非平衡量子系统的弛豫动力学
On the relaxation dynamics of non-equilibrium quantum systems
- Technical University of Munich（慕尼黑工业大学）
- Max Planck Institute for Physics (Werner Heisenberg Institute)（马克斯·普朗克物理研究所）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文研究非平衡量子系统中近似守恒荷的弛豫，提出基于Zubarev方法及局部平衡构造的弛豫率计算方法，并建立与扩散及玻尔兹曼方程的联系。
AI中文摘要：
我们研究了接近局部平衡的相互作用量子系统中近似守恒荷的弛豫。为此，我们在单一非守恒荷的最小设置下，对Zubarev非平衡统计算符方法进行了教学性回顾，并将其应用于所研究的问题。我们明确强调了导致局部弛豫定律的物理假设：弱荷破坏、微观关联的短时间尺度与荷弛豫的更长的时间尺度之间的分离，以及由此产生的微观记忆丧失。在这些条件下，主导弛豫率由荷破坏算符的平衡关联函数决定。我们表明，相同的结果可以从基于系统在中间时间尺度上演化的更简单的局部平衡构造中得出，为实际计算提供了直接替代方案，并使两种方法的共同物理要素明确化。在衰变定律本身之外，我们将弛豫率与同一荷的平衡扩散联系起来。然后我们允许荷密度在空间中变化，这导致扩散-弛豫方程。最后，我们通过电弱B+L洗脱和微扰标量模型来说明该形式体系，其中与线性化玻尔兹曼方程的一致性建立了平衡关联函数描述与动力学描述之间的直接联系。
英文摘要：
We investigate the relaxation of an approximately conserved charge in interacting quantum systems close to local equilibrium. To this end, we provide a pedagogical review of Zubarev's non-equilibrium statistical operator approach in the minimal setting of a single non-conserved charge and apply it to the problem at hand. We explicitly highlight the physical assumptions that lead to a local relaxation law: weak charge violation, a separation between the short timescale of microscopic correlations and the much longer timescale of charge relaxation, and the resulting loss of microscopic memory. Under these conditions, the leading relaxation rate is determined by an equilibrium correlation function of the charge-violating operator. We show that the same result follows from a simpler local-equilibrium construction based on the system's evolution over an intermediate timescale, providing a direct alternative for practical calculations and making the common physical ingredients of the two approaches explicit. Beyond the decay law itself, we relate the relaxation rate to the equilibrium diffusion of the same charge. We then allow the charge density to vary in space, which leads to a diffusion-relaxation equation. Finally, we illustrate the formalism through electroweak $\mathrm{B+L}$ washout and a perturbative scalar model, where agreement with the linearized Boltzmann equation establishes a direct connection between equilibrium-correlator and kinetic descriptions.
