text:
\section{Introduction\label{intro}}
The uniform electron gas (UEG) constitutes a well-known simple model for metals \cite{mahan}. At finite temperature, the spin-polarized UEG is described by the density parameter $r_s={\bar r}/a_B$ [${\bar r}$ is the mean interparticle distance related to the density by, $n^{-1}= 4\pi {\bar r}^3/3$, and $a_B$ is the Bohr radius] and the dimensionless temperature (degeneracy parameter) $\Theta= k_BT/E_F$, with the Fermi energy $E_F$. Besides being an interesting theoretical model system for studying correlated fermionic many-body systems, exact data for the exchange-correlation energy of the UEG is essential for the construction of exchange correlation functionals \cite{karasiev_prl14, brown_prb13}, for density functional theory (DFT) calculations of more realistic systems, e.g.\ atoms, molecules and novel materials. For the ground state this data has been provided many years ago by Ceperley and Alder \cite{ceperley_alder} utilizing the fixed node diffusion Monte Carlo approach. Based on these calculations Perdew and Zunger computed the density functionals \cite{perdew_zunger}, which have been the basis for countless DFT applications.

Often one is interested in properties of chemical systems or condensed matter at low temperature, not exceeding room-temperature, for which it is justified to use ground state results.
However, in recent years more and more applications have emerged where the electrons are highly excited, e.g.\ by compression of the material or by electromagnetic radiation. Examples are dense plasmas in compact stars or planet cores, e.g.\ \cite{knudson_12, Militzer:2008, Nettelmann:2012} and laser fusion experiments at the National Ignition Facility, e.g.\ \cite{lindl_04, hu_11, hurricane_nif14}, at Rochester \cite{theobald_15} or Sandia~\cite{hanson_14,hanson_14_2}. It is now widely agreed upon that the theoretical description of these experiments requires to go beyond ground state DFT. This leads to a high demand for exact data for the UEG at finite temperature and high to moderate density where fermionic exchange and correlation effects play an important role simultaneously, namely the warm dense matter (WDM) regime, where both $r_s$ and $\Theta$ are of order one.
\par

Quantum Monte Carlo (QMC) simulations are the method of choice for the computation of exact thermodynamic quantities at finite temperature. However, it is well-known that, when applied to fermions, path integral Monte Carlo (PIMC) methods suffer the fermion sign problem (FSP), which may render the simulation even of small fermionic systems impossible and was shown to be NP-hard~\cite{troyer}. In the standard PIMC formulation in coordinate space, e.g.~\cite{ceperley95rmp}, the FSP causes an exponential loss of accuracy with increasing degeneracy, i.e.~towards low temperature and high density of the system. For this reason, standard fermionic PIMC calculations of the $N=33$ spin-polarized UEG are not feasible in the warm dense matter regime~\cite{brown_prl13}. Presently, the search for accurate and efficient strategies to weaken the FSP is one of the most important questions in condensed matter and dense plasma theory.

A popular approach to avoid the FSP is the restricted (fixed-node) PIMC (RPIMC) method~\cite{ceperley_91}, which is claimed to be exact if the true nodal surface of the density matrix would be known. Usually this is not the case, and one has to rely on approximations, thereby introducing an uncontrolled systematic error.
Brown \textit{et al.}~\cite{brown_prl13} performed RPIMC calculations with ideal nodes of the UEG in a broad density-temperature range down to $r_s=1$ and $\Theta=0.0625$. These results have been used by many groups, e.g. for the construction of analytical fits for the exchange-correlation free energy \cite{karasiev_prl14, brown_prb13} and as benchmarks for models and simulations \cite{filinov15, dubois14}.

In a recent Letter~\cite{tim_prl15}, we applied the configuration path integral Monte Carlo (CPIMC) approach to the uniform electron gas and were able to obtain the first {\em ab initio} simulation results for finite temperatures and high degeneracy. These results also showed that the RPIMC data of Ref.~\cite{brown_prl13} are inaccurate for high densities, $r_s \lesssim 4$. As any fermionic PIMC approach, CPIMC as well suffers from the FSP. But,
being
 formulated in Fock space of Slater determinants~\cite{schoof_cpp_11, schoof_cpp14}, CPIMC experiences an increasing FSP with decreasing quantum degeneracy, i.e. towards low density. In the case of the UEG with $N=33$ particles, direct CPIMC simulations were possible only for $r_s \lesssim 0.4$. Nevertheless, in Ref.~\cite{tim_prl15} an extension to substantially larger $r_s$ was achieved by introducing an auxiliary kink potential which leads to a complication of the original CPIMC algorithm.

For this reason, the present article aims at giving a comprehensive explanation of the modified CPIMC approach, in particular, of the details of the kink potential and the issues of convergence and accuracy. In order to give a systematic analysis of these concepts and their capabilities, we concentrate on the simplest situation---the polarized UEG. Also, we restrict ourselves to finite particle numbers, deferring the issues of finite size effects and extrapolation to the thermodynamics limit to a future publication. Here, we explore in detail how the algorithm performs with varying particle number and what range of densities and temperatures is accessible. This allows us to extend the range of {\em ab initio} CPIMC data presented in Ref.~\cite{tim_prl15} to temperatures as high as $\Theta = 8$ and to larger $r_s$-values, where the maximum accessible value is found to be on the order of $r^{\rm max}_{s} \sim \Theta$. However, we demonstrate that it is possible to access the  entire $r_s$-range without fixed nodes. To this end, we invoke another {\em ab initio} approach---the recently developed permutation blocking PIMC method (PB-PIMC)~\cite{pb_pimc_njp, pb_pimc_jcp15} which has a complementary FSP, restricting the simulations from the side of low temperatures.
For $N=33$ spin-polarized particles, the combination of CPIMC and PB-PIMC allows us to present exact results for $\Theta \ge 0.5$, for all densities, without fixed nodes, see Fig.~\ref{fig:n-t-sketch}.

The paper is organized as follows.
After introducing the model Hamiltonian of the UEG in Sec.~\ref{sec:model}, we start with a brief but self-contained derivation of the CPIMC expansion of the partition function in Sec.~\ref{sec:expansion} and, in Sec.~\ref{sec:path}, explain the interpretation of the latter as being a sum over closed paths in Fock space, in imaginary time. In Sec.~\ref{sec:sign_direct}, we proceed with addressing the FSP in direct CPIMC simulations, where we find an abrupt drop of the average sign at a certain critical value of $r_s$ depending on particle number and temperature. Then, in Sec.~\ref{sec:kinkPot}, we demonstrate how the applicable region of the CPIMC method can be extended to significantly lower densities by the use of an auxiliary kink potential and an appropriate extrapolation scheme. In Sec.~\ref{sec:PB-PIMC}, the main ideas of PB-PIMC and its differences compared to standard PIMC are explained. Finally, in Sec.~\ref{sec:results}, we combine the two complementary methods, CPIMC and PB-PIMC, for the first time to obtain benchmark results for $N=33$ spin-polarized particles over the whole density range for several degeneracy parameters reaching from $\theta =0.5$ to $\theta=8$.

\begin{figure}
 \includegraphics[width=85mm]{overview_with_all_paper.pdf}
 \caption{Available {\em ab initio}-Quantum Monte Carlo data in the  warm dense matter range for $N=33$ spin-polarized electrons. Dots: CPIMC. Squares: PB-PIMC.
 Red: Additional combined CPIMC and PB-PIMC results of this work. Gray: Previous results from CPIMC~\cite{tim_prl15} and PB-PIMC~\cite{pb_pimc_jcp15}, respectively.
ICF: typical inertial confinement fusion parameters \cite{hu_11}. Quantum (classical) behavior dominates below (above) the line $\Theta=1$. $\Gamma=e^2/{\bar r}k_BT$  is the classical coupling parameter.}
 \label{fig:n-t-sketch}
\end{figure}
\section{Theory}
\subsection{The Jellium Hamiltonian \label{sec:model}}
In second quantization with respect to plane waves,
$\langle \mathbf{r}\;|\mathbf{k}\rangle = \frac{1}{L^{3/2}} e^{i\mathbf{k} \cdot \mathbf{r}}$ with $\mathbf{k}=\frac{2\pi}{L}\mathbf{m}$, $\mathbf{m}\in \mathbb{Z}^3$,
the Hamiltonian of the finite simulation-cell 3D uniform electron gas consisting of $N$ electrons on a uniform neutralizing background in a periodic box of length $L$ takes the familiar form (Rydberg units)
\begin{align}\label{eq:h}
& \op{H} =
\sum_{i}\mathbf{k}_i^2 \ladderup_{i}\ladderdown_{i} + 2\smashoperator{\sum_{\substack{i<j,k<l \\ i\neq k,j\neq l}}}
w^-_{ijkl}\ladderup_{i}\ladderup_{j} \ladderdown_{l} \ladderdown_{k} + E_M,
\end{align}
with the antisymmetrized two-electron integrals, $w^-_{ijkl} =w_{ijkl}-w_{ijlk}$, where
\begin{align}
\quad w_{ijkl}=\frac{4\pi e^2}{L^3 (\mathbf{k}_{i} - \mathbf{k}_{k})^2}\delta_{\mathbf{k}_i+\mathbf{k}_j, \mathbf{k}_k + \mathbf{k}_l}\;,
\label{eq:two_ints}
\end{align}
and the delta-function ensuring momentum conservation. The first (second) term in the Hamiltonian Eq.~(\ref{eq:h}) describes the kinetic (interaction) energy. The Madelung energy $E_M$ accounts for the self-interaction of the Ewald summation in periodic boundary conditions~\cite{fraser_madelung}, for which we found $E_M\approx-2.837297\cdot(3/4\pi)^{\frac{1}{3}}N^{\frac{2}{3}}r_s^{-1}$.
The operator
$\ladderup_{i}$  ($ \ladderdown_{i}$)
creates (annihilates) a particle in the orbital $|\mathbf{k}_i\rangle$.
The diverging contributions in the interaction term, i.e.\ for $\mathbf{k}_i=\mathbf{k}_k$ and $\mathbf{k}_j=\mathbf{k}_l$, cancel with the contributions due to the positive background.
Note that choosing the plane wave basis, which is the ideal, natural and Hartree-Fock basis at the same time, has the major advantage of having two-electron integrals that can be computed analytically according to Eq.~(\ref{eq:two_ints}). In an arbitrary basis one generally has to compute the two-electron integrals prior to the simulation and store them in computer memory, limiting the number of basis functions that can be taken into account. Yet, it is well-known that plane waves badly describe the Coulomb interaction, making a large number of basis functions necessary to obtain converged results.

