Impact of the temperature and size of an Ising chain environment on quantum non-Markovian dynamics

Abstract

We study how the non-Markovian dynamics of an open quantum system is affected by the properties and parameters of its environment using a solvable model consisting of a single spin coupled to an Ising chain of spins with a transverse field playing the role of the environment. By solving the model's evolution exactly, we are able to calculate the memory kernel for the Nakajima-Zwanzig master equation and examine how its characteristics change with the temperature, field strength, and size of the environment. We discover that the thermal fluctuation enhances system-environment correlation in our model, leading to increased memory effect that is more prominent in larger environment and becomes dominant at higher temperatures to give rise to non-Markovian dynamics. Near the critical point of the environment, we find Fisher zeros in the Loschmidt echo exist for finite-environment sizes satisfying certain conditions, which results in exotic memory effects that can have a major impact on the system dynamics.