Universal Stochastic Equations of Monitored Quantum Dynamics

• URL: http://arxiv.org/abs/2408.16974v1
• Date: Fri, 30 Aug 2024 02:24:54 GMT
• Title: Universal Stochastic Equations of Monitored Quantum Dynamics
• Authors: Zhenyu Xiao, Tomi Ohtsuki, Kohei Kawabata,
• Abstract summary: We derive the universal Fokker-Planck equations that govern the Gaussian time evolution of entire density-matrix spectra. 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.
• Score: 4.794899293121226
• License: http://creativecommons.org/licenses/by/4.0/
• 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 $N$ of complex fermions, algebraic decay with divergent purification time occurs for odd $N$ 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.

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