AI 中文总结
本文采用玻姆语言研究Caldeira-Leggett模型高温下开放量子系统动力学，推导得含热效应的方程，引入标度化Caldeira-Leggett方程，发现其经典极限下轨迹仍具确定性，高斯态应用显示相干性随参数与热效应逐渐被抑制。
AI 中文摘要
本文采用玻姆（Bohmian）语言研究了Caldeira-Leggett模型高温区域下开放量子系统的动力学。通过将密度矩阵表示为极式，得到了广义连续性方程和哈密顿-雅可比方程；热效应明确出现在前者中，而仅通过有效势间接影响后者。值得注意的是，有效势在经典极限下并不消失，且通常无法分解为简单可加的量子与热贡献，反而保留着非平凡结构，导致所得动力学中存在残余温度依赖性。因此，这种依赖温度的经典轨迹即使在热环境存在时仍保持确定性，该行为与朗之万（Langevin）描述中观测到的随机动力学形成对比，反映了本方法基于系综的特性。为进一步探究量子到经典的过渡，通过量子性参数对密度矩阵和普朗克常数同时进行标度，引入了标度化的Caldeira-Leggett方程；该参数在全量子区域取值为1，在经典极限下平滑趋近于0。对高斯态的应用表明，相干性与干涉会被热效应和过渡参数共同调控，呈现逐渐抑制的趋势。
英文摘要
The dynamics of an open quantum system in the high-temperature regime of the Caldeira-Leggett model using a Bohmian language is investigated. By expressing the density matrix in polar form, generalized continuity and Hamilton-Jacobi equations are obtained. Thermal effects appear explicitly in the former, while they influence the latter only indirectly through an effective potential. Remarkably, the effective potential does not vanish in the classical limit and cannot, in general, be decomposed into simple additive quantum and thermal contributions. Instead, it retains a nontrivial structure leading to a residual temperature dependence in the resulting dynamics. As a consequence, the resulting temperature-dependent-classical trajectories remain deterministic even in the presence of a thermal environment. This behavior contrasts with the stochastic dynamics observed in the Langevin description and reflects the ensemble-based nature of the present approach. To further explore the quantum-to-classical transition, a scaled version of the Caldeira-Leggett equation is introduced by scaling both the density matrix and Planck constant through a quantumness parameter. This parameter takes the value one in the fully quantum regime and smoothly approaches zero in the classical limit. Applications to Gaussian states demonstrate a gradual suppression of coherence and interference, governed jointly by thermal effects and the transition parameter.
CommentsAccepted for Publication in Phys. Scr
