. It's interesting and engaging material, to be sure, but I don't think I'll even get too old to appreciate a snow day.
Especially one like today, with some sun and reasonably mild temperatures. Just the thing for spending a few hours shoveling! I still fully trust that March will go out with a lamb, but it has plenty of time yet—and we have another 8-12 inch storm forecast for next week. Flowers or snow-forts, we'll enjoy whatever we get.
on the slopes
A very few moments from the past week.
one more nor'easter
hens appreciate the power of the March sun
Lijah had a party
In our house most days, breakfast is eggs and toast, pancakes, or waffles; maybe some bacon or potatoes every once and a while. So the kids all look forward to Sunday morning, when they get to eat cold cereal before we head off to church. I think the cake situation is similar. Used to a daily dessert menu of homemade cookies, pie, or cake, they stare in fascination at the wall of cake mixes at the grocery store. Well, when it's your birthday you get to pick what you want, and Lijah picked out a double chocolate cake from the fine chemists at Betty Crocker. He wanted a Pokemon cake for his Pokemon party, but he only wanted it to be chocolate with chocolate frosting, so I was limited in my decorative options. This is what I came up with:
birthday cake for Lijah
It was delicious. And the party was lovely and relaxing; all three of his friends came, along with their families, and enjoyed three hours of free play with a few short breaks for Pokemon sticker arts and crafts, a Moana singalong, and some eating. And then presents. Lijah has never yet been satisfied by presents, quantity or quality, in the short term; maybe his expectations are higher. But I think he was satisfied with his day, and his birthday week. He was roundly celebrated. And now he's just four.
PikaPals
equal night
half night, half day
It wasn't as big as our solstice blowout in December, but we did our part to observe the equinox today. Despite the snow in the forecast for tomorrow we took down our snowflakes from the window and replaced them with construction paper flowers, and we made the equinox cookies you see above. I wish I had recorded Lijah's excited explanation of the spring equinox, and how it relates to cookies half-covered with chocolate; he really got the idea, only he wished they were winter solstice cookies in order to have more chocolate.
cookie cutting
With the coming of spring we're trying to get back into a little more focused schoolwork—unschooling kind of focused, which means that making cookies totally qualifies. I don't know about harvesting icicles and snow cakes to sell out of the playhouse, but they had fun with that. A fine way to welcome spring.
snow cakes and icicles for sale
tagged with: spring
This morning I was delighted to wake up soon after sunrise to the delightful sound of birds singing—a song I don't notice the lack of in the winter, but sure do notice when it returns in the spring! Despite some good March snowstorms spring is well on its way. Even as more snow fell yesterday morning, the snow on the ground was melting away; another inch or two has vanished already today. It's not warm outside, particularly—but warm enough to see us playing and working outside before lunch (I finished pruning and clearing out the raspberries). And the plants are all busy doing their thing!
Friday, March 23rd, 2018 at 1:51 pm
springtime snow cake
homeschooling this week
coop Park Day moved indoors
there's three kids in there!
Today was a wonderfully sunny early spring day, and the boys and I spent all afternoon working and playing outside. My main occupation was fixing the wheelbarrows; there were three, and none of them functional. Now there are two working wheelbarrows and some trash, and I'm very proud of myself. As I worked and got dirty in the clear March sunshine I found myself appreciating the beauty of the wood and metal around me. So I took some pictures.
tools for wheelbarrow repair
That's the stump where we split our firewood; it's black because Harvey and Zion were using it to chop their own charcoal the other day. I drilled a hole in the middle so I could use it to mount the wheelbarrow tire on the rim. It was much harder than putting on a bicycle tire!
Plastic is a fine material. I was glad to have a piece of thick PVC pipe on hand: I cut lengths of it to center one of the wheels on its shaft. I would have had a much harder time cutting metal parts, even assuming I could have found pipe with the right diameter (I have lots of PVC pipe, since I grab it out of the trash whenever I see it). But as I cut it I regretted the bright white plastic bits falling around my otherwise brown and gray workbench stump. When I finished up my hands were about the same color as that wood and rusty metal, which felt about right.
leftover parts
tagged with: hippy, outdoors, fixing
why our family is weird
Yesterday Zion's friend from across the street wandered over while I was hard at work on the wheelbarrows. After watching for a few seconds, he asked, "Do you know why your family is weird?" Before I had a chance to accuse him of assuming the premise of his argument, he went on: "It's because you like to make things instead of buying them to save money." Well, that's true I suppose. I was happy to make the wheelbarrows work instead of buying new ones. But saving money isn't really my main motivator... I just happen to like making things.
Though I suppose the money is part of it; I get depressed by an existence built on making money so I can spend it. Since I don't enjoy spending money, that process seems like kind of a waste of my time, and a diminishment of my agency. In buying things I feel like a prisoner of marketing and created wants, but when I make something myself I feel empowered and capable and generally happier. It's not a huge deal; it's not revolutionary or world-changing. It's just my preference. And maybe it is a little weird in 21st century America. Fair cop.
tagged with: hippy