\subsection{CPIMC Expansion of the partition function \label{sec:expansion}}

In equilibrium many-body quantum statistics the central quantity is the partition function, which is given by the trace over the density operator
\begin{align}
Z=\text{Tr} \;{\op{\rho}}\;,
\label{eq:Z_trace}
\end{align}
where, in the canonical ensemble,
\begin{align}
\op{\rho} = e^{-\beta\op{H}},
\label{eq:rho}
\end{align}
with the inverse temperature $\beta=[k_BT]^{-1}$. In standard PIMC, the trace in Eq.~(\ref{eq:Z_trace}) is evaluated in coordinate space expressing the density operator in terms of a product of $M$ density operators at $M$-times higher temperature, which is justified by the Trotter formula. To correctly take into account Fermi statistics, one then has to antisymmetrize the density operator thereby introducing a sign change in the weight function for odd particle permutations. This is the source of the FSP in standard PIMC. In CPIMC instead we perform the trace in Eq.~(\ref{eq:Z_trace}) directly with antisymmetrized $N$-particle states (Slater determinants)
\begin{align}
|\{n\}\rangle=|n_1, n_2, \dots\rangle\;,
\end{align}
which form a complete basis of the Fock space. Here, the $n_i$ denote the fermionic occupation numbers ($n_i=0, 1$) of the orbitals $|\mathbf{k}_i\rangle$.

To bring the partition function into a form suitable for a Monte Carlo algorithm, one can split the Hamiltonian into a diagonal and off-diagonal part, i.e.\ $\op{H}=\op{D}+\op{Y}$, which is always possible for any arbitrary basis. In the interaction picture in imaginary time with respect to the diagonal operator $\op{D}$, i.e.
\begin{align}
\op{Y}(\tau)&=e^{\tau\op{D}}\op{Y}e^{-\tau\op{D}},\;\; \tau\in(0,\beta)\;,
\end{align}
the density operator can be written in terms of a perturbation expansion in orders of $\op{Y}$
\begin{align}
  e^{-\beta\op{H}}&=e^{-\beta\op{D}}\op{T}_\tau e^{-\int_0^\beta\op{Y}(\tau)\mathrm{d}\tau}\nonumber\\

&=e^{-\beta\op{D}}\sum_{K=0}^\infty \int\limits_{0}^{\beta} d\tau_1 \int\limits_{\tau_1}^{\beta} d\tau_2 \ldots \int\limits_{\tau_{K-1}}^\beta d\tau_K\nonumber\\
&\qquad\qquad(-1)^K\op{Y}(\tau_K)\op{Y}(\tau_{K-1})\cdot\ldots\cdot\op{Y}(\tau_1)\;,
\label{eq:identity}
\end{align}
where $\op{T}_\tau$ denotes the time-ordering operator. Inserting Eq.~(\ref{eq:identity}) into Eq.~(\ref{eq:Z_trace}), evaluating the trace and rearranging terms yields the following expansion of the partition function
\begin{align}
Z = &
\sum_{K=0,\atop K \neq 1}^{\infty} \sum_{\{n\}}
\sum_{s_1\ldots s_{K-1}}\,
\int\limits_{0}^{\beta} d\tau_1 \int\limits_{\tau_1}^{\beta} d\tau_2 \ldots \int\limits_{\tau_{K-1}}^\beta d\tau_K
\label{eq:Z_expansion} \\\nonumber
& (-1)^K
e^{-\sum\limits_{i=0}^{K} D_{\{n^{(i)}\}} \left(\tau_{i+1}-\tau_i\right) }
\prod_{i=1}^{K} Y_{\{n^{(i)}\},\{n^{(i-1)}\} }(s_i)\;,
\end{align}
where $s_i$ denotes a multi-index defining the orbitals in which the two sets of occupation numbers $\{n^{(i)}\}$ and  $\{n^{(i-1)}\}$ differ. Due to the trace in Eq.~(\ref{eq:Z_trace}) it has to be  $\{n\}=\{n^{(0)}\}=\{n^{(K)}\}$. According to the Slater-Condon rules the Fock space matrix elements of the UEG Hamiltonian do not vanish only if the states differ in no (diagonal part) or exactly four occupation numbers (off-diagonal part) so that
\begin{align}
 &D_{\{n^{(i)}\}} = \sum_l \mathbf{k}_l^2 n^{(i)}_{l} + \sum_{l<k}w^-_{lklk}n^{(i)}_{l}n^{(i)}_{k} \;,\label{eq:diagonal}\\
&Y_{ \{n^{(i)}\},\{n^{(i-1)}\} }(s_i) =w^-_{s_i}(-1)^{\alpha^{\phantom{-}}_{s_i}}\;
\label{eq:off_diagonal}
\end{align}
with $s_i=(pqrs)$ defining the four occupation numbers in which  $\{n^{(i)}\}$ and $\{n^{(i-1)}\}$ differ, where it is $p<q$ and $r<s$. In this notation, the exponent of the fermionic phase factor is given by
\begin{align}
\alpha^{\phantom{-}}_{s_i} &=\alpha^{(i)}_{pqrs}=\sum_{l=p}^{q-1}n^{(i-1)}_{l}+\sum_{l=r}^{s-1}n^{(i)}_{l}\;.
\nonumber
\end{align}
Monte Carlo estimators of observables are readily computed as derivatives of the partition function Eq.~(\ref{eq:Z_expansion}),
e.g. for the internal energy one obtains
\begin{align}
\langle\op{H}\rangle=& - \frac{\partial}{\partial \beta} \ln Z \\
=&
\sum_{K=0,\atop K \neq 1}^{\infty} \sum_{\{n\}}
\sum_{s_1\ldots s_{K-1}}\,
\int\limits_{0}^{\beta} d\tau_1 \int\limits_{\tau_1}^{\beta} d\tau_2 \ldots \int\limits_{\tau_{K-1}}^\beta d\tau_K \nonumber\\
&\biggl(\frac{1}{\beta} \sum_{i=0}^K D_{\{n^{(i)}\}}(\tau_{i+1}-\tau_i) -\frac{K}{\beta}\biggr) W\;. \label{eq:energy_estimator}
\end{align}
We point out that the expansion~(\ref{eq:Z_expansion}) is exact and system-independent. Monte Carlo methods using this expansion belong to the so-called continuous time QMC methods (in the interaction picture) since there is no imaginary time discretization left. This concept has been developed by Prokof'ev \textit{et al.}~\cite{prokofiev96,prokofiev98} and extensively applied to lattice models, e.g.~\cite{prokofiev96,prokofiev98,houcke06,rombouts06}. We have presented an alternative derivation of Eq.~(\ref{eq:Z_expansion}) by starting from the Trotter formula and developed an algorithm for continuous systems~\cite{schoof_cpp_11} requiring more involved Monte Carlo steps compared to lattice models.

\subsection{Closed path in Fock space\label{sec:path}}
\begin{figure}
 \input{cpimc_sketch.tikz.tex}
 \caption{Typical closed path in Slater determinant (Fock) space. The state with three occupied orbitals $|{\vec k}_0\rangle, |{\vec k}_1\rangle, |{\vec k}_3\rangle$ undergoes a two-particle excitation $s_1$ at time $\tau_1$ replacing the occupied orbitals $|{\vec k}_0\rangle, |{\vec k}_3\rangle$ by
$|{\vec k}_2\rangle, |{\vec k}_5\rangle$. Two further excitations occur at $\tau_2$ and $\tau_3$.
The states at the ``imaginary times'' $\tau = 0$ and $\tau = \beta$ coincide. All possible paths contribute to the partition function $Z$, Eq.~(\ref{eq:Z_expansion}). (Fig.~from \cite{tim_prl15})}
 \label{fig:sketch}
\end{figure}
A contribution to the partition function Eq.~(\ref{eq:Z_expansion}) can be interpreted as a $\beta-$periodic path in Fock space, in imaginary time, that is uniquely defined by the initial determinant $\{n\}=\{n^{(0)}\}$ at $\beta=0$ and the $K$ two-particle excitations of type $s_i=(pqrs)$ at times $\tau_i$, where two particles are excited from the orbitals $r$ and $s$ to $p$ and $q$. An example of such a path is illustrated in Fig.~\ref{fig:sketch}. Due to their visual appearance, the excitations are called ``kinks''. The weight of each path is determined by the weight function which, according to Eq.~(\ref{eq:Z_expansion}) and~(\ref{eq:off_diagonal}), reads
\begin{align}
& W(K,\{n\}, s_1,\ldots,s_{K-1},\tau_1,\ldots,\tau_K)=\label{eq:weight}\;\\ \nonumber
&\qquad\qquad (-1)^K
e^{-\sum\limits_{i=0}^{K} D_{\{n^{(i)}\}} \left(\tau_{i+1}-\tau_i\right) }
\prod_{i=1}^{K} w^-_{s_i}(-1)^{\alpha^{\phantom{-}}_{s_i}}\;.
\end{align}
The set of occupation numbers of a determinant between kinks contributes to the exponential function with its corresponding diagonal matrix element, cf.\ Eq.~(\ref{eq:diagonal}), weighted with the length of the time interval on which the determinant is realized in the path. On the other hand, each kink enters the product over all kinks in the path with its corresponding antisymmetrized two-electron integral and phase factor of the involved orbitals. Since the two-electron integrals can be both positive and negative, there are altogether three sources of sign changes in the weight function.

\section{Sign problem of CPIMC \label{sec:sign_in_CPIMC}}
\subsection{Sign problem of the direct CPIMC method \label{sec:sign_direct}}
Since the weight function $W$ takes both positive and negative values, it is not a probability density. Therefore, the Metropolis algorithm can only be used to generate a Markov chain of paths distributed according to the modulus of the weight. This is achieved with an ergodic set of six Monte Carlo steps in which single or paired kinks are added or changed. A detailed description of these steps can be found in~\cite{schoof_cpp14}. By generating a Markov chain of paths according to the modulus of the weight, we actually simulate a system described by
\begin{align}
Z'=& \sum_{K=0,\atop K \neq 1}^{\infty} \sum_{\{n\}} \sum_{s_1\ldots s_{K-1}}\int\limits_{0}^{\beta} d\tau_1 \int\limits_{\tau_1}^{\beta} d\tau_2 \ldots \int\limits_{\tau_{K-1}}^\beta d\tau_K\,\label{eq:primed_system} \\ \nonumber
&\qquad\qquad |W(K,\{n\}, s_1,\ldots,s_{K-1},\tau_1,\ldots,\tau_K)| \;,
\end{align}
rather than the true physical system described by the partition function Eq.~(\ref{eq:Z_expansion}). Physical expectation values of observables are then obtained via
\begin{align}
\langle O \rangle = \frac{\langle Os\rangle^\prime}{\langle s \rangle^\prime}\;,
\label{eq:average}
\end{align}
where $O$ is the Monte Carlo estimator, e.g.\ for the internal energy the term in brackets in Eq.~(\ref{eq:energy_estimator}), $\langle\cdot\rangle^\prime$ denotes the expectation value with respect to the modified partition function, Eq.~(\ref{eq:primed_system}), and $s=\text{sign} (W)$ measures the sign of each path. For the expectation value of $s$, which is called the \emph{average sign}, it holds
\begin{align}
\braket{s}'= \frac{Z}{Z'}=e^{-\beta N(f-f')}
\end{align}
with f being the free energy per particle. It is straight forward to show that the relative statistical error of quantities computed with Monte Carlo methods via Eq.~(\ref{eq:average}) is inversely proportional to the average sign. Therefore, it grows exponentially with particle number and inverse temperature while it can only be reduced by the square root of the number of Monte Carlo samples. Depending on the available computational resources acceptable statistical errors can be obtained for average signs larger than about $10^{-4}$. This is the FSP.

