Entropy Linear Response Theory with Non-Markovian Bath

Abstract

We developed a perturbative calculation for entropy dynamics considering a sudden coupling between a system and a bath. The theory we developed can work in general environment without Markovian approximation. A perturbative formula is given for bosonic environment and fermionic environment, respectively. We find the Renyi entropy response is only related to the spectral functions of the system and the environment, together with a specific statistical kernel distribution function. We find a t^2 growth/decay in the short time limit and a t linear growth/decay in longer time scale for second Renyi entropy. A non-monotonic behavior of Renyi entropy for fermionic systems is found to be quite general when the environment's temperature is lower. A Fourier's law in heat transport is obtained when two systems' temperature are close to each other. A consistency check is made for Sachdev-Ye-Kitaev model coupling to free fermions, a Page curve alike dynamics is found in a process dual to black hole evaporation. An oscillation of entanglement entropy is found for a gapped spectrum of environment.

17 pages, 6 figures

References in corpus (9)

• Spread of entanglement in a Sachdev-Ye-Kitaev chain
• Replica wormhole and information retrieval in the SYK model coupled to Majorana chains
• Evaporation dynamics of the Sachdev-Ye-Kitaev model
• Subsystem Rényi Entropy of Thermal Ensembles for SYK-like models
• Entanglement Entropy of Two Coupled SYK Models and Eternal Traversable Wormhole
• The Coupled SYK model at Finite Temperature
• Entanglement Entropy and its Quench Dynamics for Pure States of the Sachdev-Ye-Kitaev model
• Renyi entanglement entropy of Fermi liquids and non-Fermi liquids: Sachdev-Ye-Kitaev model and dynamical mean field theories
• Perturbative calculations of entanglement entropy

Cited by in corpus (4)

• Lindbladian dissipation of strongly-correlated quantum matter
• Renyi Entropy Dynamics and Lindblad Spectrum for Open Quantum System
• Entanglement Transition and Replica Wormhole in the Dissipative Sachdev-Ye-Kitaev Model
• Dissipation- versus Chaos-Induced Relaxation in Non-Markovian Quantum Many-Body Systems