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Journal of Experimental and Theoretical Physics Letters

On the Decay of an “Isolated” Oscillator Nonlinearly Coupled to a Damped Oscillator

Andrew I. Trubilko, Ashat M. Basharov

Published Oct 1, 2019• 9 citations
Publisher

Abstract

Mechanisms of pumping and decay of an “isolated” oscillator which can nonlinearly interact with a neighboring oscillator having a different frequency have been discussed. It has been shown that, if this neighboring oscillator is coupled to a broadband thermostat field, the isolated oscillator begins to interact with this thermostat field. As a result, a new relaxation channel appears because of the quantum interference of interacting systems, which can hardly be explained within traditional approaches.

DOI
10.1134/s0021364019190123

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Mechanisms of pumping and decay of an “isolated” oscillator which can nonlinearly interact with a neighboring oscillator having a different frequency have been discussed. It has been shown that, if this neighboring oscillator is coupled to a broadband thermostat field, the isolated oscillator begins to interact with this thermostat field. As a result, a new relaxation channel appears because of the quantum interference of interacting systems, which can hardly be explained within traditional approaches.
Abstract The mechanisms for the pumping and decay of an “isolated” oscillator that can interact only nonresonantly with a neighboring oscillator of different frequency are presented. We show that if this neighboring oscillator is coupled to a broadband heat-bath field, the isolated oscillator begins to interact with this heat-bath field. A new relaxation channel attributable to the quantum interference of the interacting systems that is difficult or impossible to justify in terms of traditional approaches emerges as a result.
The paper shows mechanisms of both the pumping and energy decay of an "isolated" oscillator. The oscillator is only non-resonantly coupled with the adjacent oscillator which resonantly interacts with the thermal bath environment. Under these conditions the "isolated" oscillator begins interacting with the thermal bath environment of the adjacent oscillator. The conclusion is based on the kinetic equation derived relative to anti-rotating terms of the initial Hamiltonian, with the latter being the Hamiltonian of two oscillators and environment of one of them.
Abstract The paper shows mechanisms of both the pumping and energy decay of an ‘isolated’ oscillator. The oscillator is only coupled non-resonantly with the adjacent oscillator which resonantly interacts with the thermal bath environment. Under these conditions the ‘isolated’ oscillator begins interacting with the thermal bath environment of the adjacent oscillator. The conclusion is based on the kinetic equation derived relative to anti-rotating terms of the initial Hamiltonian. The original model is reduced to two ‘independent’ open systems, with each containing original oscillators connected with their effective independent thermal baths, whose parameters are determined. The paper also gives a description of the obtained model in terms of quantum stochastic differential equations.
Abstract It is shown that an ensemble of Nc independent identical quantum oscillators interacting nonresonantly with a damped oscillator can be effectively described as an ensemble of identical oscillators decaying in the field of a common thermostat. The emission rate of such an ensemble exhibits a peculiar dependence on number Nc of oscillators and can be suppressed completely depending on the number of oscillators in the ensemble for zero thermostat photon number density in a certain frequency range of the spectrum. This feature reflects the non-Wiener nature of the oscillator ensemble dynamics and appears when all antirotating and rapidly varying (with time) terms (in the Dirac pattern) in the oscillator interaction operators, which are usually neglected, are taken into account correctly.
Abstract Using algebraic perturbation theory, the applicability of the quantum oscillator model within the theory of open quantum systems is demonstrated. The case of resonant and nonresonant interactions between two spatially separated oscillators is considered, where each oscillator interacts with its own thermostat at different temperatures. The possibility of the decay of an isolated oscillator into the thermostat of the oscillator-mediator under conditions of its nonresonant interaction with the latter is demonstrated. In all the cases presented, algebraic perturbation theory does not lead to any nonphysical features or contradictions, such as violations of the second law of thermodynamics or discrepancies in the description of these cases within the frameworks of the global and local approaches.
Quantum phenomena appear in a macroscopic scale in Bose-Einstein condensates. The Gross-Pitaevskii (GP) equation describes the dynamics of the weakly interacting Bose-Einstein condensates. The GP equation has a form of the Schroedinger equation with self-interaction. The coupled Gross-Pitaevskii equations are used to describe some mixtures of Bose-Einstein condensates. In this paper, we will show some numerical results of coupled Gross-Pitaevskii equations without self-interaction, which has a form of nonlinearly-coupled Schroedinger equations. We demonstrate that the macroscopic oscillation and the interference of two quantum wave packets decay in time owing to mutual interaction, which is analogous to the decoherence in quantum mechanics of many particles.