Initial value formulation of a quantum damped harmonic oscillator

• URL: http://arxiv.org/abs/2303.04829v2
• Date: Mon, 6 May 2024 18:44:08 GMT
• Title: Initial value formulation of a quantum damped harmonic oscillator
• Authors: Nishant Agarwal, Yi-Zen Chu,
• Abstract summary: We study the initial state-dependence, decoherence, and thermalization of a quantum damped harmonic oscillator. We find that the dynamics must include a non-vanishing noise term to yield physical results for the purity. We briefly consider time-nonlocal dissipation as well, to show that the fluctuation-dissipation relation is satisfied for a specific choice of dissipation kernels.
• Score: 0.18416014644193066
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The in-in formalism and its influence functional generalization are widely used to describe the out-of-equilibrium dynamics of unitary and open quantum systems, respectively. In this paper, we build on these techniques to develop an effective theory of a quantum damped harmonic oscillator and use it to study initial state-dependence, decoherence, and thermalization. We first consider a Gaussian initial state and quadratic influence functional and obtain general equations for the Green's functions of the oscillator. We solve the equations in the specific case of time-local dissipation and use the resulting Green's functions to obtain the purity and unequal-time two-point correlations of the oscillator. We find that the dynamics must include a non-vanishing noise term to yield physical results for the purity and that the oscillator decoheres in time such that the late-time density operator is thermal. We show that the frequency spectrum or unequal-time correlations can, however, distinguish between the damped oscillator and an isolated oscillator in thermal equilibrium, and obtain a generalized fluctuation-dissipation relation for the damped oscillator. We briefly consider time-nonlocal dissipation as well, to show that the fluctuation-dissipation relation is satisfied for a specific choice of dissipation kernels. Lastly, we develop a double in-out path integral approach to go beyond Gaussian initial states and show that our equal-time results for time-local dissipation are in fact non-perturbative in the initial state.

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