\begin{figure}[t]
\includegraphics{{averageSign_vs_rs}.pdf}
\includegraphics{{averageKinks_vs_rs}.pdf}
\caption{(color online). Average sign \textbf{a)} and average number of kinks \textbf{b)} of direct CPIMC, plotted versus the density parameter for different particle numbers in $N_B=2109$ basis functions at $\theta=0.125$.}
\label{fig:avg_sign}
\end{figure}
Fig.~\ref{fig:avg_sign} a) shows the dependency of the average sign in CPIMC simulations of the UEG on the density parameter at a fixed degeneracy parameter $\theta=0.125$ for different particle numbers. The number of basis functions is fixed to $N_B=2109$, which is sufficient to obtain converged results (within reasonable statistical errors) for all data points. We generally observe a rather sharp drop of the average sign from almost $1$ to about $10^{-3}$. This effect clearly increases and shifts towards smaller $r_s$ with particle number. Consequently, for $N=33$ particles at this temperature we obtain negligible small statistical errors for $r_s\lesssim 0.4$, whereas for slightly larger values of $r_s$ direct simulations are not feasible. To investigate this behavior in more detail, in Fig.~\ref{fig:avg_sign}~b) we plot the average number of kinks in the simulations for the same parameters. This quantity is closely connected to the average sign since each additional kink in the paths comes with three potential sources of sign changes, cf.\ Sec.~\ref{sec:path}. In CPIMC simulations with on average more than $30$ kinks we find that, depending on the temperature, the average sign is too small to obtain results with reasonable statistical errors.

In the high density regime, the average number of kinks grows linearly with $r_s$, see Fig.~\ref{fig:avg_sign}~b), then at some critical value of $r_s$ it starts growing exponentially. The slope of this exponential growth increases with particle number so that for $N=33$ it appears to be rather a jump from below $1$ to about $200$ kinks at $r_s\sim 0.4$ explaining the sudden drop of the average sign in Fig.~\ref{fig:avg_sign}~a). Interestingly, for further reduced density, the average number of kinks grows again linearly with $r_s$. We have carefully checked that this is not an effect of the finite number of basis functions. However, in this regime, even for $N=4$ particles the average number of kinks is larger than $1000$ resulting in a practically vanishing average sign.
\begin{figure}[t]
\includegraphics{{averageKinks_vs_rs_N=4}.pdf}
\caption{(color online). Average number of kinks of direct CPIMC, plotted versus the density parameter for $N=4$ particles in $N_B=5575$ basis functions at different temperatures. }
\label{fig:avgKink_diff_temp}
\end{figure}
For $N=4$ particles, Fig.~\ref{fig:avgKink_diff_temp} shows the average number of kinks in dependence on $r_s$ for different degeneracy parameters. In the linear regimes (both at very large and small values of $r_s$), the average number of kinks depends also linearly on the degeneracy parameter while the onset of the exponential growth shifts towards smaller $r_s$, for increasing degeneracy, i.e.\ for decreasing $\theta$. Further, the transition from the exponential to the linear $r_s$ dependency is smoother the lower is the temperature, cf.\ red and brown curve in Fig.~\ref{fig:avgKink_diff_temp}. Summarizing, the direct CPIMC method suffers an abrupt drop of the average sign in particular for larger systems and lower temperature caused by a strong increase of the average number of kinks in the simulated paths.
\begin{figure}[t]
\includegraphics{{E_vs_kappa_different_kinkPots_cesaro_and_fermi}.pdf}
\caption{(color online). Convergence of the internal energy with respect to the kink potential parameter $\kappa$, using different parameters $\delta$. The system consists of $N=4$ particles in $N_B=19$ basis functions at $\theta=0.5$ and $r_s=40$ for which the energy can be computed with an exact configuration interaction (CI) method (dashed black line). Each point is the result of a whole CPIMC simulation, where integer numbers from $5$ to $28$ have been used for $\kappa$.}
\label{fig:demonstrate_kinPot}
\end{figure}

\subsection{Extending CPIMC towards lower density\label{sec:kinkPot}}
In this section, the use of the auxiliary kink potentials is explained, and its influence on the CPIMC method is investigated in detail. These kink potentials have been introduced in~\cite{tim_prl15} to obtain the results for $r_s> 0.4$.

The average number of kinks in the simulation is only connected to the number of kinks $K$ necessary for the partition function of the primed system to be converged, cf.\ Eq.~(\ref{eq:primed_system}). However, to obtain correct physical observables via Eq.~(\ref{eq:average}) it is sufficient to include only those paths in the simulation that actually contribute to the physical partition function Eq.~(\ref{eq:Z_expansion}), which, due to cancellations of contributions with opposite sign, may converge for a much smaller value of $K$ than the primed partition function. In other words, if this cancellation applies, then we can restrict the simulation paths to a certain number of kinks and thereby strongly reduce the sign problem while still obtaining exact results for the observables. In addition, since both, Eq.~(\ref{eq:Z_expansion}) and~(\ref{eq:primed_system}), are  exact perturbation series in orders of the number of kinks $K$, it is reasonable to investigate the convergence of this series with respect to $K$. For this purpose, we have introduced an auxiliary Fermi-like kink potential
\begin{align}
V_{\delta,\kappa}(K)=\frac{1}{e^{-\delta(\kappa-K+0.5)}+1}\;,
\label{eq:fermiPot}
\end{align}
which becomes a step function at $K=\kappa+0.5$ in the limit $\delta \to \infty$. We add this potential as an auxiliary factor in the primed partition function so that it acts as a penalty, depending on the values of $\delta$ and $\kappa$, for paths with a large number of kinks. Hence, the simulated partition function is now parametrized by $\delta$ and $\kappa$ reading
\begin{align}
Z'(\delta,\kappa)=& \sum_{K=0,\atop K \neq 1}^{\infty} \sum_{\{n\}} \sum_{s_1\ldots s_{K-1}}\int\limits_{0}^{\beta} d\tau_1 \int\limits_{\tau_1}^{\beta} d\tau_2 \ldots \int\limits_{\tau_{K-1}}^\beta d\tau_K\,\label{eq:primed_system_potential} \\ \nonumber
&V_{\delta,\kappa}(K)|W(K,\{n\}, s_1,\ldots,s_{K-1},\tau_1,\ldots,\tau_K)| \;.
\end{align}
Obviously, for any non-negative value of $\delta$, we recover the original primed partition function in the limit $\kappa\to\infty$
\begin{align}
Z'=\lim_{\kappa \to \infty} Z'(\delta,\kappa)\;,\quad \forall\; \delta \geq 0\;.
\end{align}
Therefore, performing CPIMC simulations for different values of $\kappa$ at fixed $\delta$ converges to the exact result in the limit $1/\kappa\to 0$.

This is demonstrated in Fig.~\ref{fig:demonstrate_kinPot}, where the convergence of the internal energy is shown for three different values of $\delta$. The system size has been chosen to be very small, i.e.\ $N=4$ particles in $N_B=19$ basis functions at $\theta=0.5$ and $r_s=40$, so that the energy can be computed with an exact diagonalization method (dashed black line). For the parameter $\kappa$ integer values have been used from $\kappa=5$ to $28$. At $\delta=10$ (red points), the kink potential practically resembles a step function restricting paths in the simulation to a maximum of $K_{\text{\tiny max}}=\kappa$ kinks. Interestingly, in this case the energy converges not monotonically towards the exact result but oscillates with even and odd numbers of $\kappa$. Strictly speaking, for only odd numbers of $\kappa$ the energy does converge monotonically while for even numbers it first drops below the exact value before eventually converging. This behavior may be explained by the factor $(-1)^K$ in the weight function, c.f.~Eq.~(\ref{eq:weight}), dominating the other two sign changing sources of the phase factor and the two-electron integrals. Nevertheless, these oscillations render a reliable extrapolation to the exact limit $1/\kappa\to 0$ difficult and hence, simply restricting the number of kinks is not a good choice. For smaller values of $\delta$ (green points in Fig.~\ref{fig:demonstrate_kinPot}) where we, to a larger extent, allow paths with a larger number of kinks than $\kappa$, the oscillations are significantly reduced. At $\delta=1$ (blue points), the oscillations finally vanish completely and the energy converges monotonically towards the exact result.
In fact, we always observe an s-shaped convergence behavior with $1/\kappa$ for Fermi potentials with $\delta \lesssim 1$. This allows for a very robust extrapolation scheme to the exact result in the limit $1/\kappa\to \infty$ after the onset of convergence that is clearly indicated by the change in curvature (at $\kappa\sim 17$ in Fig.~\ref{fig:demonstrate_kinPot}).
\begin{figure}[t]
 \includegraphics{{extrapolation_kappa_N=4_theta=1.0_rs=10}.pdf}
  \includegraphics{{extrapolation_kappa_N=33_theta=1.0_rs=1}.pdf}
 \caption{(color online). Convergence of the internal energy with respect to the kink potential parameter $\kappa$ and extrapolation to $1/\kappa \to 0$, corresponding to $K \to \infty$, at $\theta=1.0$.
\textbf{a)} $N=4$ particles and $r_s=10.0$ in $N_B=5575$ basis functions. \textbf{b)} $N=33$ and $r_s=1.0$ in $N_B=4169$ basis functions. The asymptotic values (black points) are enclosed between the blue and green lines and, within error bars, coincide with the PB-PIMC result (orange points).}
 \label{fig:kinkPot_fit}
\end{figure}

In Fig.~\ref{fig:kinkPot_fit}~a), we demonstrate this extrapolation scheme for a more difficult system of $N=4$ particles in $N_B=5575$ basis functions at $\theta=1$ and $r_s=10$, for which the direct CPIMC method without the kink potential is not applicable due to on average more than $50$ kinks, cf.~orange curve in Fig.~\ref{fig:avgKink_diff_temp}, and a resulting vanishing sign. To obtain an upper bound of the exact energy, we perform a horizontal fit (blue line) to those points after the onset of the convergence, while for the lower bound a linear fit is performed to those points (green line). The concrete fitting procedure is explained in appendix~\ref{fit_procedure}. For comparison the result for the energy of the likewise exact PB-PIMC method [cf. Sec.~\ref{sec:PB-PIMC}] is shown (orange point), which is well enclosed by the horizontal and linear fit and hence perfectly confirms our approach. Note that for the $N=4$ particles in only $N_B=19$ basis functions in Fig.~\ref{fig:demonstrate_kinPot} the energy is entirely converged for $\kappa=20$ so that all points for $\kappa>20$ lie on the horizontal line of the CI energy. This is because here the direct CPIMC algorithm converges to an average number of $20$ kinks. In contrast, in Fig.~\ref{fig:kinkPot_fit}~a), after the change in curvature at approximately $\kappa=8$, the energy is not entirely converged and still slowly decreasing. In this regime a near cancellation of all contributions for increasing $\kappa$ occurs. However, in the limit $\kappa\to \infty$ the energy does not converge linearly towards the exact value, because the direct CPIMC algorithm always converges at a finite value of $\braket{K}^\prime$, cf. Fig.~\ref{fig:avg_sign}~b) and Fig.~\ref{fig:avgKink_diff_temp}. Therefore, from some value of $\kappa$ onwards, depending on the average number of kinks in the direct CPIMC algorithm, the points will be on a horizontal line getting no further contributions for increasing $\kappa$. For this reason, the linear fit (green line) is indeed a true lower bound of the exact energy for the used number of basis function. Our extrapolation scheme also works well for larger systems, which is illustrated in Fig.~\ref{fig:kinkPot_fit}~b) for the example of $N=33$ particles at $\theta=1$ and $r_s=1$ in $N_B=4169$ basis functions. Here, the extrapolated value (black point) also agrees with the PB-PIMC result (orange point), which has a larger statistical error than in Fig.~\ref{fig:kinkPot_fit}~a), due to the larger density. For a convergence plot for the same system at a lower temperature of $\theta=0.0625$, where no other results are available, we refer to Ref.~\cite{tim_prl15}.

