弛豫时间近似的Lindbladian方法：应用于环境温度淬灭引发的Kibble-Zurek过程及Lindbladian微扰理论
Lindbladian way for the relaxation time approximation, application to Kibble-Zurek processes due to environment temperature quench, and to Lindbladian perturbation theory
AI总结：
本文构建了可实现热化的全局Lindbladian形式的弛豫时间近似（RTA），验证了其可与其他Lindbladian结合，应用于温度慢变的Kibble-Zurek过程和守恒量期望值的一阶微扰计算。
AI中文摘要：
本文构建了一种全局Lindbladian假设形式，该形式可使温度为$T$的系统热化至所研究系统的Gibbs态。该假设形式连接哈密顿量的每两个本征态，并推导出一个简单的主方程，即文献中所称的弛豫时间近似（relaxation time approximation, RTA）。本文的核心观点是，RTA本身作为一种Lindbladian方法，在对物理过程建模时可作为确保热化的Lindbladian项使用，并且可与其他会驱动系统偏离平衡态的Lindbladian项结合。本文通过两个应用对该观点进行了验证。第一个应用是通过将环境温度变化至临界点来实现量子系统的缓慢冷却（或加热）。借助这种RTA-Lindblad假设形式，可直接关联系统的平衡行为；若序参量具有指数$Ψ$，则相变处的剩余序参量值将随$1/τ^Ψ$下降，其中$τ$是该缓慢过程的总时长。在第二个应用中，研究了守恒量（与哈密顿量对易的算符）的期望值变化：系统同时存在热化用的RTA-Lindbladian项，以及一个会驱动系统偏离平衡的额外Lindbladian项。本文仅利用原始热平衡中计算得到的期望值，给出了新稳态下该期望值的一阶闭合微扰表达式。
英文摘要：
In the present paper, a global Lindbladian ansatz is constructed which leads to thermalization at temperature $T$ to the Gibs state of the investigated system. This ansatz connects every two eigenstates of the Hamiltonian and leads to a simple master equation known in the literature as the relaxation time approximation (RTA). The main message of this paper is that RTA, being a Lindbladian approach itself, can be used as Lindbladian securing thermalization when modeling physical processes, and can be consequently combined with other types of Lindbladians which would drive the system of the equilibrium state. I demonstrate it with two applications. The first application is the slow cooling (or heating) of quantum systems by varying the environment temperature to a critical point. With this RTA-Lindblad ansatz, one can directly relate to the equilibrium behavior of the system, and if an order parameter has the exponent $Ψ$, the remaining value at the phase transition will decrease with $1/τ^Ψ$, where $τ$ is the overall time of the slow process. In the second application, I investigate the change in the expectation value of a conserved quantity (an operator commuting with the Hamiltonian) due to an extra Lindbladian term which would drive the system out from equilibrium, while the thermalizing RTA-Lindbladian term is also present. I give a closed perturbative expression in the first order for the expectation value in the new steady state using only expectation values calculated in the original thermal equilibrium.
