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arXiv:2502.17891 · Communications in Theoretical Physics

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

Faisal Farooq, Irfan Ahmad Dar, Muzaffar Qadir Lone

Published Feb 24, 2025• 2 citations
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Abstract

Abstract We analyze the steady-state characteristics of a damped harmonic oscillator (system) in the 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 function 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.

DOI
10.1088/1572-9494/adb948

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The heat-bath frequency distribution, necessary to maintain the canonical commutation relations for all time for a quantum mechanical oscillator with non-Markovian features like memory-dependent damping, is shown to satisfy certain constraint relations. An algorithm is given to explicitly find the heat-bath frequency distribution in terms of a series expansion for all processes where the timescale for the non-Markovian memory kernel is much smaller than the inverse of the strength of damping term. In the non-Markovian case, the heat-bath distribution function exhibits dependence on the system characteristics. The KS periodicity conditions on the system Green functions as the system approaches equilibrium are established for the present case.
The aim of the present study is to investigate the effect of the counter-rotating terms on the quantum dynamics of a harmonic oscillator in the presence of a deformed bath. We first obtain the Langevin equation of motion for damped oscillator with and without the rotating-wave approximation (RWA). Then, we study the effect of the counter-rotating terms on the diffusion coefficients. Then, we obtain the equation of motion for the harmonic oscillator correlation function with and without the RWA. Finally, we investigate the influence of the counter-rotating terms on the oscillator correlation function.
We investigate the quantum Zeno and anti-Zeno effects in quantum dissipative systems by employing a hierarchical equations of motion approach which is beyond the usual Markovian approximation, the rotating wave approximation, and the perturbative approximation. The quantum Zeno and anti-Zeno dynamics of a biased qubit-boson model and a biased qutrit-boson model are provided as illustrative examples. It is found that (i) there exists multiple Zeno--anti-Zeno crossover phenomena, (ii) the non-Markovian characteristic of the bath may be favorable for the accessibility of the Zeno dynamics, and (iii) high bath temperature may add the difficulty in observing the quantum Zeno effect in quantum dissipative systems.
The purpose of this paper is to investigate the occurrence of the Zeno and anti-Zeno effects for the quantum Brownian motion of a harmonic oscillator. We show a controlled decay suppression and decay acceleration for a dissipative quantum harmonic oscillator. We demonstrate that the system–bath coupling parameter as well as the confining potential can critically control the Zeno and anti-Zeno dynamics. In this context, we discuss several heat bath models such as ohmic, Drude, and the black body radiation model.
Abstract In the field of quantum information theory, the intersection of the complex dynamics related to non-Markovianity and information is a crucial frontier. Non-Markovian effects, which take memory and temporal correlations into account, challenge conventional wisdom in the fields of quantum biology, metrology, cryptography, and communication. In this work, we analyze the non-Markovian dynamics of a dephasing model in presence of initial system-bath (SB) correlations. These SB correlations are generated via projective measurements on a predefined equilibrium state. Using the non-Markovian measures based on trace distance and quantum Fisher information, it is shown that these correlations have significant impact in the non-Markovian regime at high temperatures while it does not play any role in the Markovian case. Furthermore, it is shown that the oscillatory behaviour of the decoherence function does not always show non-Markovian behaviour.