In general, the use of the kink potential combined with the extrapolation scheme actually more  than doubles the accessible density parameter within the CPIMC approach at fixed other system parameters. Nevertheless, our procedure is still limited by the FSP, which is indicated by the increasing error bars of the last points in Fig.~\ref{fig:kinkPot_fit}~a). For example, at $\kappa=10$ there are on average $\braket{K}^\prime\sim 9.4$ kinks with a corresponding average sign $\braket{s}^\prime\sim 0.05$, while at $\kappa=16$ (last point) there are $\braket{K}^\prime\sim15.3$ kinks with a corresponding average sign $\braket{s}^\prime\sim 5\cdot10^{-3}$ causing a large statistical error. Of course, if the sign problem becomes too severe before the onset of convergence (indicated by the change in curvature), our procedure is not applicable.

\section{Basic idea of PB-PIMC\label{sec:PB-PIMC}}
In contrast to CPIMC, our permutation blocking PIMC approach is essentially standard PIMC in coordinate space but combines two well-known concepts: 1) antisymmetric imaginary time propagators, i.e., determinants \cite{det1,det2,det3}, and 2) a fourth-order factorization of the density matrix \cite{chin1,chin2,sakkos}. In addition, to sample this more complicated configuration space, one of us has developed an efficient set of Monte Carlo updates based on the temporary construction of artificial trajectories. Since PB-PIMC and its application to the UEG have been introduced in detail in Refs.~\cite{pb_pimc_njp} and \cite{pb_pimc_jcp15}, here we shall restrict ourselves to a brief overview.

We start from the coordinate representation of the canonical partition function (\ref{eq:Z_trace}) describing a system of $N$ spin-polarized fermions at inverse temperature $\beta$
\begin{eqnarray}
 Z = \frac{1}{N!} \sum_{\sigma\in S_N} \textnormal{sgn}(\sigma) \int \textnormal{d}\mathbf{R}\ \bra{ \mathbf{R} } e^{-\beta\op{H}} \ket{ \op{\pi}_\sigma \mathbf{R}} \;, \label{boseZ}
\end{eqnarray}
with $\op{\pi}_\sigma$ being the exchange operator that corresponds to a particular element $\sigma$ from the permutation group $S_N$ with associated sign $\textnormal{sgn}(\sigma)$.
However, since the low-temperature matrix elements of $\op{\rho}$ are not known, we use the group property $\op\rho (\beta) = \prod_{\alpha=0}^{P-1} \op\rho(\epsilon)$, with $\epsilon=\beta/P$, and approximate each of the $P$ factors at a $P$ times higher temperature by the fourth-order factorization \cite{chin2,sakkos}
\begin{eqnarray}
 \label{cchin} e^{-\epsilon\op{H}} &\approx& e^{-v_1\epsilon\op{W}_{a_1}} e^{-t_1\epsilon\op{K}}\\ & & \nonumber e^{-v_2\epsilon\op{W}_{1-2a_1}} e^{-t_1\epsilon\op{K}} e^{-v_1\epsilon\op{W}_{a_1}} e^{-2t_0\epsilon\op{K}}\;,
\end{eqnarray}
which allows for sufficient accuracy, for small $P$.
The $\op{W}$ operators in Eq.\ (\ref{cchin}) denote a modified potential that combines the usual potential energy $\op{V}$ with
double commutator terms of the form
\begin{eqnarray}
 [[\op{V},\op{K}],\op{V}] = \frac{\hbar^2}{m} \sum_{i=1}^N |\mathbf{F}_i|^2 \;, \quad \mathbf{F}_i = -\nabla_i V(\mathbf{R})\;,
\end{eqnarray}
where $\op{K}$ denotes the operator of the kinetic energy. Therefore, PB-PIMC requires the additional evaluation of all forces, and the final result for the partition function is given by
\begin{eqnarray}
\label{finalz} Z &=& \frac{1}{(N!)^{3P}} \int \textnormal{d}\mathbf{X} \prod_{\alpha=0}^{P-1} \Big( e^{-\epsilon\tilde V_\alpha}e^{-\epsilon^3u_0\frac{\hbar^2}{m}\tilde F_\alpha} \\ & & \textnormal{det}(\rho_\alpha)\textnormal{det}(\rho_{\alpha A})\textnormal{det}(\rho_{\alpha B}) \Big)\;.
\end{eqnarray}
Here, $\tilde V_\alpha$ and $\tilde F_\alpha$ contain all contributions of the potential energy and the forces, respectively, and the diffusion matrix is given by
\begin{eqnarray}
 \rho_\alpha(i,j) &=& \lambda_{t_1\epsilon}^{-D} \textnormal{exp} \left( -\frac{\pi}{\lambda^2_{t_1\epsilon}} ( \mathbf{r}_{\alpha,j} - \mathbf{r}_{\alpha A,i})^2 \right)\;, \label{diffusion}
\end{eqnarray}
with $\lambda_{t_1\epsilon}=\sqrt{2\pi\epsilon t_1\hbar^2/m}$ being the thermal
wavelength of a single ``time slice''.

Instead of explicitly sampling each permutation cycle, as in standard PIMC, we combine both positively and negatively signed configuration weights in the determinants, which leads to a cancellation of terms and, therefore, a significantly increased average sign in our simulations.
However, this ``permutation blocking'' is only effective when $\lambda_{t_1\epsilon}$ is comparable to the mean inter-particle distance.
With increasing $P$, $\lambda_{t_1\epsilon}$ decreases and the average sign eventually converges towards that of standard PIMC.
Hence, it is crucial to combine the determinants with the fourth order factorization from Eq.\ (\ref{cchin}), which allows for sufficient accuracy with as few as two or three propagators and thereby maximizes the benefit of the blocking by the determinants.

\section{CPIMC and PB-PIMC benchmark results for the polarized UEG\label{sec:results}}
Due to the complementary character of the FSP the CPIMC and PB-PIMC approaches are well suited to be combined and, thereby, to circumvent the sign problem. Concerning the $N=33$ spin-polarized UEG, CPIMC is applicable practically over the entire temperature range from $\theta=0.01$ to $10$ and suffers an increasing sign problem for increasing $r_s$. The critical region at which the FSP becomes severe is around $r_s\sim 1$ for $\theta\lesssim 0.5$ and $r_s\sim \theta$ for $\theta\gtrsim 1$. On the other hand, the PB-PIMC method suffers a weak increase of the FSP for decreasing $r_s$, yet it is in principle capable of providing results over the entire density range for degeneracy parameters $\theta\gtrsim 0.75$. At temperatures $\theta < 0.5$, PB-PIMC is not feasible at high density.
\begin{figure}[t]
\includegraphics{{CPIMC_vs_RPIMC_E_XC}.pdf}
\caption{(Color online) Exchange-correlation energy $E_{xc}$ times $r_s$ of the $N=33$ particle spin-polarized UEG over the density parameter $r_s$ for different degeneracy parameters $\theta$. Results have been obtained by combining the CPIMC (dots) and PB-PIMC (crosses) approach taking the most accurate values of each method (connected by the solid line). In addition, RPIMC results from~\cite{brown_prl13} are plotted for comparison (open circles).}
\label{fig:E_xc}
\end{figure}

\begin{figure}[t]
\includegraphics{{CPIMC_vs_RPIMC_E_XC_theta}.pdf}
\caption{(Color online) Exchange-correlation energy $E_{xc}$ times $r_s$ of the $N=33$ particle spin-polarized UEG over the degeneracy parameter $\theta$ for different density parameters $r_s$. Shown are results from CPIMC (dots) and PB-PIMC (crosses) calculations. In addition, RPIMC results from~\cite{brown_prl13} are plotted for comparison (lines with light colors and open circles, for $r_s=1$ and $r_s=4$).}
\label{fig:E_xc_theta}
\end{figure}

For the construction of density functionals the exchange-correlation energy $E_{xc}$ (per particle) of the UEG is of particular importance, which is obtained by subtracting the ideal energy $U_0$ from the total internal energy
\begin{align}
E_{xc}=E-U_0\;.
\end{align}
In Fig.~\ref{fig:E_xc}, we show our results for the exchange-correlation energy. Note that we plot $E_{xc}\cdot r_s$ which converges towards the finite Hartree-Fock energy in the limit $r_s\to 0$. We always took the most accurate value of CPIMC (solid dots) or PB-PIMC (crosses), in cases where both are available. These data complement our earlier results that are included here as well, to have a complete set [for CPIMC, data for four isotherms $\theta=0.5,1,2,4$ have been reported in Ref.~\cite{tim_prl15}, while for PB-PIMC, the internal energy for the three isotherms $\theta=1,2,4$ has been presented in Ref.~\cite{pb_pimc_jcp15}, where the application of the method to the UEG is explained in detail]. At $\theta=0.5$, CPIMC can provide data up to $r_s=1$, while PB-PIMC suffers a too strong FSP below $r_s=2$ leaving a gap between both approaches. We have fitted a spline of order 4 to the available points and are thereby able to accurately close the gap (dotted line). With this, we are able to present {\em ab initio} results for this system for the entire density range, for all temperatures $\Theta \ge 0.5$.

In Tab.~\ref{tab:1}, we present all CPIMC and PB-PIMC data points shown in Fig.~\ref{fig:E_xc}. In addition to the exchange-correlation energy, the ideal, kinetic and potential energy are listed. Note that even the ideal energy in the canonical ensemble cannot be calculated analytically. Further, we added the number of basis functions $N_B$ that have been used in the corresponding CPIMC simulation, where we have carefully checked convergence of the energy (within statistical errors) with respect to $N_B$.
The origin of the fluctuations at the highest temperature are easily understood:
 at $\theta=8$, the relative contribution of the exchange-correlation energy to the internal energy becomes very small since the kinetic energy dominates for increasing temperature. Hence, $E_{xc}$ is obtained by subtracting two large numbers of similar size which, of course, is ill-conditioned and, therefore, increases the statistical error of $E_{xc}$. The same applies in the limit $r_s\to 0$. Nevertheless, our  exchange-correlation energies represent the most accurate results published to date.