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Westoba is the eighth largest credit union in Manitoba with 16 locations. The full-service financial institution is committed to enriching lives and communities by helping to make financial dreams come true.
"[Environics Analytics] goes above and beyond to make sure the end products they deliver meet your needs and you fully understand how to implement them. This is a big help because when it comes to data analytics, not everyone is an expert and having people to lean on for assistance is key."
—Amy Doerksen, Marketing & Communications Director | Westoba Credit Union
Westoba strives to be a community leader that puts its members first. To deliver on that promise, it needed to develop a clear picture of its member base by identifying their needs and serving them effectively. Westoba wanted to leverage its member behavior data to identify growth opportunities, optimize its retention strategies and develop customized sales and marketing plans. However, it would often struggle to find ways of making these data meaningful and actionable. With big ambitions and aggressive goals, Westoba had no plans to allow their smaller size stop them from accessing sophisticated tools used by their larger competitors.
With branches in urban, exurban and rural settings, Westoba serves a highly diverse membership, with different financial needs and challenges. To simplify its messaging and help members and staff understand its product lineup, Westoba needed to plug its research gaps to answer questions that it couldn't effectively address with its own data. The project began with hygiene of the Westoba member files, which involved removing invalid postal codes and retired businesses. Once that was completed, we integrated data from across departments to develop a single view of its membership.
With the groundwork in place, custom segments were developed to capture all of Westoba's members and Manitoba's households. The 10 resulting segments describe their demographics, lifestyles, finances and social values. Personas were developed for key segments to highlight the products and services that the members prefer. These personas led to differentiation in advertising strategies between urban and rural markets.
An interactive dashboard was developed to help Westoba socialize the segments and personas across its entire operation. The dashboard summarizes the essential learnings for the front-line staff. The new data-driven insights are being used to influence everything from product development to marketing strategy. At the branch level, Westoba was able to analyze the market and inform their retention and acquisition strategies. In other areas, it helped the credit union optimize and target its direct-marketing initiatives by knowing which regions offer the greatest return.
The project resulted in several quick wins. For instance, the targeting of key member segments contributed to strong results in Westoba's digital e-blasts, which had a 30% open rate and a 13% click rate, which are far higher than the financial industry's standards of 20% and 2.5%, respectively. Guided by the member segmentation system, Westoba targeted four market segments for its preferred shares offering. The targeted approach resulted in a strong response rate, enabling Westoba to sell out its offering and develop a waiting list of members interested in its next offering. The learnings also informed the creation of a new chequing account for youth, students and seniors called WestobaONE, which offers more free transactions per month.


Currently in Barcelona, DJ Douds plays reggae roots, dancehall and hip hop at several social associations and bars, and Afro-electro music at the Jokoo BCN festival to promote African culture and contemporary music. Douds is a Senegalese DJ resident in Spain, who always displays his eclectic musical universe, which in addition to the styles mentioned, includes Afrobeatz, funk, Afro-house, and a special selection of Senegalese music. Expect a sharp selection to keep you on your feet all night long.


