Fluctuation–dissipation relation for a quantum Brownian oscillator in a parametrically squeezed thermal field

Journal Article · Fri Oct 15 04:00:00 EDT 2021 · Annals of Physics

DOI:https://doi.org/10.1016/J.AOP.2021.168594· OSTI ID:23183210

Hsiang, Jen-Tsung ^[1]; Hu, Bei-Lok ^[2]

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1. Center for High Energy and High Field Physics, National Central University, Chungli 32001, Taiwan, ROC (China)
2. Maryland Center for Fundamental Physics and Joint Quantum Institute, University of Maryland, College Park, MD 20742 (United States)

In this paper we study the nonequilibrium evolution of a quantum Brownian oscillator, modeling the internal degree of freedom of a harmonic atom or an Unruh–DeWitt detector, coupled to a nonequilibrium and nonstationary quantum field bath and inquire whether a fluctuation–dissipation relation (FDR) can exist after/if it approaches equilibration. This is a nontrivial issue because a squeezed field bath cannot reach equilibration and yet, as this work shows, the system oscillator indeed can, which is a necessary condition for FDRs. We discuss three different settings: (A) The bath field essentially remains in a squeezed thermal state throughout, whose squeeze parameter is a mode- and time-independent constant. This situation is often encountered in quantum optics and quantum thermodynamics. (B) The bath field is initially in a thermal state, but is subjected to a parametric process leading to mode- and time-dependent squeezing. This scenario is encountered in cosmology and dynamical Casimir effects. The squeezing in the bath in both types of processes will affect the oscillator’s nonequilibrium evolution. We show that at late times it approaches equilibration and this stationarity condition warrants the existence of a FDR. The trait of squeezing is marked by the oscillator’s effective equilibrium temperature, and the proportionality factor in the FDR is only related to the stationary component of the noise kernel of the bath field. Setting (C) is more subtle: A finite system–bath coupling strength can set the oscillator in a squeezed state even though the bath field is stationary and does not engage in any parametric process. The squeezing of the system in this case is in general time-dependent but becomes constant when the internal dynamics is fully relaxed. We begin with comments on the broad range of physical processes involving squeezed thermal baths and end with some remarks on the significance of FDRs in capturing the essence of quantum backreaction in nonequilibrium and stochastic systems.

• OSTI ID: 23183210
• Journal Information: Annals of Physics, Journal Name: Annals of Physics Vol. 433; ISSN APNYA6; ISSN 0003-4916
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
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COMPUTERIZED SIMULATION
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EXCITED STATES
FIELD THEORIES
HARMONICS
PARAMETRIC OSCILLATORS
QUANTUM OPTICS
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TIME DEPENDENCE