For comparison we also plot the RPIMC data from Ref.~\cite{brown_prl13}. It is evident that they not only have a significantly larger statistical error, but they clearly deviate systematically from our results. Interestingly, the deviations increase from $\theta=1$ to $\theta=2$, and even at $\theta=4$, there is a significant discrepancy. This observation stands in contrast to the assumption that the systematic error due to the fixed node approximation vanishes for increasing temperature.

Finally, Fig.~\ref{fig:E_xc_theta} shows the dependence of the exchange-correlation energy on temperature for four fixed densities.
We again show the most accurate points of either CPIMC and PB-PIMC.
CPIMC allows for calculations practically down to the ground state, for $r_s\lesssim 1$. On the other hand, PB-PIMC is limited, at larger densities, to temperatures $\theta\geq 0.5$.
We observe that all isochores are nearly parallel and do not cross.
An interesting feature is the existence of a minimum around $\Theta\sim 0.25$, for all densities [some uncertainty remains for the lowest density, $r_s=4$, as our simulations are confined to $\Theta \ge 0.5$]. Similar observations have been made in the fit results of Ref.~\cite{karasiev_prl14} and in the computation of the screened potential of an ion in a streaming quantum plasma \cite{zhandos_pre_15}.

The origin of this non-monotonic behavior is a competition of two effects. The governing trend is a decrease of the (modulus of the) interaction energy with temperature arising from a thermal broadening of the particle density. At low temperatures there exists a second trend arising from quantum diffraction effects: the thermal DeBroglie wavelength is reduced with temperature increase which increases the Coulomb interaction. A similar trend of an intermediate increase of correlations with temperature has been predicted for Wigner crystallization in 2D~\cite{ceperley_prl_09}.

In addition to the {\em ab initio data}, Fig.~\ref{fig:E_xc_theta} also includes the fixed node RPIMC data of Ref.~\cite{brown_prl13} which are available for the two lowest densities, $r_s=1$ and $r_s=4$. For the case $r_s=4$ the RPIMC results are systematically too high by a few percent. More severe deviations are observed for $r_s=1$ where the energies are too low. Particularly strong deviations are seen for low temperatures, $\theta \lesssim 1$ where the error exceeds $10\%$, giving even rise to a crossing of two isochores.

\section{Summary and Discussion}
This paper was devoted to a detailed discussion of the CPIMC simulation results for the uniform electron gas reported in a recent Letter \cite{tim_prl15}. We presented a systematic analysis of the fermion sign problem of direct CPIMC for the polarized UEG. For increasing particle number, a sharp drop of the average sign, at a certain critical value of $r^{\rm cr}_s(\Theta, N)$, has been observed and was shown to be connected to a strong increase in the average number of kinks in the simulation paths in Fock space. By introducing an auxiliary Fermi-like kink potential we introduced a modified CPIMC approach for which
the accessible $r_s$-range could be increased by more than a factor $2$, for a fixed particle number and temperature \cite{tim_prl15}. When restricting the number of kinks to a maximum number $K_{\text{\small max}}$, it turned out that the energy does not converge monotonically but rather oscillates towards the exact result with increasing $K_{\text{\small max}}$, which renders a reliable extrapolation scheme difficult. However, by choosing the kink potential parameter $\delta$ such that it acts as a smooth penalty for paths with a larger number of kinks, a monotonic convergence of the energy could be achieved. We have developed a robust extrapolation scheme that provides  strict upper and lower bounds thereby yielding an accurate value for the thermodynamic quantities of the UEG.

An independent confirmation of our extrapolation procedure could be obtained by a comparison to accurate PB-PIMC results. Interestingly, utilizing the kink potential, the energy of the simulation typically converges at about $20-30$ kinks (on average in the simulation paths), whereas the direct CPIMC approach (without the potential) equilibrates at several thousand kinks. This is explained by an almost complete cancellation of contributions of paths with a large number of kinks in the partition function, which sets the limitation of the auxiliary kink potential method: it works only if we are able to reach the onset of this near cancellation, before the sign problem becomes too severe. This is clearly detectable from the convergence behavior of the energy, cf. Fig.~\ref{fig:kinkPot_fit}: only when the energy approaches the horizontal asymptote, as a function of $1/\kappa$, the method is applicable.

The second goal of this paper was to extend the available {\em ab initio} results for the exchange-correlation energy of the polarized electron gas to higher temperatures and lower densities. This was achieved by combining two complementary independent methods---CPIMC and PB-PIMC. With this we were able to avoid the sign problem for $N=33$ electrons over the entire density range, for all temperatures  $\theta \ge 0.5$, and we presented data up to $\theta=8$, completely avoiding fixed nodes or similar approximations. In all cases where both methods overlap we observed perfect agreement (within error bars), allowing for extremely valuable cross-checks.

Below $\theta=0.5$, the present combination of two methods accesses only parts of the density range. Within the current implementations (and reasonable numerical effort) PB-PIMC is not applicable, for high densities, whereas CPIMC can only provide accurate results up to a minimum density around $r_s\sim 1$, leaving open a gap in the density which further increases with the particle number. Work is presently under way to access larger particle numbers and, eventually, perform an extrapolation to the thermodynamic limit, as was successfully demonstrated for very high densities in Ref.~\cite{tim_prl15}.

The present benchmark results should be useful for the development of improved quantum Monte Carlo simulations including density matrix QMC \cite{foulkes_14,foulkes_15} and tests of improved fermionic nodes for RPIMC. The present scheme of combining CPIMC and PB-PIMC should also be suitable to produce first-principle results for the paramagnetic electron gas for which an increased sign problem of CPIMC was observed~\cite{tim_prl15}.

\section*{Acknowledgements}
This work is supported by the Deutsche Forschungsgemeinschaft via project BO 1366-10 and via SFB TR-24 project A9 as well as grant shp00015 for CPU time at the Norddeutscher Verbund f\"ur Hoch- und H\"ochstleistungsrechnen (HLRN).

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text:
Q: yii2 authclient unknown property: app\models\User::github I'm using yii 2 authclient extension  and Exemple code here
When I login from Facebook following error occurs

Setting unknown property: app\models\User::github

I can't find function github().
Please help me. Thanks

A: Maybe in your code, somewhere, you have a code like

*

*$user->github = ...

*Yii::$app->user->github = ...

and your User class haven't the github property:
php
class User {
    private $github; // <- I suspect this property is missed
}

A: Exemple code here but i don't know property 'github'

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12/02/2019 4:46 AM AEDT | Updated 12/02/2019 6:06 AM AEDT
The Grammys All But Ignored 21 Savage's ICE Detainment
Only one person mentioned the Atlanta-based rapper's plight during the 3.5-hour broadcast of the annual music awards ceremony.
The Grammy Awards on Sunday was chock full of heart-stopping performances and thought-provoking acceptance speeches. But one major issue went largely unacknowledged: rapper 21 Savage's arrest by Immigration and Customs Enforcement a week earlier.
Most producers and musicians at the ceremony steered clear of his detainment ― one of the most prominent news stories of the last week. ICE agents arrested the "Bank Account" rapper ― whose given name is She'yaa Bin Abraham-Joseph ― on Feb. 3 for overstaying a visa.
ICE said 21 Savage is a British native who legally entered the U.S. in 2005 as a minor and overstayed his visa, which expired in July 2006.
His lawyers argue that he has never hidden his immigration status. If he is deported, he could be barred from returning to the U.S. for 10 years.
As stars sauntered down the red carpet at the Staples Center in Los Angeles on Sunday, 21 Savage remained locked up at an immigration detention center in Georgia. It should have been a joyous night for the Atlanta-based rapper, who was nominated for two Grammys.
Yet only one person acknowledged the rapper's plight during the Grammys' more than three-hour broadcast. Swedish record producer Ludwig Göransson briefly mentioned 21 Savage while accepting the Record of the Year award for Childish Gambino's "This Is America."
"We want to thank all of the rappers that are featured on this song," he said. "21 Savage, you should be here tonight."
21 Savage getting a shoutout from Childish Gambino's producer Ludwig Göransson 🔥 #GRAMMYspic.twitter.com/z4EJ003Jyw
— Chris Montano (@gswchris) February 11, 2019
The broadcast quickly cut to rapper Post Malone applauding the mention. He and 21 Savage were nominated for Record of the Year and Best Rap/Sung Performance for their hit single "Rockstar."
Post Malone wore a shirt emblazoned with "21 Savage" under his jacket during his performance with the Red Hot Chili Peppers earlier in the night. But many fans were disappointed that he didn't address the controversy on stage.
"How is Post Malone going to perform ["Rockstar"] and not even shout out free 21 Savage?" one Twitter user wrote.
pic.twitter.com/TlwkqgMvMY
— not a salad dressing (@cmigueldelpozo) February 11, 2019
About 15 activists with the #Free21Savage Coalition rallied outside the Staples Center before the telecast to protest his detainment, The Los Angeles Times reported.
The demonstration was also intended to raise awareness about struggles facing the roughly 600,000 black undocumented immigrants living in the U.S.
while some are walking the grammys red carpet, another small group is protesting in front of the grammy museum on behalf of 21 savage. #free21savagepic.twitter.com/V8iiGsA70m
— makeda (@makedaeaster) February 10, 2019
Though 21 Savage's situation was barely mentioned during the live broadcast, some artists addressed the issue during red carpet interviews with the Times.
"I think that we all got to just speak up ― it's not money, it's not just saying it, you really have to believe in it," DJ Mustard said. "I think they got to get that man back home because he has kids."
As the #GRAMMYs are underway, @21savage is still being held in an immigration detention center. @KaceyMusgraves, @Ashanti, @CeeLoGreen, @MissMargoPrice and more speak out for his support https://t.co/aQ299MNY2tpic.twitter.com/3TcaEOM43h
— LAT Entertainment (@latimesent) February 11, 2019
Dozens of high-profile figures, including Rep. Alexandria Ocasio-Cortez (D-N.Y.) and Cardi B, have spoken out against his detainment. Rapper Jay-Z hired New York–based attorney Alex Spiro to represent 21 Savage in his case.
"At the end, the attention on the case is important for all the other incarcerated people and that's important to me," Spiro told NBC News. "And it's important to Jay."
MORE: 21 savage celebrity entertainment grammys music U.S. Immigration and Customs Enforcement
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2. Login to the Plesk 7 Control Panel.
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7. Click on the name of the Certificate from the list.
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12. Click the Server item from the left hand menu.
13. Click the Service Management menu item.
14. You need to Stop and Start the Apache process.


