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首页> 外文期刊>The journal of physical chemistry, A. Molecules, spectroscopy, kinetics, environment, & general theory >Coherent State-Based Path Integral Methodology for Computing the Wigner Phase Space Distribution
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Coherent State-Based Path Integral Methodology for Computing the Wigner Phase Space Distribution

机译：计算Wigner相空间分布的相干状态路径积分方法

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摘要

The accurate evaluation of the Wigner phase space density for multidimensional system remains a challenging task. Path integral Monte Carlo methods offer a numerically exact approach for obtaining the Boltzmann density in coordinate space, but the Fourier-type integral required to construct the Wigner distribution generally leads to poor convergence. This paper describes a path integral method for constructing the Wigner density which substantially mitigates the Monte Carlo sign problem and thus is applicable to systems with many degrees of freedom. The starting point is the path integral representation of the coherent state density, which does not involve a Fourier integral and thus converges rapidly. We then use the relation between the coherent state and Wigner densities to construct the Wigner function, taking advantage of destructive phase cancellation to truncate the infinite series and thus confine the integrand, avoiding highly oscillatory regions. We also describe the use of information-guided noise reduction (IGNoR) to improve the Monte Carlo statistics in the most challenging regimes. The method is applied to strongly anharmonic one-dimensional models, a system-bath Hamiltonian, as well as the formamide molecule within an ab initio quartic potential, and the results are compared to those obtained by various approximate methods. These calculations suggest that the coherent state-based path integral method described in this paper offers an efficient, numerically exact approach for constructing the Wigner phase space density in systems of many degrees of freedom, and thus will be useful for quantizing the initial condition in classical trajectory-based simulations of dynamical properties.
机译：用于多维系统的Wigner相空间密度的准确评估仍然是一个具有挑战性的任务。路径整体蒙特卡罗方法提供了一种用于获得坐标空间中的Boltzmann密度的数值精确的方法，但构造Wigner分布所需的傅里叶型积分通常导致收敛不良。本文介绍了一种用于构建基本上减轻蒙特卡罗标志问题的Wigner密度的路径积分方法，因此适用于具有多种自由度的系统。起始点是相干状态密度的路径积分表示，其不涉及傅里叶积分，从而迅速收敛。然后，我们使用相干状态和Wigner密度之间的关系来构建Wigner功能，利用破坏性相位取消来截断无限系列，从而限制积分，避免高度振荡区域。我们还描述了使用信息引导降噪（Ignor）来改善最具挑战性制度的蒙特卡罗统计数据。该方法适用于强谐波一维模型，一个系统浴Hamiltonian，以及AB初始潜力内的甲酰胺分子，并将结果与​​各种近似方法获得的结果进行比较。这些计算表明，相干基于状态的路径积分方法在本文中提供描述了用于在许多自由度，并因此系统构成的Wigner相空间密度的高效，数值精确的方法将是有用的用于经典量化初始条件基于轨迹的动态特性模拟。

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