Perturbative Page Curve Induced by External Impulse

• URL: http://arxiv.org/abs/2305.18329v1
• Date: Wed, 24 May 2023 07:08:12 GMT
• Title: Perturbative Page Curve Induced by External Impulse
• Authors: Pengfei Zhang
• Abstract summary: We extend the recent study of entropy dynamics induced by an external impulse in open quantum systems. For small system-bath coupling $kappa$, we expect that the entropy first increases exponentially $kappa2 evarkappa t$ in the early-time regime. In the second stage, the entropy of the system is equal to the coarse-grained entropy.
• Score: 5.623221917573403
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: In this work, we extend the recent study of entropy dynamics induced by an external impulse in open quantum systems, where the entropy response follows the Page curve. For small system-bath coupling $\kappa$, we expect that the entropy first increases exponentially $\kappa^2 e^{\varkappa t}$ in the early-time regime $t\lesssim |\log \kappa|$ due to quantum many-body chaos, and then decreases as $~e^{-\lambda_0 t}$ with $\lambda_0 \propto \kappa^2$ due to the energy relaxation. These results are confirmed through explicit calculations using two methods: 1) generalized Boltzmann equation for systems with quasi-particles; 2) scramblon effective theory in the early-time regime and perturbation theory in the late-time regime for 0+1-d systems. We also prove that in the second stage, the entropy of the system is equal to the coarse-grained entropy.

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