Musculoskeletal and Integumentary Systems

Bentov, Itay; Reed, May J.

doi:10.1007/978-3-319-66878-9_14

Cited by 1 publication

(1 citation statement)

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“…In this section, we obtain the generating functional of a quantum harmonic oscillator that is initialized in a Gaussian initial state and undergoes non-unitary/dissipative evolution described by a quadratic dissipative action; also see [23] for a recent review. We denote the initial state of the oscillator at time t 0 by the density operator ρ(t 0 ) and first ignore dissipation, so that the oscillator evolves unitarily with the Hamiltonian Ĥ = 1 2m P 2 + 1 2 mω 2 X2 , m being the mass of the oscillator, ω its frequency [32], X the position operator, and P the momentum operator.…”

Section: In-in Generating Functionalmentioning

confidence: 99%

Initial value formulation of a quantum damped harmonic oscillator

Agarwal¹,

Chu²

2023

Preprint

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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. In particular, we find that the dynamics must include a non-vanishing noise term to yield physical results. We show that the oscillator decoheres in time such that the late-time density operator is thermal, and find the parameter regime for which the fluctuation-dissipation relation is satisfied. We next develop a double in-out path integral approach to go beyond Gaussian initial states and show that our equal-time results are in fact non-perturbative in the initial state.

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Section: In-in Generating Functionalmentioning

confidence: 99%