Open quantum dynamics theory on the basis of periodical system-bath model for discrete Wigner function
Open quantum dynamics theory on the basis of periodical system-bath model for discrete Wigner function
复制标题
DOI：
10.1007/s10825-021-01754-z
复制
发表时间：
2021-07
影响因子：
2.1
通讯作者：
Yuki Iwamoto;Y. Tanimura
中科院分区：
文献类型：
--
作者：
Yuki Iwamoto;Y. Tanimura
离散相空间中的分布函数以进行有效的量子动力学模拟是一个不小的挑战，特别是对于系统进一步耦合到环境自由度的情况。这种开放量子动力学通过简化运动方程 (REOM) 来描述，尤其是维格纳分布函数 (WDF) 的量子福克-普朗克方程 (QFPE)。为了开发一种对于 REOM 方法的数值模拟稳定的离散化方案，我们采用具有两个热浴的二维 (2D) 周期性不变系统浴 (PISB) 模型。该模型不仅对于周期系统而且对于受势限制的非周期系统都是一个理想的平台。然后，我们根据坐标和动量空间中的周期不变算子推导出离散 WDF 的数值“精确”分层运动方程 (HEOM)。所获得的方程可以在有限温度下以非微扰方式处理非马尔可夫热浴，而与网格尺寸无关。作为演示，我们使用具有涉及奇异性的初始条件的粗网格，对高温马尔可夫情况下的二维自由转子和谐波势系统的离散 QFPE 进行数值积分。
Discretizing a distribution function in a phase space for an efficient quantum dynamics simulation is a non-trivial challenge, in particular for a case in which a system is further coupled to environmental degrees of freedom. Such open quantum dynamics is described by a reduced equation of motion (REOM), most notably by a quantum Fokker–Planck equation (QFPE) for a Wigner distribution function (WDF). To develop a discretization scheme that is stable for numerical simulations from the REOM approach, we employ a two-dimensional (2D) periodically invariant system-bath (PISB) model with two heat baths. This model is an ideal platform not only for a periodic system but also for a non-periodic system confined by a potential. We then derive the numerically “exact” hierarchical equations of motion (HEOM) for a discrete WDF in terms of periodically invariant operators in both coordinate and momentum spaces. The obtained equations can treat non-Markovian heat-bath in a non-perturbative manner at finite temperatures regardless of the mesh size. As demonstrations, we numerically integrate the discrete QFPE for a 2D free rotor and harmonic potential systems in a high-temperature Markovian case using a coarse mesh with initial conditions that involve singularity.