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"Unforgettable Lovers" Multi-author Event Day 2: Danita Minnis and P.L. Parker
Welcome! This is the second post in the "Unforgettable Lovers" Multi-author Event. I'm featuring two more authors today. Each author's chosen POV (point of view) character will tell what, in his or her opinion, makes someone an unforgettable lover. I personally love to get an intimate view of the characters.
Along the way, we'll use my blog and Facebook to play games and complete some important missions (for prizes, of course) LOL. Make sure to click on the link above and join the party for all the juicy details!
Today, I'm featuring books and POV characters by Danita Minnis and P.L. Parker...
Adderley's Bride
Danita Minnis
Sofie is a singer, baker and a serious planner. When she finds her rocker boyfriend up against the wall in a vocal booth with a back-up singer, her five-year plan for a home and family is dubbed over like a bad music track.
Gray, a lusty ghost who acts like she is his long-dead fiancée invades her dreams and works her body over, night and after night. It isn't long before Sofie's plans include her beguiling lover, a ghost man with a plan of his own; be with me. Nice plan if you call that living.
Grayson Adderley: Love is not a ghostly illusion
I wasn't born in this time, no. It took a few centuries before I was reunited with the love of my life. Sofie. Hair, thick and creamy like a cup of chocolate and skinny jeans reminiscent of pantaloons. The bluest eyes. I swam in them long ago when I was alive and still see in them the purest love, adoration and trust. You might ask, what does a
spirit and a living, breathing beauty have in common? An unforgettable love.
Need outweighs logic in the most memorable ways. My need to be near her again, uncover her body's secret desires and make them a reality like no human man can. Her need to know secrets of the past in order to change her future. Want and ye shall receive. Never were there truer words spoken.
My advice to you is to be ready for your dreams when they come true. Sophie was ready for me. She brought me back to life. Well, not exactly but you know what I mean. Her need, my greed for what she poured into those skinny jeans…understand this; love is not a ghostly illusion.
Adderley's Bride Excerpt
"Ah, Sweet Sofie." He shifted until he was nestled between her legs. His arms came over her and as he helped her knead the dough, his shaft slid in and out between her legs.
She leaned her head against his chest. Watching his big hands over hers with flecks of the flour and sugar mixture coating the hair on his knuckles was an erotic vision of teamwork. She wondered how those hands would feel as they kneaded her flesh.
Their hands worked in time to the rhythm of his slide, in and out. Their fingers clenched onto the mound of dough as he pushed forward, and released as he slid out from between her thighs. Their heavy breathing was the only sound as they clenched and released, clenched and released…
A lazy heat flared between her legs, warming her to the core and making her hips rock back and forth. Her legs were giving way and she spread them wider to stay upright. She stopped kneading the dough to lean over and hold onto the island.
He grabbed her hair, wrapping it around his hand so that she had to lean her head back against him. "Don't stop," his gentle scolding tickled her ear. "I have not had a decent beignet since I arrived in these United States." He released her hair and pressed closer. She was now trapped between the island and his lean hips. "I'll hold you up." His low chuckle was a hot vibration between her thighs.
Decimated by the savage Deg'Nara and teetering on the brink of extinction, the last surviving males of the once great Chiagan-Se embark on a quest to salvage what is left of their civilization. They send their remaining seeker ships into the void, searching for genetically compatible females. Time is running out, but in the far reaches of the universe, on an obscure and primitive planet, a match is discovered.
One thousand panic-stricken women awaken two hundred years in the future, captives aboard an unmanned alien spacecraft bound for parts unknown! How had they gotten there and why?
The males thought they came willingly. The females believed they'd been kidnapped. Full of hopeful expectation, the Chiagan-Se prepare for the arrival of their new mates. Terrified and furious at the inexplicable abduction, the women prepare for combat! And when the two sides meet, the battle commences.
POV: Tegan from "The Chalice"
Tegan scrubbed his face, brushing back strands of the silvery white hair.
"Love was a dream, a respite from the harshness of my existence. Then I met Kara, the human woman who was chosen to be my Chalice. She is unlike any female I have ever known. With her, I know laughter. Joy. Hope! My warriors and I were denied the warmth of a female's breast, the promise of a family, a chance for a new beginning."
It is hard to express what I feel for my Chalice! "She is the keeper of my soul, nurturing the darkness until it becomes light. When I join with my Chalice, we are one and I am made whole."
He licked the vee at the base of her throat, noting the flutter of the heightened pulse beneath his lips. He tasted first one breast and then the other, laving the budding nubs and then suckling until the crests grew hard.
She moaned, sliding around to straddle his thighs, slim hands working at the cloth draped around his waist. "I want you naked," she muttered, almost purring as she wiggled against his throbbing shaft. "Naked and ready."
Ready? How could he be otherwise? He was not a half-male.
"I am," he laughed, rotating his hips against her moist heat. "More than ready."
He traced the tantalizing curves of his Chalice, memorizing every line and feature. Beautiful and exciting. Akin to the Chiagan-Se but distinctly human.
Did human females experience pleasure by means other than what he'd been taught? Were they aroused by the same methods as a Chiagan-Se female?
New Concepts Publishing:
Blog Spot:
Danita Minnis excerpts Giveaway P.L. Parker Paranormal romance sci-fi romance Time travel romance
Dariel, thanks for having Gray on today! He is always ready to talk about his love for Sofie. :)
Gray sounds like a dream lover, Danita :-) Love the cover, too!
P.L. Parker said…
Tegan is happy he gets to tell his story.
Donna Reynolds said…
I will have to start with these two, I love the covers and sounds fantastic! Mrscrabbyfan@gmail.com


