Understanding thermalization in isolated quantum many-body systems is a fundamental challenge. A key question is how to diagnose whether a subsystem has reached equilibrium, especially when the equilibrium state is not known a priori. We propose that the subsystem evolution speed, defined as the time derivative of the trace distance between reduced density matrices at infinitesimally separated instants, serves as a powerful indicator of both relaxation and eigenstate thermalization. Unlike conventional measures, which require explicit knowledge of the thermal or generalized Gibbs ensemble state, our approach requires only the dynamics of the subsystem. This speed decays to zero as the subsystem thermalizes, whereas it remains finite for non-thermalizing cases. Furthermore, we extend the method to perturbed eigenstates to probe eigenstate thermalization without knowing the equilibrium reduced density matrix. The subsystem evolution speed shows distinct subsystem-size-dependent behaviors for thermalizing and non-thermalizing eigenstates. Our findings establish the subsystem evolution speed as a practical and universal diagnostic for quantum thermalization.

Biography

张甲举，天津大学理学院物理系与量子交叉研究中心副教授，2009年于山东师范大学完成本科学业，2014年在北京大学取得博士学位，随后分别在中国科学院高能物理研究所、意大利米兰比可卡大学与国际高等研究院（SISSA）从事博士后研究，2020年加入天津大学担任副教授。目前研究聚焦于引力全息性与多体量子纠缠。

Inviter: Jie-Qiang Wu