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Joker Jack Amira Pocher: "Ich habe es gehasst, schwanger zu sein"
Der Joker ist eine fiktive Figur, die überwiegend in Comics des Verlages DC, einer Tochtergesellschaft von WarnerMedia, auftritt. Jack Napier ist die rechte Hand des Mafiabosses Carl Grissom. Vor Jahren, war er es, der die. Wachsfigur des Joker in Anlehnung an die Darstellung durch Jack Nicholson. Figur des Joker in Anlehnung an die Darstellung durch Heath Ledger. Joker im Film Suicide Squad (Dreharbeiten). Der Joker (englisch The Joker) ist eine fiktive Figur, die überwiegend in Comics des Verlages. Die Besetzung der Hauptrollen war ein Thema der Klatschpresse: Jack Nicholson zögerte bis zur letzten Sekunde, ehe er die Rolle des Joker akzeptierte. Joker-Stars: Von Jack Nicholson bis Joaquin Phoenix. Foto: Warner Bros. Im beim Filmfestival in Venedig gefeierten Siegerfilm.
Jack Napier ist die rechte Hand des Mafiabosses Carl Grissom. Vor Jahren, war er es, der die. Jack Napier, Arthur Fleck oder etwa Melvin White? +. Filme Der Joker ist wohl einer der mysteriösesten Comic-Charaktere, die es gibt. Keiner. Jack Nicholson als Joker – Der Wahnsinn hat einen Namen. Mit Jack Nicholson in der Rolle des Jokers für Tim Burtons ".
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Auf die charakteristische chemisch gebleichte Haut und Sliders Ghost verzerrten bzw. Gespielt wird der Joker in diesem Film von Joaquin Phoenix. Danny Elfman. Er bezeichnet Batman gelegentlich als Spielverderber und ist trotz seines Wahns ein kriminelles Genie, so dass er zum Beispiel den Polizisten Ethan Benneth gegen seinen Chef auflehnt und ihn unabsichtlich in Clayface verwandelt. Das ist im grunde ein herzensguter Typ,mental nicht ganz auf der Höhe aber nicht gewaltätig oder so,jedenfalss bis er am Ende Beste Spielothek in Bargdorf finden er vom Schicksal nur auf die Fresse bekommt.
The volume I had was The Man Who Laughs — his face had been permanently operated on so that he will always have this perpetual grin.
And it looked absolutely weird. I cut the picture out of the book and gave it to Bob, who drew the profile and gave it a more sinister aspect.
Then he worked on the face; made him look a little clown-like, which accounted for his white face, red lips, green hair. And that was the Joker!
Although Kane adamantly refused to share credit for many of his characters and refuted Robinson's claim until Kane's death , many comic historians credit Robinson with the Joker's creation and Finger with the character's development.
The Joker debuted in Batman 1 April as the eponymous character's first villain, about a year after Batman's debut in Detective Comics 27 May The Joker initially appeared as a remorseless serial killer, modeled after a joker playing card with a mirthless grin, who killed his victims with "Joker venom," a toxin that left their faces smiling grotesquely.
Finger wanted the Joker to die because of his concern that recurring villains would make Batman appear inept, but was overruled by then-editor Whitney Ellsworth ; a hastily drawn panel, indicating that the Joker was still alive, was added to the comic.
The character's regular appearances quickly defined him as the archenemy of the Dynamic Duo — Batman and Robin ; he killed dozens of people, and even derailed a train.
Around the same time, DC Comics found it easier to market its stories to children without the more mature pulp elements that had originated many superhero comics.
During this period, the first changes in the Joker began to appear, portraying him more as a prankster than a threat; when he kidnaps Robin, Batman pays the ransom by check, meaning that the Joker cannot cash it without being arrested.
The cover of Detective Comics 69, known as "Double Guns" with the Joker emerging from a genie lamp, aiming two guns at Batman and Robin , is considered one of the greatest superhero comic covers of the Golden Age and is the only image of the character using traditional guns.
Robinson said that other contemporary villains used guns, and the creative team wanted the Joker—as Batman's adversary—to be more resourceful.
The Joker was one of the few popular villains continuing to appear regularly in Batman comics from the Golden Age into the Silver Age, as the series continued during the rise in popularity of mystery and romance comics.
In , Finger wrote an origin story for the Joker in Detective Comics , which introduced the characteristic of him formerly being the criminal Red Hood , and his disfigurement the result of a fall into a chemical vat.
By , the Comics Code Authority had been established in response to increasing public disapproval of comic book content. The backlash was inspired by Frederic Wertham , who hypothesized that mass media especially comic books was responsible for the rise in juvenile delinquency , violence and homosexuality, particularly in young males.
Parents forbade their children from reading comic books, and there were several mass burnings. The character appeared less frequently after , when Julius Schwartz who disliked the Joker became editor of the Batman comics.
As the show's popularity waned, however, so did that of the Batman comics. In , after a four-year disappearance, [2] the Joker was revived and revised by writer Dennis O'Neil and artist Neal Adams.
Beginning with Batman 's "The Joker's Five-Way Revenge", the character returns to his roots as an impulsive, homicidal maniac who matches wits with Batman.
I went to the DC library and read some of the early stories. I tried to get a sense of what Kane and Finger were after. DC Comics was a hotbed of experimentation during the s, and in the character became the first villain to feature as the title character in a comic book series, The Joker.
Although he murdered thugs and civilians, he never fought Batman; this made The Joker a series in which the character's villainy prevailed over rival villains, instead of a struggle between good and evil.
The series never found an audience, and The Joker was canceled after nine issues despite a "next issue" advertisement for an appearance by the Justice League.
In , DC Comics reissued the series as a trade paperback. When Jenette Kahn became DC editor in , she redeveloped the company's struggling titles; during her tenure, the Joker would become one of DC's most popular characters.
In "The Laughing Fish", the Joker disfigures fish with a rictus grin resembling his own expecting copyright protection , and is unable to understand that copyrighting a natural resource is legally impossible.
I really wanted to get back to the idea of Batman fighting insane murderers at 3 a. Years after the end of the television series, sales of Batman continued to fall and the title was nearly cancelled.
Although the s restored the Joker as an insane, lethal foe of Batman, it was during the s that the Batman series started to turn around and the Joker came into his own as part of the "Dark Age" of comics: mature tales of death and destruction.
The shift was derided for moving away from tamer superheroes and villains , but comic audiences were no longer primarily children.
Todd was unpopular with fans; rather than modify his character, DC opted to let them vote for his fate and a vote plurality had the Joker beat Todd to death with a crowbar.
This story altered the Batman universe: instead of killing anonymous bystanders, the Joker murdered a core character in the Batman fiction; this had a lasting effect on future stories.
Alan Moore and Brian Bolland 's graphic novel The Killing Joke expands on the Joker's origins, describing the character as a failed comedian who adopts the identity of the Red Hood to support his pregnant wife.
The animated series introduced the Joker's female sidekick: Harley Quinn , a psychiatrist who falls for—and ends up in an abusive relationship with—the Joker, becoming his supervillain accomplice.
The character was popular, and was adapted into the comics as the Joker's romantic interest in Breyfogle conceived the idea as a means to expand on Anarky's characterization, but O'Neil by then the editor for the Batman series of books was opposed to it, and only allowed it to be written under protest, and with a promise that the revelation would eventually be revealed incorrect.
However, the Anarky series was cancelled before the rebuttal could be published. The story arc explores the symbiotic relationship between the Joker and Batman, and sees the villain shatter the trust between Batman and his adopted family.
The Joker has undergone many revisions since his debut. The most common interpretation of the character is that he is disguised as the criminal Red Hood and pursued by Batman.
The Joker falls into a vat of chemicals that bleaches his skin, colors his hair green and his lips red, and drives him insane.
The reasons why the Joker was disguised as the Red Hood, and his identity before his transformation have changed over time.
The character was introduced in Batman 1 , in which he announces that he will kill three of Gotham's prominent citizens including Henry Claridge.
Although the police protect Claridge, the Joker had poisoned him before making his announcement and Claridge dies with a ghastly grin on his face; Batman eventually defeats him, sending him to prison.
His resulting disfigurement led him to adopt the name "Joker", from the playing card figure he came to resemble. In this story, the Joker is obsessed with maintaining his illusion of wealth and celebrity as a criminal folk hero, afraid to let Gotham's citizens know that he is penniless and was tricked out of his fortune.
Batman: The Killing Joke built on the Joker's origin story, portraying him as a failed comedian pressured into committing crime as the Red Hood to support his pregnant wife.
Batman's interference causes him to leap into a chemical vat, which disfigures him. This, combined with the trauma of his wife's earlier accidental death, causes him to go insane and become the Joker.
Although the Joker refuses, he shows his appreciation by sharing a joke with Batman. In the story "A Death in the Family", the Joker beats Jason Todd with a crowbar and leaves him to die in an explosion.
Todd's death haunts Batman, and for the first time he considers killing the Joker. In the " No Man's Land " storyline, the Joker murders Commissioner Gordon's second wife, Sarah , as she shields a group of infants.
The Joker, lamenting that he may never walk again, collapses with laughter when he realizes that the commissioner has avenged Barbara's paralysis.
The s began with the crossover story "Emperor Joker", in which the Joker steals Mister Mxyzptlk 's reality-altering power and remakes the universe in his image torturing and killing Batman daily, before resurrecting him.
When the supervillain then tries to destroy the universe, his reluctance to eliminate Batman makes him lose control, and Superman defeats him.
Instead, the Joker flanked by an army of "Jokerized" supervillains launches a final crime spree.
Believing that Robin Tim Drake has been killed in the chaos, Dick Grayson beats the Joker to death although Batman revives his foe to keep Grayson from being a murderer , and the villain succeeds in making a member of the Bat-family break their rule against killing.
In " Under the Hood " , a resurrected Todd tries to force Batman to avenge his death by killing the Joker. Batman refuses, arguing that if he allows himself to kill the Joker, he will not be able to stop killing other criminals.
The supervillain returns in "The Clown at Midnight" as a cruel, enigmatic force who awakens and tries to kill Harley Quinn to prove to Batman that he has become more than human.
When the Joker escapes, he attacks the Black Glove, burying its leader Simon Hurt alive after the supervillain considers him a failure as an opponent; the Joker is then defeated by the recently returned Batman.
The Mobius Chair revealed there "are three. Although a number of backstories have been given, a definitive one has not yet been established for the Joker.
An unreliable narrator , the character is uncertain of who he was before and how he became the Joker: "Sometimes I remember it one way, sometimes another Here, the character is a laboratory worker who becomes the Red Hood a masked criminal to steal 1 million dollars and retire.
He falls into a vat of chemical waste when his heist is thwarted by Batman, emerging with bleached white skin, red lips, green hair and a permanent grin.
This story was the basis for the most often-cited origin tale, Moore's one-shot The Killing Joke. Unsuccessful, he agrees to help mobsters with a robbery and becomes the Red Hood.
The heist goes awry; the comedian leaps into a chemical vat to escape Batman, surfacing disfigured.
This, combined with the earlier accidental death of his wife and unborn child, drives the comedian insane and he becomes the Joker.