"What she didn't know is that I needed it. How has someone kept you going?"
Following the tragic news of Kate Spade and Anthony Bourdain's passing, countless individuals have take to social media to share their own battles with depression and mental illness. Bringing awareness to these issues is so important, especially in light of the Centers for Disease Control and Prevention's recent report stating that U.S. suicide rates have increased by 25 percent since 1999. But, as the public mourns these public figures, others have seized the opportunity to discuss mental health and suicide prevention.
On Twitter, author Ana Marie Cox shared her own battle with depression, along with an instance in which a complete stranger gave her the will to carry on through a simple act of kindness. Cox then asked her followers to share their own stories about people who helped keep them going when they'd almost lost all hope.
1. Like Cox's example, an unsolicited pack of tissues helped this woman dry her tears.
2. While cashiers often dole out change, this one's gesture changed a man's life.
3. When everyone else fled, this person's friends showed them unconditional support.
4. A kind stranger gave this woman the strength to keep walking — literally.
I was walking down a city street crying my eyes out during a rain storm. This woman passed me, then turned around and asked me if I was okay. I shook my head no. She proceeded to walk me home and stay with me for awhile, until I felt stable enough to be alone.
5. These flight attendants proved that, on this journey called life, no one goes it alone.
6. In the midst of her loss, someone helped this woman find strength and peace.
7. This elderly woman's words helped this man come to terms with his mom's death.
8. One teacher's genuine concern gave this person the strength to keep going.
9. This man's boss extended her hand instead of handing him a pink slip.
Once I was so depressed I slept in until 6 pm. I explained why to my boss the next day. She didn't fire me. She invited me to Shabbat dinner. #livethroughthis.
10. This child's kindness made this woman feel welcome in an unfamiliar country.
11. When she didn't have any money, a stranger paid it forward to help her heal.
12. This woman's sister-in-law proved that siblings don't have to be blood relatives.
13. One random compliment helped this girl realize she's truly worthwhile.


