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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Time-dependent variational Monte Carlo ： ウィキペディア英語版 Time-dependent variational Monte Carlo The time-dependent variational Monte Carlo (t-VMC) method is a quantum Monte Carlo approach to study the dynamics of closed, non-relativistic quantum systems in the context of the quantum many-body problem. It is an extension of the variational Monte Carlo method, in which a time-dependent pure quantum state is encoded by some variational wave function, generally parametrized as : $\backslash Psi(X,t)\; =\; \backslash exp\; \backslash left\; (\; \backslash sum\_k\; a\_k(t)\; O\_k(X)\; \backslash right\; )$ where the complex-valued $a\_k(t)$ are time-dependent variational parameters, $X$ denotes a many-body configuration and $O\_k(X)$ are time-independent operators that define the specific ansatz. The time evolution of the parameters $a\_k(t)$ can be found upon imposing a variational principle to the wave function. In particular one can show that the optimal parameters for the evolution satisfy at each time the equation of motion : $i\; \backslash sum\_\}\backslash rangle\_t^c\; \backslash dot\_\backslash rangle\_t^c,$ where $\backslash mathcal$ is the Hamiltonian of the system, $\backslash langle\; AB\; \backslash rangle\_t^c=\backslash langle\; AB\backslash rangle\_t-\backslash langle\; A\backslash rangle\_t\backslash langle\; B\backslash rangle\_t$ are connected averages, and the quantum expectation values are taken over the time-dependent variational wave function, i.e., $\backslash langle\backslash cdots\backslash rangle\_t\; \backslash equiv\backslash langle\backslash Psi(t)|\backslash cdots|\backslash Psi(t)\backslash rangle$. In analogy with the Variational Monte Carlo approach and following the Monte Carlo method for evaluating integrals, we can interpret $\backslash frac$ as a probability distribution function over the multi-dimensional space spanned by the many-body configurations $X$. The Metropolis–Hastings algorithm is then used to sample exactly from this probability distribution and, at each time $t$, the quantities entering the equation of motion are evaluated as statistical averages over the sampled configurations. The trajectories $a(t)$ of the variational parameters are then found upon numerical integration of the associated differential equation. == References == * * * 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Time-dependent variational Monte Carlo」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.