However, the Joker's unreliable memory has allowed writers to develop other origins for the character. He has his fateful first meeting with Batman, which results in his disfigurement.
It is suggested that the Joker is sane, and feigns insanity to avoid the death penalty. In Batman Confidential 7—12, the character, Jack, is a talented criminal who is bored with his work.
He encounters and becomes obsessed with Batman during a heist, embarking on a crime spree to attract his attention.
After Jack injures Batman's girlfriend, Batman scars Jack's face with a permanent grin and betrays him to a group of mobsters, who torture him in a chemical plant.
Jack escapes, but falls into an empty vat as gunfire punctures chemical tanks above him. The flood of chemicals used in anti-psychotic medication alters his appearance and completes his transformation.
The Joker has claimed a number of origins, including being the child of an abusive father who broke his nose, and the long-lived jester of an Egyptian pharaoh.
As Batman says: "Like any other comedian, he uses whatever material will work. A number of alternate universes in DC Comics publications allow writers to introduce variations on the Joker, in which the character's origins, behavior, and morality differ from the mainstream setting.
Renowned as Batman's greatest enemy, [] [] [] [] the Joker is known by a number of nicknames, including the Clown Prince of Crime, the Harlequin of Hate, the Ace of Knaves, and the Jester of Genocide.
The original, dominant image is that of an extreme psychopath , [] with genius-level intelligence and a warped, sadistic sense of humor.
This appearance is such a fundamental aspect of the character that when the animated series The Batman placed the Joker in a straitjacket, it quickly redesigned him in his familiar suit.
The Joker is obsessed with Batman, the pair representing a yin-yang of opposing dark and light force; although it is the Joker who represents humor and color and Batman who dwells in the dark.
Spectacle is more important than success for the Joker, and if it is not spectacular it is boring. Despite this body count, he is always found not guilty by reason of insanity and sent to Arkham Asylum, avoiding the death penalty.
The villain displays no instinct for self-preservation, and is willing to die to prove his point. The Joker's main characteristic is his apparent insanity, although he is not described as having any particular psychological disorder.
Like a psychopath, he lacks empathy, a conscience, and concern over right and wrong. In Arkham Asylum: A Serious House on Serious Earth , the Joker is described as capable of processing outside sensory information only by adapting to it.
This enables him to create a new personality every day depending on what would benefit him and explains why, at different times, he is a mischievous clown or a psychopathic killer.
The Killing Joke in which the Joker is the unreliable narrator explains the roots of his insanity as "one bad day": losing his wife and unborn child and being disfigured by chemicals, paralleling Batman's origin in the loss of his parents.
He tries and fails to prove that anyone can become like him after one bad day by torturing Commissioner Gordon, physically and psychologically.
Englehart's "The Laughing Fish" demonstrates the character's illogical nature: trying to copyright fish that bear his face, and not understanding why threatening the copyright clerk cannot produce the desired result.
The Joker is alternatively depicted as sexual and asexual. Frank Miller interpreted the character as fixated on death and uninterested in sexual relationships, while Robinson believed that the Joker is capable of a romantic relationship.
Harley loves him, but the Joker does not reciprocate her feelings, chiding her for distracting him from other plans.
Snyder's "Death of the Family" describes the Joker as in love with Batman, although not in a traditionally romantic way.
The Joker believes that Batman has not killed him because he makes Batman better and he loves the villain for that.
The Joker is often depicted as defining his existence through his conflict with Batman. In 's "Going Sane", the villain tries to lead a normal life after Batman's apparent death, only to become his old self again when Batman reappears; in "Emperor Joker", an apparently omnipotent Joker cannot destroy Batman without undoing himself.
Since the Joker is simply "the Joker", he believes that Batman is "Batman" with or without the costume and has no interest in what is behind Batman's mask, ignoring opportunities to learn Batman's secret identity.
The Joker is portrayed as having no fear; when fellow supervillain Scarecrow doses him with fear toxin in Knightfall , the Joker merely laughs and says "Boo!
At these moments, the Joker is depicted as expressing remorse for his acts; [] [] however, during a medically induced period of partial sanity in Batman: Cacophony he tells his opponent, "I don't hate you 'cause I'm crazy.
I'm crazy 'cause I hate you," and confirms that he will only stop murdering when Batman is dead. The Joker has no inherent superhuman abilities.
The flower in his lapel sprays acid, and his hand often holds a lethal joy buzzer conducting a million volts of electricity, although both items were introduced in as harmless joke items.
The Joker has used venom since his debut; only he knows the formula, and is shown to be gifted enough to manufacture the toxin from ordinary household chemicals.
Another version of the venom used in Joker: Last Laugh makes its victims resemble the Joker, susceptible to his orders. The character's arsenal is inspired by his nemesis' weaponry, such as batarangs.
In "The Joker's Utility Belt" , he mimicked Batman's utility belt with non-lethal items, such as Mexican jumping beans and sneezing powder.
His technical genius is not limited by practicality, allowing him to hijack Gotham's television airwaves to issue threats, transform buildings into death traps, launch a gas attack on the city and rain poisoned glass shards on its citizens from an airship.
The Joker is portrayed as skilled in melee combat, from his initial appearances when he defeats Batman in a sword fight nearly killing him , and others when he overwhelms Batman but declines to kill him.
The Joker's unpredictable, homicidal nature makes him one of the most feared supervillains in the DC Universe; the Trickster says in the miniseries Underworld Unleashed , "When super-villains want to scare each other, they tell Joker stories.
He has collaborated with criminals like the Penguin , the Riddler and Two-Face , although these partnerships rarely end well due to the Joker's desire for unbridled chaos, and he uses his stature to lead others such as Killer Croc and the Scarecrow.
Although they have a friendly partnership in 's World's Finest Comics 88, later unions emphasized their mutual hostility and clashing egos.
Despite his tendency to kill subordinates on a whim, the Joker has no difficulty attracting henchmen with a seemingly infinite cash supply and intimidation: they are too afraid of their employer to refuse his demands that they wear red clown noses or laugh at macabre jokes.
Although Quinn loves the Joker, he is obsessed with Batman and uses her to achieve his goals at her expense. Despite violent abuse, she returns to him.
Although his chief obsession is Batman, the character has occasionally ventured outside Gotham City to fight Batman's superhero allies.
The story is notable for the Joker taking on a relative god and the ease with which Superman defeats him—it took only 17 pages.
Asked why he came to Metropolis, the Joker replies simply: "Oh Superman, why not? Since the Bronze Age of Comics, the Joker has been interpreted as an archetypal trickster , displaying talents for cunning intelligence, social engineering, pranks, theatricality, and idiomatic humor.
Like the trickster, the Joker alternates between malicious violence and clever, harmless whimsy. The trickster is simultaneously subhuman and superhuman, a being that indicates a lack of unity in body and mind.
Rather than the typical anarchist interpretation, others have analysed the character as a Marxist opposite to Batman's capitalist , arguing that anarchism requires the rejection of all authority in favor of uncontrolled freedom.
Ryan Litsey described the Joker as an example of a " Nietzschean Superman ," arguing that a fundamental aspect of Friedrich Nietzsche 's Superman , the "will to power," is exemplified in all of the Joker's actions, providing a master morality to Batman's slave morality.
The Joker's controlling and abusive relationship with Harley Quinn has been analyzed as a means of the Joker reinforcing his own belief in his power in a world where he may be killed or neutralized by another villain or Batman.
Harley's co-creator, Paul Dini, describes their relationship as Harley being someone who makes the Joker feel better about himself, and who can do the work that he does not want to do himself.
The Joker is considered one of the most-recognizable and iconic fictional characters in popular culture, [] [] [] one of the best comic villains, and one of the greatest villains of all time.
These debates weigh the positive stopping the Joker permanently against its effect on Batman's character and the possibility that he might begin killing all criminals.
The Joker's popularity and his role as Batman's enemy has involved the character in most Batman -related media, from television to video games.
The Joker has appeared in a variety of media, including television series, animated and live-action films. WorldCat a catalog of libraries in countries records over productions featuring the Joker as a subject, including films, books, and video games, [] and Batman films featuring the character are typically the most successful.
The role was a defining performance in Nicholson's career and was considered to overshadow Batman's, with film critic Roger Ebert saying that the audience must sometimes remind themselves not to root for the Joker.
Voiced by Mark Hamill , the Joker retained the darker tone of the comics in stories acceptable for young children. After Christopher Nolan 's successful Batman film reboot, Batman Begins , which ended with a teaser for the Joker 's involvement in a sequel, the character appeared in 's The Dark Knight , played by Heath Ledger as an avatar of anarchy and chaos.
The film received critical acclaim for Phoenix's performance, and criticism for its portrayal of mental illness and violence.
The Joker has also been featured in video games. Hamill returned to voice the character in 's critically acclaimed Batman: Arkham Asylum , its equally praised sequel Batman: Arkham City and the multiplayer DC Universe Online.
From Wikipedia, the free encyclopedia. Redirected from Joker comics. For other characters or uses of The Joker, see Joker.
Fictional character in the DC Universe. Injustice League Injustice Gang. Veidt's grinning visage inspired the Joker design.
That doesn't seem to matter—just how he is now. I never intended to give a reason for his appearance.
We discussed that and Bill [Finger] and I never wanted to change it at that time. I thought—and he agreed—that it takes away some of the essential mystery.
Main article: Alternative versions of Joker. See also: List of Batman Family enemies. Main article: Joker in other media.
Mark Hamill has voiced the Joker in animation and video games since , and Heath Ledger won a posthumous Academy Award for his interpretation of the character in 's The Dark Knight.
Joaquin Phoenix won an Academy Award for his interpretation of the character in 's Joker. MTV News. New York City: Viacom. Archived from the original on July 26, Retrieved August 9, July 11, Comic Book Resources.
Archived from the original on February 23, Retrieved February 23, Jerry Robinson, creator of the Joker".
The A. Archived from the original on October 14, Retrieved October 12, The Daily Telegraph. London: Telegraph Media Group. December 12, Archived from the original on November 4, Jerry Robinson December 15, Den of Geek.
Archived from the original on December 27, Retrieved December 26, Archived from the original on February 26, Retrieved October 18, Bleeding Cool.
July 15, Archived from the original on October 15, Retrieved February 20, Archived from the original on February 4, Retrieved August 28, The Ongoing Adventures of Rocket Llama.
July 21, August 5, Archived from the original on July 23, Retrieved August 1, Page 8 archived and Page 9 archived from the originals on August 17, The New York Times.
Archived from the original on November 13, Archived from the original on April 8, What Culture. Archived from the original on October 16, Los Angeles Times.
