Non-Markovian effects on the steady state properties of a damped harmonic oscillator

TL;DR

This paper investigates how non-Markovian environments influence the steady-state behavior of a damped harmonic oscillator, revealing tunable effects on quantum Zeno phenomena through spectral and dissipation parameters.

Contribution

It provides a detailed analysis of non-Markovian effects on steady states using Green's functions, extending understanding beyond Markovian assumptions.

Findings

Non-Markovian baths alter steady-state properties significantly.

Transition between Zeno and anti-Zeno effects can be controlled.

Effective temperature and distribution functions are affected by bath characteristics.

Abstract

We analyze the steady-state characteristics of a damped harmonic oscillator (system) in presence of a non-Markovian bath characterized by Lorentzian spectral density. Although Markovian baths presume memoryless dynamics, the introduction of complex temporal connections by a non-Markovian environment radically modifies the dynamics of the system and its steady-state behaviour. We obtain the steady-state Green's functions and correlation functions of the system using the Schwinger-Keldysh formalism. In both rotating and non-rotating wave approximation, we analyzed various emergent properties like effective temperature and distribution function. We also explore the impact of dissipation and non-Markovian bath on the quantum Zeno and anti-Zeno effects. We show that a transition between Zeno to anti-Zeno effect can be tuned by bath spectral width and the strength of dissipation.