The characterisation of homeopathy as witchcraft by the British Medical Association has sparked a similar debate on the system of medicine in India where it has a considerable patronage.
Senior doctors and scientists say it's now time for the union health ministry to withdraw all forms of support, including recognition of homeopathy medical colleges for the "unscientific medical" stream. While the Central Council for Homeopathy vehemently denies any form of criticism, doctors' bodies are now planning to challenge the ministry to show evidence that it is ineffective.
"Many scientists have said it is humbug. We don't say that about all alternative streams," says PM Bharghava, former vice–chairman of National Knowledge Commission. "In fact, we have been recommending research on streams like Ayurveda and Siddha because these have shown evidence. I am glad doctors in the UK are making a noise about it. But the department of homeopathy should be pulled out of the health ministry," he said.
Members of the Indian Medical Association argue that by allowing streams like homeopathy that the ministry has failed to abide by the principle that its policies should be evidence–based. There is no robust evidence that homeopathy is effective, they argue. "Research has showed that homeopathy works no better than placebo. They believe dilution of the vital ingredient puts better fight with infections, which defies logic," said Dr George Thomas, editor, Indian Journal of Medical Ethics.
Homeopaths disagree. "A tiny dose of a substance linked to the cause of the malady is diluted to an almost negligible quantity. Water retains the memory of the substance. And what apparently defies logic may not always be something impossible. Logic too is subjective," says Chennai–based senior homeopath Dr S Baskaran.
Central Council for Homeopathy secretary Dr Lalit Vema said homeopathy had been recognised in India since 1973. "We have 186 medical colleges and over 35 PG centres. Why do our doctors have to question scientific evidence now? If they say human beings are cured by placebo what about studies on plants and animals? Do they have placebo effect too?," he said.
Homeopathy has found support among some allopaths too. "Just because we don't know something it is unfair to say it is unscientific. I have seen patients getting relief with homeopathy," said Bangalore–based senior cardiac surgeon Dr Devi Prasad Shetty, who heads Narayana Hrudayala. Doctors' associations like the state wing of the Tamil Nadu State Medical Council said they would write to the Centre.
"Homeopathic preparations may not kill patients but when medicines do not do the needful during a crisis, it does amount to killing," said Dr K Prakasam, president of the TN medical Council.
A form of alternative medicine–was first proposed by German physician Samuel Hahnemann in 1796. The treatment is given with heavily diluted preparations and works on the principle called law of similars. That is preparations which cause certain symptoms in healthy individuals are given as the treatment for patients exhibiting similar symptoms.
What defies logic need not be untrue.
Homeopathy medicines defies logic as they say dilution increases strength.


The U.S. military's cybersecurity capabilities aren't advancing fast enough to stay ahead of the "onslaught of multipronged" attacks envisioned by adversaries, the Pentagon's combat testing office is warning.
Despite some progress in fending off attacks staged by in-house "Red Teams," the testing office said, "We estimate that the rate of these improvements is not outpacing the growing capabilities of potential adversaries who continue to find new vulnerabilities and techniques to counter fixes."
Automation and artificial intelligence are beginning to "make profound changes to the cyber domain," a threat that the military hasn't yet fully grasped how to counter, Robert Behler, the Defense Department's director of operational test and evaluation, said in his annual assessment of cyber threats, which was obtained by Bloomberg News.
The test office's findings may be discussed on Tuesday during a Senate Armed Services hearing focused on Pentagon cyber policy with Chief Information Officer Dana Deasy.
The evaluation, part of the testing office's annual report that may be released as early as this week, comes amid other critical appraisals of the military's ability to maintain and improves its defense against computer attacks.
A newly revealed Al Qaeda video calls on followers to launch cyberattacks on Western targets, a message called "alarming" by U.S. lawmakers in light of the increase in such attacks last year. Sens. Susan Collins and Joe Lieberman, who top the Senate Homeland Security Committee, say they first learned of the Al Qaeda video a week ago in a meeting with Homeland Security Secretary Janet Napolitano. The six-minute video instructs Al Qaeda followers that the U.S. is vulnerable to cyberattacks in the same way airline security was vulnerable in 2001 before the terrorist attacks of Sept. 11. The video calls on Muslims "with expertise in this domain to target the websites and information systems of big companies and government agencies." Without getting into classified information, Lieberman confirmed that there has been a spike in cyber intrusions -- believed to originate with Iran. "There is real evidence that the Al Qaeda groups want to pursue and are beginning to pursue the capacity to launch a cyberattack against America," he emphasized.


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Christopher Lillis (ur. 4 października 1998 w Rochester) – amerykański narciarz dowolny, specjalizujący się w skokach akrobatycznych, mistrz olimpijski.

