量子多体动力学的非平凡阻尼
Nontrivial damping of quantum many-body dynamics
摘要：
理解一个给定的具有多个自由度的量子系统的动力学是如何被一般微扰的存在所改变的是一个众所周知的困难问题。最近的工作预测，在绝大多数情况下，未扰动动力学只是由一个简单的函数阻尼，例如，正如费米黄金法则所预期的那样。虽然这些预测依赖于随机矩阵参数和典型性，但它们只能通过与实际解决方案或测量进行比较来验证特定的物理情况。至关重要的是，目前还不清楚典型行为的反例发生的频率和条件。在这项工作中，我们讨论了这个问题的投影算子技术的角度来看，指数衰减的密度矩阵发生在相互作用的图片，但不一定在薛定谔图片。我们表明，一个非平凡的阻尼薛定谔图片可以出现，如果在未扰动系统的动力学具有丰富的功能，例如由于存在强相互作用。这个建议对关联函数的时间依赖性有影响。我们证实了我们的理论论点，通过大规模的数值模拟扩展费米-哈伯德链中的电荷输运，其中最近邻相互作用被视为扰动的可积参考系。
英文摘要：
Understanding how the dynamics of a given quantum system with many degrees of freedom is altered by the presence of a generic perturbation is a notoriously difficult question. Recent works predict that, in the overwhelming majority of cases, the unperturbed dynamics is just damped by a simple function, e.g., exponentially as expected from Fermi's golden rule. While these predictions rely on random-matrix arguments and typicality, they can only be verified for a specific physical situation by comparing to the actual solution or measurement. Crucially, it also remains unclear how frequent and under which conditions counterexamples to the typical behavior occur. In this work, we discuss this question from the perspective of projection-operator techniques, where exponential damping of a density matrix occurs in the interaction picture but not necessarily in the Schrödinger picture. We show that a nontrivial damping in the Schrödinger picture can emerge if the dynamics in the unperturbed system possesses rich features, for instance due to the presence of strong interactions. This suggestion has consequences for the time dependence of correlation functions. We substantiate our theoretical arguments by large-scale numerical simulations of charge transport in the extended Fermi-Hubbard chain, where the nearest-neighbor interactions are treated as a perturbation to the integrable reference system.
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