高效变分极化子主方程用于非马尔可夫自旋-玻色子动力学：变换初始态与一般可观测量
An efficient variational polaron master equation for non-Markovian spin-boson dynamics: Transformed initial states and general observables
- National Taiwan University（台湾大学）
- National Center for Theoretical Sciences（国家理论科学研究中心）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本研究提出一种高效变分极化子主方程方法，通过变换初始态并引入非齐次项，准确描述非马尔可夫自旋-玻色子动力学，实现一般可观测量的统一处理，并揭示中等耦合下的延迟现象与相干叠加态的更强非平衡效应。
AI中文摘要：
我们使用一种高效的变分极化子主方程方法，研究了初始态对量子自旋-玻色子模型动力学的影响。将因子化的系统-环境初始态变换到变分极化子框架中，会在主方程中引入非齐次项，这对于在弱耦合区域之外准确描述非马尔可夫动力学至关重要。为了有效考虑这些效应，我们在扩展的辅助刘维尔空间中表述动力学，将所得的积分微分方程转化为耦合的常微分方程。我们进一步引入一种简化的变分极化子技术，用于计算一般可观测量的期望值的时间演化，包括那些不与极化子变换对易的可观测量，克服了先前方法的一个主要限制，并实现了相干性和布居动力学的统一处理。由任意因子化初始态生成的变换初始态的效应，通过期望值和迹距离分析被系统地刻画，从而在广泛的隧穿振幅、温度和耦合强度范围内提供了对相关浴弛豫动力学的洞察。与弱耦合主方程的比较揭示了与多浴量子过程相关的延迟现象，该现象在中等耦合强度和隧穿振幅下尤为显著。我们进一步表明，相干叠加初始态比局域态诱导更强的非平衡效应，其中非齐次项在短时动力学中起着关键作用。所提出的形式适用于无驱动和共振驱动的自旋-玻色子模型，为具有任意因子化初始态和一般物理可观测量的开放量子系统动力学提供了一个计算高效的框架。
英文摘要：
We investigate the effects of initial states on the dynamics of a quantum spin-boson model using an efficient variational polaron master equation approach. The transformation of a factorized system-environment initial state into the variational polaron frame introduces inhomogeneous terms in the master equation, essential for accurately describing non-Markovian dynamics beyond the weak coupling regime. To efficiently account for these effects, we formulate the dynamics in an extended auxiliary Liouville space, converting the resulting integro-differential equations into coupled ordinary differential equations. We further introduce a simplified variational polaron technique for computing the time evolution of expectation values of general observables, including those that do not commute with the polaron transformation, overcoming a major limitation of previous approaches and enabling the unified treatment of coherence and population dynamics. The effects of transformed initial states generated from arbitrary factorized initial states are systematically characterized through expectation values and trace-distance analysis, providing insight into the associated bath-relaxation dynamics over a broad range of tunneling amplitudes, temperatures, and coupling strengths. Comparison with the weak-coupling master equation reveals a delay phenomenon associated with multi-bath-quanta processes, pronounced at intermediate coupling strengths and tunneling amplitudes. We further show that coherent superposition initial states induce stronger nonequilibrium effects than localized states, with inhomogeneous terms playing a crucial role in the short-time dynamics. The proposed formalism applies to both undriven and resonantly driven spin-boson models, providing a computationally efficient framework for open quantum-system dynamics with arbitrary factorized initial states and general physical observables.