W 2015 roku wystartował na mistrzostwach świata juniorów w Chiesa in Valmalenco, zajmując szóste miejsce. Podczas rozgrywanych rok później mistrzostw świata juniorów w Chiesa in Valmalenco był piąty. W zawodach Puchar Świata zadebiutował 4 lutego 2016 w Deer Valley, zajmując 9. miejsce. Tym samym już w swoim debiucie wywalczył pierwsze pucharowe punkty. Na podium zawodów tego cyklu po raz pierwszy stanął 20 lutego 2016 roku w Mińsku, gdzie zwyciężył w skokach akrobatycznych. W zawodach tych wyprzedził Maksima Huscika z Białorusi i Rosjanina Ilję Burowa. W 2019 roku, na mistrzostwach świata w Deer Valley zajął 7. pozycję. Dwa lata później zdobył srebrny medal indywidualnie oraz brązowy w drużynie podczas mistrzostw świata w Ałmaty.

Osiągnięcia

Igrzyska olimpijskie

Mistrzostwa świata

Puchar Świata

Miejsca w klasyfikacji generalnej
 sezon 2015/2016: 26.
 sezon 2016/2017: 53.
 sezon 2018/2019: 36.
 sezon 2019/2020: 29.
Od sezonu 2020/2021 klasyfikacja skoków akrobatycznych jest jednocześnie klasyfikacją generalną.
 sezon 2020/2021: 12.
 sezon 2021/2022: 25.

Miejsca na podium w zawodach
  Mińsk – 20 lutego 2016 (skoki akrobatyczne) – 1. miejsce
  Raubicze – 22 lutego 2020 (skoki) – 3. miejsce
  Ałmaty – 28 lutego 2020 (skoki) – 1. miejsce
  Moskwa – 23 stycznia 2021 (skoki) – 2. miejsce

Przypisy

Bibliografia
 Profil na stronie FIS

Amerykańscy narciarze dowolni
Amerykańscy medaliści olimpijscy
Medaliści Zimowych Igrzysk Olimpijskich 2022
Ludzie urodzeni w Rochester (stan Nowy Jork)
Urodzeni w 1998

