Hidden Dynamical Symmetry and Quantum Thermodynamics from the First Principles: Quantized Small Environment
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 o...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2021-08-01
|
| Series: | Symmetry |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2073-8994/13/8/1546 |
| _version_ | 1797521963439095808 |
|---|---|
| author | Ashot S. Gevorkyan Alexander V. Bogdanov Vladimir V. Mareev |
| author_facet | Ashot S. Gevorkyan Alexander V. Bogdanov Vladimir V. Mareev |
| author_sort | Ashot S. Gevorkyan |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-10T08:19:59Z |
| format | Article |
| id | doaj.art-d8f47e6b0ba848df85972a15b955726a |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-10T08:19:59Z |
| publishDate | 2021-08-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-d8f47e6b0ba848df85972a15b955726a2023-11-22T10:03:16ZengMDPI AGSymmetry2073-89942021-08-01138154610.3390/sym13081546Hidden Dynamical Symmetry and Quantum Thermodynamics from the First Principles: Quantized Small EnvironmentAshot S. Gevorkyan0Alexander V. Bogdanov1Vladimir V. Mareev2Institute for Informatics and Automation Problems NAS of RA, 1, P. Sevak Str., Yerevan 0014, ArmeniaFaculty of Applied Mathematics and Control Processes, Saint-Petersburg State University, 198504 Saint-Petersburg, RussiaFaculty of Applied Mathematics and Control Processes, Saint-Petersburg State University, 198504 Saint-Petersburg, RussiaEvolution 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.https://www.mdpi.com/2073-8994/13/8/1546open quantum systemLangevin–Schrödinger equationnon-Hermitian quantum mechanicsfunctional integral representationsmall quantized environmentBell states |
| spellingShingle | Ashot S. Gevorkyan Alexander V. Bogdanov Vladimir V. Mareev Hidden Dynamical Symmetry and Quantum Thermodynamics from the First Principles: Quantized Small Environment Symmetry open quantum system Langevin–Schrödinger equation non-Hermitian quantum mechanics functional integral representation small quantized environment Bell states |
| title | Hidden Dynamical Symmetry and Quantum Thermodynamics from the First Principles: Quantized Small Environment |
| title_full | Hidden Dynamical Symmetry and Quantum Thermodynamics from the First Principles: Quantized Small Environment |
| title_fullStr | Hidden Dynamical Symmetry and Quantum Thermodynamics from the First Principles: Quantized Small Environment |
| title_full_unstemmed | Hidden Dynamical Symmetry and Quantum Thermodynamics from the First Principles: Quantized Small Environment |
| title_short | Hidden Dynamical Symmetry and Quantum Thermodynamics from the First Principles: Quantized Small Environment |
| title_sort | hidden dynamical symmetry and quantum thermodynamics from the first principles quantized small environment |
| topic | open quantum system Langevin–Schrödinger equation non-Hermitian quantum mechanics functional integral representation small quantized environment Bell states |
| url | https://www.mdpi.com/2073-8994/13/8/1546 |
| work_keys_str_mv | AT ashotsgevorkyan hiddendynamicalsymmetryandquantumthermodynamicsfromthefirstprinciplesquantizedsmallenvironment AT alexandervbogdanov hiddendynamicalsymmetryandquantumthermodynamicsfromthefirstprinciplesquantizedsmallenvironment AT vladimirvmareev hiddendynamicalsymmetryandquantumthermodynamicsfromthefirstprinciplesquantizedsmallenvironment |