Open quantum dynamics theory for a complex subenvironment system with a quantum thermostat: Application to a spin heat bath

TL;DR

This paper develops a quantum dynamics model for complex environments using a quantum thermostat to simulate a subenvironment's effects on a two-level system, revealing how phase transitions influence decoherence and relaxation.

Contribution

It introduces a hierarchical Schrödinger equations approach to model a quantum thermostat coupled with a subenvironment, enabling detailed study of decoherence in complex quantum systems.

Findings

Decoherence occurs at finite temperature regardless of large anisotropy.

Relaxation dynamics vary with spin anisotropy and magnetic order.

Quantum phase transitions significantly affect system dynamics.

Abstract

Complex environments, such as molecular matrices and biological material, play a fundamental role in many important dynamic processes in condensed phases. Because it is extremely difficult to conduct full quantum dynamics simulations on such environments due to their many degrees of freedom, here we treat in detail the environment only around the main system of interest (the subenvironment), while the other degrees of freedom needed to maintain the equilibrium temperature are described by a simple harmonic bath, which we call a quantum thermostat. The noise generated by the subenvironment is spatially non-local and non-Gaussian and cannot be characterized by the fluctuation-dissipation theorem. We describe this model by simulating the dynamics of a two-level system (TLS) that interacts with a subenvironment consisting of a one-dimensional $XXZ$ spin chain. The hierarchical Schr\"odinger equations of motion are employed to describe the quantum thermostat, allowing time-irreversible simulations of the dynamics at arbitrary temperature. To see the effects of a quantum phase transition of the subenvironment, we investigate the decoherence and relaxation processes of the TLS at zero and finite temperatures for various values of the spin anisotropy. We observed the decoherence of the TLS at finite temperature, even when the anisotropy of the $XXZ$ model is enormous. We also found that the population relaxation dynamics of the TLS changed in a complex manner with the change of the anisotropy and the ferromagnetic or antiferromagnetic orders of the spins.