redpajama_set_name: RedPajamaWikipedia


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Operator Algebras
Org: Marcelo Laca and John Phillips (Victoria)
BEATRIZ ABADIE, Universidad de la Republica, Montevideo, Uruguay
Morita equivalence for Quantum Heisenberg Manifolds [PDF]
Quantum Heisenberg manifolds were constructed by M. Rieffel as a quantization deformation of certain homogeneous spaces H/Nc, H being the Heisenberg group. We describe Morita equivalence within this family by adapting to this setting some of the techniques employed in the analogous discussion for non-commutative tori and Heisenberg C*-algebras. One of the main tools employed is the generalization of a result of P. Green and M. Rieffel about Morita equivalence of transformation group C*-algebras corresponding to two commuting free and proper actions on a topological space; this result is generalized to the context of crossed products by Hilbert C*-bimodules.
BERNDT BRENKEN, University of Calgary
The isolated ideal of a correspondence associated with a topological quiver [PDF]
For a general C*-correspondence over a C*-algebra A we identify a hereditary saturated ideal of isolated points of A. The Cuntz-Pimsner C*-algebra of the quotient correspondence is both a relative Cuntz-Pimsner algebra and a quotient of the Cuntz-Pimsner algebra of the original correspondence. For the C*-correspondence arising from a topological quiver one obtains a correspondence associated with the restriction of the quiver to the non-isolated vertices. The restricted topological quiver satisfies conditions (L) or (K) if and only if the original quiver does.
KEN DAVIDSON, University of Waterloo
Nest representations of directed graph algebras [PDF]
To each directed graph, there are two natural non-self-adjoint operator algebras. We investigate nest representations of these algebras, i.e., representations with range that is dense in an algebra of upper triangular matrices or a nest algebra. In particular, we show that the finite dimensional nest representations separate points and we characterize when there is a faithful nest representation.
This is joint work with Elias Katsoulis.
GEORGE ELLIOTT, University of Toronto, Toronto, Ontario M5S 2E4
On the classification of non-simple inductive limits of matrix algebras over the interval-the theorem of Robert [PDF]
An outline is given of the statement and proof of the theorem of Leonel Robert the brief statement of which is as follows: The inductive limits of matrix algebras over the interval are classified by certain elementary K-theoretical invariants (including traces). (At the date of writing, the statement is restricted to the case that the set of closed two-sided ideals of the inductive limit C*-algebra is totally ordered.)
HEATH EMERSON, University of Victoria
A Gysin sequence in noncommutative geometry [PDF]
For a class of group actions on compact spaces, we construct an analogue of the Gysin sequence in classical topology (which computes the map on cohomology induced by the projection from the sphere bundle of a compact manifold, to the manifold). The noncommutative sequence computes the map on K-theory induced by the inclusion of the reduced C*-algebra of G into the cross-product C(X) ×G. Applications are given to a problem in index theory: namely, we give a KK-theoretic proof of the theorem of Luck and Rosenberg identifying the class of the de Rham operator in equivariant KK, with the class of a certain combinatorial Euler class.
THIERRY GIORDANO, University of Ottawa, Ottawa
Topological orbit equivalence of free, minimal actions of Z2 on the Cantor set [PDF]
In 1959, H. Dye introduced the notion of orbit equivalence and proved that any two ergodic finite measure preserving transformations on a Lebesgue space are orbit equivalent. He also conjectured that an arbitrary action of a discrete amenable group is orbit equivalent to a Z-action. This conjecture was proved by Ornstein and Weiss and its most general case by Connes, Feldman and Weiss by establishing that an amenable non-singular countable equivalence relation R can be generated by a single transformation, or equivalently is hyperfinite, i.e., R is up to a null set, a countable increasing union of finite equivalence relations.
In the Borel case, Weiss proved that actions of Zn are (orbit equivalent to) hyperfinite Borel equivalence relations, whose classification was obtained by Dougherty, Jackson and Kechris.
In 1995, Giordano, Putnam and Skau proved that minimal Z-actions on the Cantor set were orbit equivalent to approximately finite (AF) relations and their classification was given. Since then some special classes of minimal free actions of Z2 on the Cantor set were shown to be affable (i.e., orbit equivalent to AF-relations).
In this talk I will indicate the main steps of the proof of the general result obtained in a joint effort with H. Matui, I. Putnam and C. Skau and whose statement is the following:
Theorem: Any minimal, free Z2-action on the Cantor set is affable.
DANIEL GONCALVES, University of Victoria
An Introduction to New C*-algebras from Tilings [PDF]
Given a tiling that satisfies some standard conditions, we introduce an equivalence relation on Rd by saying that two points, x and y, are equivalent if the patch defined by y on the tiling matches the patch defined by x translated by y-x. We then consider the C*-algebra associated to this equivalence relation and describe some of its ideals. If time permits we will show that this is a recursive subhomogeneous C*-algebra.
In the case of a substitution tiling we use the inflation map to get an inductive limit of C*-algebras, which is simple. We finish with a few K-theory computations for some examples.
CRISTIAN IVANESCU, University of Northern British Columbia
Continuous trace C*-algebras with spectrum [0,1], inductive limits of continuous trace C*-algebras and their classification [PDF]