Los Angeles, California: Tronc. Archived from the original on October 23, Macmillan Publishing Co. Retrieved March 29, London: The Jerusalem Post Group.
November 9, Archived from the original on November 12, Retrieved November 20, The Jerusalem Post. Jerusalem: The Jerusalem Post Group.
Associated Press. Archived from the original on November 20, The Joker". February 26, Archived from the original on October 21, Comics Alliance.
Archived from the original on October 20, Retrieved October 19, Archived from the original on February 8, Retrieved January 25, July 16, Archived from the original on September 9, Archived from the original on April 21, Retrieved November 18, London, England: Dennis Publishing.
Abingdon, England: Routledge. August 9, Archived from the original on October 19, Los Angeles, California: j2 Global. Archived from the original on October 11, Archived from the original on April 22, Retrieved April 22, Sci Fi.
March 28, Archived from the original on April 11, Retrieved May 2, Even though their Batman run was only six issues, the three laid the foundation for later Batman comics.
Their stories include the classic 'Laughing Fish' in which the Joker's face appeared on fish ; they were adapted for Batman: The Animated Series in the s.
Daily News. New York. Archived from the original on June 21, Archived from the original on May 14, Archived from the original on August 14, Retrieved August 14, Archived from the original on December 30, Retrieved October 11, Archived from the original on January 7, Retrieved October 15, Pandora Archive.
Archived from the original on October 22, Batman arrived in the Batwing , took away the balloons, and released them into the night sky, which caused Joker to kill Bob to vent out his frustration.
Batman then made a strafing run on the Joker, but Joker shot down the Batwing with an explosive round that was fired from his long barreled gun.
Joker then took Vicki hostage and led her at gunpoint into the Gotham Cathedral where he forced her to dance the waltz with him. He also used his Acid Flower to disconnect one of the bells which fell to the ground and blocked the only entrance to the stairs so they wouldn't be followed, but Batman who was already following them, narrowly missed the falling bell and continued the pursuit.
Joker then ordered three of his henchmen to get rid of the Dark Knight should he succeed in following them.
Batman eventually reached the belfry and after he defeated Joker's henchmen, confronted Joker, and vowed to kill him for murdering his parents years ago, although Joker, who had apparently murdered several parents since he himself was a kid, did not know what Batman was talking about and eventually mocked him for how he made the revelation of Joker making Batman first.
During their confrontation, Batman repeatedly beat up Joker and managed to knock him off the balcony, but Joker reached up with both of his arms and pulled both Batman and Vicki down.
Batman and Vicki held on for dear life from a narrow ledge, while Joker insanely taunted them.
Joker's Helicopter then arrived to get Joker to safety. Batman fired a bolo launcher that then tied Joker's ankle to a large and heavy stone gargoyle.
The Joker sealed his fate when it broke loose. Unable to break free from the heavy burden of the gargoyle, Joker lost his grip on his helicopter's rope ladder, fell to his death, and hit the Cathedral's flight of steps below hard, which then broke every bone in his body.
Ironically, just a few seconds beforehand, Joker said: " Sometimes I just kill myself! Gordon then reached into Joker's coat and pulled out a laugh box that was activated by the landing.
Though the madness of the Joker was ended forever, the decline of the Gotham mob and the Joker's initial rise paved the way for the appearance of numerous villains with a similar theatricality to both Batman and Joker, such as The Penguin , Catwoman , The Riddler , Mr.
Freeze , Poison Ivy and Bane , while Harvey Dent himself would suffer a horrific incident that would transform him into the villainous Two-Face.
Bruce continued to have bad memories of Jack Napier killing his parents for the next several years. Jack Napier was seen as quite vain, with a penchant for nice suits and Alicia Hunt as his trophy girlfriend.
In contrast to Joker, Napier was quite humorless, though when he committed his crimes, he made large smiles on his face after he murdered the Waynes' or when he enjoyed killing Eckhardt.
However, Napier was still equally as psychotic, although not as outwardly, with hints of his psychopathic nature that oozed out when he watched Harvey Dent's speech about making Gotham safe for decent people, noted that "decent people" needed to move elsewhere and also stated he'd "hand [Dent's] lungs to him by now" should Dent even dare try to move in against Grissom, which showed that Napier had no qualms with killing any threats to the mob in an extremely graphic manner.
Napier was also not above murdering children, as he was clearly preparing to execute Bruce Wayne on a whim after he murdered his parents and would have gone through with it with zero remorse had Chill not told him to flee the scene.
Even prior to killing Grissom upon becoming the Joker as revenge for being set up, Napier mentioned that Grissom was a tired old man who "couldn't run the city without [Napier]", which indicated that he was treacherous against his boss and was content with waiting until the mob boss died before he could take over the mob.
Napier's treachery was also retained after he became the Joker, where told his friend, Bob, that he was his number one guy in a very similar manner to how Grissom himself told Jack that right before he sent him off to Axis Chemicals to die, which implied that he may have been planning a similar fate for Bob in the future.
While he discussed Grissom and Eckhardt's future within the mob, Eckhardt retorted to Napier that he was: " An A-1 nut boy ".
After he read Napier's Police File Report, Bruce summed up to the Joker his opinion of what he was before: " Mean kid, bad seed, hurt people He had a head full of bad wiring, I guess.
Couldn't keep it straight up here. He was the kind of guy who couldn't hear the train until it was two feet from him.
Then he had his lights out! Like many criminals before him, Napier was just as terrified of Batman when he first met him.
However, after he became the Joker, Napier had absolutely no fear of Batman, and, in fact, not only was he unphased by Batman vowing to kill him, but reminded Batman bluntly that he was the reason why Joker existed, and even when told that he himself had been responsible for Batman's existence, he didn't lose his composure and continued to mock him.
When he sought out surgery after he fell into the vat of chemicals, it was possible that Napier finally lost his remaining sanity upon seeing his new appearance, although he explained to Batman that he tried to get over it.
As a result, the Joker was born cackling madly. Joker also was shown to "talk" to Antoine Rotelli's corpse as if he were still alive and was even "told" by him to "grease" the remaining mobsters at the summit, although it was unclear whether he genuinely believed that he was being told that by Rotelli or was simply mocking the deceased mobster, as shortly afterwards, he laughed exhilarated over his own words about how he's "glad that [Rotelli's] dead.
Joker killed a mob boss with a quill, another with a supercharged Joy Buzzer, and was frequently seen using an Acid Flower.
Also, Joker had a tendency to wear gag chattering teeth so that he could shock the enemy if he was punched in the face long enough to attempt a retaliatory blow, as he attempted to do with Batman in their final encounter.
In addition to his trademark gadgets, the Joker also had a macabre sense of humor, which was both surreal and morbid.
The Joker was also quite sadistic, as seen when he shot Grissom and laughed, deliberately disfigured Alicia it's strongly implied also that he threw her to her death out of a window and found humor in killing Mob boss, Rotelli.
It's also implied that when he killed Grissom, that Joker actually seemed to enjoy death in itself, and not just the deaths of other people, and even went as far as referred to it as " therapy " from his experience.
That belief was contradicted near the end of the film, though, when Joker was seen screaming as he fell to his death.
However, that might have been because there was no way that he could have survived. Included were two mugshots, one of Napier from recent years, and one of him from the time period that he murdered the Waynes.
The following were known segments of the report. All underscores indicated sections of words or numbers that were currently unverifiable:.
Name: Jack Napier. Sex: Male. Age: Height: 5 ft. Bruce then summarized the remainder of the report. Results of psychological profile: Violent mood swings, highly intelligent, emotionally unstable.
Er war ein harmloser Ulk-Charakter. Dies erscheint https://c-m-s.co/online-casino-games-reviews/welche-geldanlagen-gibt-es.php logische Antwort der Autoren darauf, dass der Joker eine der Figuren im Bat-Universum ist, die über Joker Jack Jahrzehnte die meisten Veränderungen durchlaufen hat. Ehrung der Schauspielkollegen. Anmerkung: Filme und Serien here die Justice League und über die Teen Titansin welchen Batman vorkommt, werden in der Auflistung nicht berücksichtigt. Wozu braucht der noch Schminke? An Geld ist er nicht interessiert, vielmehr tötet und zerstört er aus reiner Freude und um Gotham City ins Chaos zu stürzen. Mehr wollen wir an dieser Stelle aus Spoiler-Gründen nicht verraten. Er plante die Machtübernahme seines Unterweltbosses und das ging gewaltig schief — Jack Napier fiel in ein Säurefass und kommt Beste Spielothek in finden Joker zurück. Batman Unlimited. Hannibal Lecter in diesem Prequel gemacht haben. Er trägt eine rote Maske, wodurch er für die Polizei von Gotham als Rädelsführer dasteht. Es war aber nicht nur seine Performance, die diese Inkarnation zu einem der besten Joker machte. Hier wird gezeigt, wie ein Mensch durch seine See more gebrochen Osterwaal finden Spielothek in Beste und durchdreht. Jack Nicholson als Joker – Der Wahnsinn hat einen Namen. Mit Jack Nicholson in der Rolle des Jokers für Tim Burtons ". Vor 30 Jahren brillierte Hollywood-Star Jack Nicholson (82) als fieser "Batman"-Bösewicht. Und verlieh dem "Joker" nach Cesar Romero einen. Jack Napier, Arthur Fleck oder etwa Melvin White? +. Filme Der Joker ist wohl einer der mysteriösesten Comic-Charaktere, die es gibt. Keiner. In Tim Burtons "Batman" von ist der Joker ein Kleinkrimineller namens Jack Napier (Jack Nicholson), der dasselbe Schicksal erleidet wie. Der Joker Jack. Der Joker Jack hat nur eine Bedeutung in Verbindung mit unseren Zusatzchancen Twins und Crazy-Twins. Roulette · Black Jack · So geht`s. Despite this body count, he is always found not guilty by reason of insanity and sent to Arkham Asylum, avoiding the death penalty. July 11, Even though their Batman run was only six issues, the three laid the foundation for later Batman comics. Batman then drove to Axis Chemicals to stop the manufacturing learn more here Joker's poisonous products once article source for read more. You ain't got no future, Jack! Joker Jack December 27, I'm giving away free money. Mark HamillTroy Bakerand others have provided the character's voice. Archived from the original on January 16, The Times. And it Joker Jack absolutely weird. Napier kills Eckhart and shoots at Batman, who deflects the bullet with one of his gauntlets, ricocheting it into Napier's face. The gargoyle eventually breaks free from its foundations, sending Joker falling to his death. Archived from the original on October 16, One of the most iconic characters in popular culture, Slots Tricks Scatter Joker has been listed among the greatest comic book villains and fictional opinion Hit The Top something ever created. And yes, it would be a crime to attempt to [step in or to] follow Jack Nicholson's footpath that he so heavily stands into my memory of The Joker.
Joker Jack - Die Ahnengalerie der "Joker"-Stars
Wenn Ihr nicht auf meiner Seite seid, seit ihr ein Feind ist wohl dein Motto? Aber tolle Joker-Darsteller gab es schon einige. Primär verdient er sein Geld als Clown. Dies lässt den Joker Mannschaften Frauen Wm 2020 einem Wahnsinnigen werden. Oktober in den deutschen Kinos. Hamill erlangte Kultstatus durch seine Rolle als Luke Skywalker. Sein Markenzeichen ist ein gackerndes Lachen. Wikis entdecken Community-Wiki Wiki erstellen. Publisher: DC Comics. Aber gestern hatten sie die definitiv. Aufgrund von Ledgers Tod wurden diese Pläne jedoch wieder verworfen und man setzte stattdessen Bane als Schurken im nächsten Film ein.
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