Universal Stochastic Equations of Monitored Quantum Dynamics
Abstract
We investigate the monitored quantum dynamics of Gaussian mixed states and derive the universal Fokker-Planck equations that govern the stochastic time evolution of entire density-matrix spectra, obtaining their exact solutions. From these equations, we reveal an even-odd effect in purification dynamics: whereas entropy exhibits exponential decay for an even number of complex fermions, algebraic decay with divergent purification time occurs for odd as a manifestation of dynamical criticality. Additionally, we identify the universal fluctuations of entropy in the chaotic regime, serving as a non-unitary counterpart of the universal conductance fluctuations in mesoscopic electronic transport phenomena. Furthermore, we elucidate and classify the universality classes of non-unitary quantum dynamics based on fundamental symmetry. We also validate the universality of these analytical results through extensive numerical simulations across different types of models.
Cite
@article{arxiv.2408.16974,
title = {Universal Stochastic Equations of Monitored Quantum Dynamics},
author = {Zhenyu Xiao and Tomi Ohtsuki and Kohei Kawabata},
journal= {arXiv preprint arXiv:2408.16974},
year = {2025}
}