A classification result will be presented for the class of simple separable C*-algebras which are inductive limits of continuous trace C*-algebras with spectrum [0,1] or finitely many copies of such a space. An important step that will be discussed is the pulling back of the invariant from the inductive limit stage to the finite stage. As will be explained, a new technique is necessary, namely the use of what we call "a gap" interpreted in a suitable sense.
Joint work with George A. Elliott.
DAVID KERR, Texas A&M University, College Station, TX, USA 77843-3368
Dynamics and rigidity in simple C*-algebras [PDF]
The achievements of the Elliott classification program have established a striking picture of cohomological rigidity within a large class of simple nuclear C*-algebras. I will discuss some consequences of this rigidity for the dynamics of typical automorphisms.
CLAUS KOESTLER, Carleton University
Central Limit Laws on Jones Towers [PDF]
The re-interpretation of commuting squares as a noncommutative version of stochastic independence gives rise to the notion of Bernoulli shifts on Jones towers. We investigate central limit theorems on such towers and show that such laws exist for shifts with a homogeneous product representation. In particular, we report experimental results indicating that Wigner's semicircle law is among them.
This is joint work with Rolf Gohm.
HANGFENG LI, SUNY at Buffalo, Buffalo, New York
A Topology for Ergodic Actions of Compact Quantum Groups [PDF]
We show that there is a natural topology on the set of all isomorphism classes of ergodic actions of any fixed compact quantum group.
HUAXIN LIN, University of Oregon
The Rokhlin property for automorphisms on simple C*-algebras [PDF]
We study a general Kishimoto's problem for automorphisms on simple C*-algebras with tracial rank zero. The original problem of Kishimoto is the following: Let A be a unital simple AT-algebra with real rank zero and a is an approximately inner automorphism. Is A\rtimesaZ again a simple AT-algebra? Let A be a unital separable simple C*-algebra, with tracial rank zero and let a be an automorphism. Under the assumption that a has certain Rokhlin property, A\rtimesaZ has tracial rank zero. We also show that if the induced map a*0 on K0(A) fixes a "dense" subgroup of K0(A) then the tracial Rokhlin property implies a stronger Rokhlin property. Consequently, the induced crossed product C*-algebras have tracial rank zero. By applying the classification theorem, this answers affirmatively Kishimoto's original question.
JAMIE MINGO, Queen's University
Second Order Freeness and Compound Wishart Matrices [PDF]
In 1986, D. Voiculescu introduced the R-transform of a random variable. The coefficients of this power series, now called free cumulants, were shown in 1994 by R. Speicher to have a combinatorial interpretation using non-crossing partitions. In 2004, A. Nica and I showed that the covariance, when suitably magnified, of the traces of some standard families of random matrices has a limiting value that can be interpreted in terms of non-crossing annular partitions. Indeed the order of elements in a block of a partition is now significant and the relevant concept is a non-crossing permutation. These non-crossing annular permutations give rise to second order cumulants which in turn form the basis of second order freeness. We shall give a number of natural examples of families of matrices that exhibit second order freeness.
This work was done in collaboration with B. Collins, A. Nica, P. Sniady, and R. Speicher.
IAN PUTNAM, University of Victoria
Relative K-theory for C*-algebras and applications [PDF]
I will give a description for a relative K-theory determined by an inclusion of a pair of C*-algebras. I will describe a result which shows two such pairs have isomorphic relative K-groups. Finally, I will present some examples arising from problems in orbit equivalence of Cantor minimal systems and from projection method tilings.
GUNNAR RESTORFF, University of Copenhagen, Denmark
Classification of Cuntz-Krieger algebras [PDF]
Mikael Rørdam and Danrun Huang initiated the classification of Cuntz-Krieger algebras in the mid-nineties, and, recently, the classification up to stable isomorphism of Cuntz-Krieger algebras (satisfying the condition (II) of Cuntz) was completed. This work raised other new interesting questions.
In my talk I will talk about the classification of Cuntz-Krieger algebras, and state the classification theorem. Also, I am planning to comment on some of the questions raised by this classification result.
ANA SAVU, University of Northern British Columbia
Closed and exact functions in interacting particle systems [PDF]
Statistical physics has developed a whole variety of interacting particle systems to explain the transition from microscopic to macroscopic scale. One of the main difficulties in finding the scaling limit of a nongradient particle system is to make rigorous sense of the fluctuation-dissipation equations. As has been shown by Varadhan, the fluctuation-dissipation equation is equivalent to a certain direct sum decomposition of a Hilbert space. For a general vector field we exhibit two Hilbert spaces, namely the space of so called "closed functions" and the space of "exact functions" and we calculate the codimension of the space of "exact functions" inside the space of "closed functions". In particular we provide a new approach based on Fourier analysis for the two known cases, the Glauber field and the second-order Ginzburg-Landau field, and we provide a solution for a new case, the fourth-order Ginzburg-Landau field.
The author is grateful to George A. Elliott for many discussions and ideas that led to the completion of this work.
Copyright © Canadian Mathematical Society - Société mathématique du Canada.
Any comments or suggestions should be sent to - Commentaires ou suggestions envoyé à: eo@cms.math.ca.