Hidden Dynamical Symmetry and Quantum Thermodynamics from the First Principles: Quantized Small Environment

Gevorkyan, Ashot S.; Bogdanov, Alexander V.; Mareev, Vladimir V.

doi:10.3390/sym13081546

Open AccessArticle

Hidden Dynamical Symmetry and Quantum Thermodynamics from the First Principles: Quantized Small Environment

by

Ashot S. Gevorkyan

^1,2,*

,

Alexander V. Bogdanov

³ and

Vladimir V. Mareev

³

¹

Institute for Informatics and Automation Problems NAS of RA, 1, P. Sevak Str., Yerevan 0014, Armenia

²

Institute of Chemical Physics NAS of RA, 5/2, P. Sevak Str., Yerevan 0014, Armenia

³

Faculty of Applied Mathematics and Control Processes, Saint-Petersburg State University, 198504 Saint-Petersburg, Russia

^*

Author to whom correspondence should be addressed.

Symmetry 2021, 13(8), 1546; https://doi.org/10.3390/sym13081546

Submission received: 22 June 2021 / Revised: 21 July 2021 / Accepted: 12 August 2021 / Published: 23 August 2021

(This article belongs to the Special Issue Symmetry in Particle Physics II)

Download

Browse Figures

Versions Notes

Abstract

Evolution of a self-consistent joint system (JS), i.e., a quantum system (QS) + thermal bath (TB), is considered within the framework of the Langevin–Schrödinger (L-Sch) type equation. As a tested QS, we considered two linearly coupled quantum oscillators that interact with TB. The influence of TB on QS is described by the white noise type autocorrelation function. Using the reference differential equation, the original L-Sch equation is reduced to an autonomous form on a random space–time continuum, which reflects the fact of the existence of a hidden symmetry of JS. It is proven that, as a result of JS relaxation, a two-dimensional quantized small environment is formed, which is an integral part of QS. The possibility of constructing quantum thermodynamics from the first principles of non-Hermitian quantum mechanics without using any additional axioms has been proven. A numerical algorithm has been developed for modeling various properties and parameters of the QS and its environment.

Keywords: open quantum system; Langevin–Schrödinger equation; non-Hermitian quantum mechanics; functional integral representation; small quantized environment; Bell states; quantum thermodynamics; numerical simulation of the 2D Fokker–Planck equation

Share and Cite

MDPI and ACS Style

Gevorkyan, A.S.; Bogdanov, A.V.; Mareev, V.V. Hidden Dynamical Symmetry and Quantum Thermodynamics from the First Principles: Quantized Small Environment. Symmetry 2021, 13, 1546. https://doi.org/10.3390/sym13081546

AMA Style

Gevorkyan AS, Bogdanov AV, Mareev VV. Hidden Dynamical Symmetry and Quantum Thermodynamics from the First Principles: Quantized Small Environment. Symmetry. 2021; 13(8):1546. https://doi.org/10.3390/sym13081546

Chicago/Turabian Style

Gevorkyan, Ashot S., Alexander V. Bogdanov, and Vladimir V. Mareev. 2021. "Hidden Dynamical Symmetry and Quantum Thermodynamics from the First Principles: Quantized Small Environment" Symmetry 13, no. 8: 1546. https://doi.org/10.3390/sym13081546

APA Style

Gevorkyan, A. S., Bogdanov, A. V., & Mareev, V. V. (2021). Hidden Dynamical Symmetry and Quantum Thermodynamics from the First Principles: Quantized Small Environment. Symmetry, 13(8), 1546. https://doi.org/10.3390/sym13081546

Note that from the first issue of 2016, this journal uses article numbers instead of page numbers. See further details here.

Article Menu

Hidden Dynamical Symmetry and Quantum Thermodynamics from the First Principles: Quantized Small Environment

Abstract

Share and Cite

Article Metrics

Article Access Statistics

Further Information

Guidelines

MDPI Initiatives

Follow MDPI