Effects of Quantum Pair Creation and Annihilation on a Classical Exclusion Process: the transverse XY model with TASEP

TL;DR

This paper explores how quantum particle pair creation and annihilation influence the steady states and spectral properties of a classical exclusion process, revealing phase-dependent effects linked to the quantum XY model's phase transition.

Contribution

It introduces a perturbative framework to analyze the non-equilibrium steady state and Liouvillian gap in a quantum-classical hybrid system, highlighting the impact of XY model anisotropy.

Findings

Liouvillian gap can remain finite in the thermodynamic limit with non-zero anisotropy

The gap's behavior varies with the XY model phase

Quantum phase transition affects the spectral properties of the system

Abstract

We investigate how particle pair creation and annihilation, within the quantum transverse XY model, affects the non-equilibrium steady state (NESS) and Liouvillian gap of the stochastic Totally Asymmetric Exclusion Process (TASEP). By utilising operator quantization we formulate a perturbative description of the NESS. Furthermore, we estimate the Liouvillian gap by exploiting a Majorana canonical basis as the basis of super-operators. In this manner we show that the Liouvillian gap can remain finite in the thermodynamic limit provided the XY model anisotropy parameter remains non-zero. Additionally, we show that the character of the gap with respect to the anisotropy parameter differs depending on the phase of the XY model. The change of character corresponds to the quantum phase transition of the XY model.