标题： 基于本征态热化假设流的动态预测 显示英文标题

标题： Predicting Dynamics from Flows of the Eigenstate Thermalization Hypothesis

摘要： 远离平衡的量子动力学的解析处理很少，即使是在良好热化的系统中。 著名的本征态热化假设（ETH）为热化哈密顿量本征基中可观测量的矩阵元提供了一个事后假设，给定这些可观测量的各种响应函数作为输入。 然而，ETH无法预测这些响应函数。 我们引入了一种称为统计雅可比近似（SJA）的方法，在哈密顿量受到摄动后更新ETH假设，并预测受扰的响应函数。 雅可比算法通过一系列两级旋转对摄动进行对角化。 SJA在整个对角化过程中假设ETH，并为ETH假设中的各种形式因子生成积分微分流动方程。 我们近似求解了某些类别的可观测量的这些流动方程，并预测了受扰哈密顿量热态下的猝发动力学和自相关子。 预测的动力学与随机矩阵模型和一维自旋链中的精确数值结果相比表现良好。 显示英文摘要

摘要： Analytical treatments of far-from-equilibrium quantum dynamics are few, even in well-thermalizing systems. The celebrated eigenstate thermalization hypothesis (ETH) provides a post hoc ansatz for the matrix elements of observables in the eigenbasis of a thermalizing Hamiltonian, given various response functions of those observables as input. However, the ETH cannot predict these response functions. We introduce a procedure, dubbed the statistical Jacobi approximation (SJA), to update the ETH ansatz after a perturbation to the Hamiltonian and predict perturbed response functions. The Jacobi algorithm diagonalizes the perturbation through a sequence of two-level rotations. The SJA implements these rotations statistically assuming the ETH throughout the diagonalization procedure, and generates integrodifferential flow equations for various form factors in the ETH ansatz. We approximately solve these flow equations for certain classes of observables, and predict both quench dynamics and autocorrelators in the thermal state of the perturbed Hamiltonian. The predicted dynamics compare well to exact numerics in both random matrix models and one-dimensional spin chains.