2023-Sustainable Industrial Processing Summit
Intl. Symp on Physics, Mathematics and Multiscale Mechanics
| Editors: | F. Kongoli, A. B. Bhattacharya, A.C. Pandey, G. Sandhu, F. Quattrocchi, L. Sajo-Bohus, S. Singh, H.S. Virk, R.M. Santilli, M. Mikalajunas, E. Aifantis, T. Vougiouklis, P. Mandell, E. Suhir, D. Bammann, J. Baumgardner, M. Horstemeyer, N. Morgan, R. Prabhu, A. Rajendran |
| Publisher: | Flogen Star OUTREACH |
| Publication Year: | 2023 |
| Pages: | 298 pages |
| ISBN: | 978-1-989820-96-4 (CD) |
| ISSN: | 2291-1227 (Metals and Materials Processing in a Clean Environment Series) |
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OPEN AND CLOSED QUANTUM MECHANICAL SYSTEMS
Alexander Filonov1; Valentin Danilov2; Artur Abkaryan3; Aleksandr Ivanenko3;1INSTITUTE OF NONFERROUS METALS AND MATERIALS SCIENCE SIBERIAN FEDERAL UNIVERSITY KRASNOYARSK PR. IMENI GAZETY KRASNOYARSKII RABOCHII 95 RUSSIAN FEDERATION, ΠΡΠ°ΡΠ½ΠΎΡΡΡΠΊ, Russian Federation; 2INSTITUTE OF SPACE AND INFORMATIC TECHNOLOGIES, SIBERIAN FEDERAL UNIVERSITY, Krasnoyarsk, Russian Federation; 3INSTITUTE OF ENGINEERING PHYSICS AND RADIOELECTRONICS, SIBERIAN FEDERAL UNIVERSITY, Krasnoyarsk, Russian Federation;
Type of Paper: Regular
Id Paper: 476
Topic: 38
Abstract:
The Frenkel-Kontorova model (FK model) is a closed mechanical system with conserved total energy and number of particles.
The developed Frenkel-Kontorova model (DFK model) is an open mechanical system with non-conserved energy and numbers of interacting particles.
The quantum analogue of the FK model is the theory of a quantum mechanical particle in a periodic potential.
Quantum analogues of the DFK model are open quantum mechanical theories with periodic potentials, for example, the Kronig-Penney model with a constant friction force and the model of a quantum mechanical particle tunneling through the cut ends of a periodic potential [1].
It is known that in closed quantum mechanical theories there are no transitions between discrete energy levels, therefore their wave functions do not decay, and the energy spectra are purely real.
The energy spectra of open quantum systems are described by complex values with damped wave functions.
For us, superradiant states are of greatest interest. Preliminary quote from [2]: - βas an example of a physical phenomenon possible during the interaction of an intense electromagnetic wave with matter, we cite the phenomenon of superradiance or, to be precise, coherent spontaneous radiation predicted by R. Dicke [3]. This prediction is nontrivial, since it is known from the elementary theory of radiation that spontaneous emission is an incoherent process. However, there may be excited states of a system of π atoms in which the radiation intensity is π2 times greater than that of an individual atom.β
Qualitatively, the resulting state of N identical atoms brought to one point can be conveniently represented as atoms with two levels, the width of the upper one increases N times compared to the initial one.
An even more interesting case is when the levels are not identical, quote from [4]: -
βThe problem of the influence of energy dissipation on the properties of the unstable states themselves remains one of the main problems of modern quantum physics. The irreversible flow of energy from the observed system to another (continuum) leads to the fact that each excited level of the spectrum of the observed system has a finite width. In reality, all excited states of physical systems have a finite lifetime. Their properties are studied using external fields that excite these states, which then decay along one or another channel. The weak influence of the continuum on the spectrum of the system can be taken into account using standard perturbation theory, but as soon as the widths of the levels are compared with the distance between them, the perturbation theory stops working. New approaches are required to analyze the emerging situation.β
In [4,5], several theorems were proven based on general provisions of local field theory. Of these, we will highlight two that are of key importance for our work.
In two systems of N energy levels with identical quantum numbers, in the first the levels decay one at a time, in the second through L channels.
As shown in [4, 5], when the widths of the levels of the corresponding decay channels intersect, in the first case one, and in the second L, fast-decay levels are identified, the widths of which, depending on the degree of overlap, take up almost the entire width of the initial levels (NΞ³). The widths of the remaining NβL levels decrease at a fixed total zone width W and the widths of the initial levels Ξ³ by (NΞ³/W)2 times.
Despite the fact that the results of theorems [4,5] are confirmed by exact solutions of nonlocal models [1], optical experiments - the absence of superradiant states in microcrystals - cast doubt on these results.
Keywords:
FK model; Open quantum systems; Mechanical systemsReferences:
[1] A.N. Filonov. Exactly solvable models with applications. LAP LAMBERT Academic Publ., M. (2012). 103 pp.[2] V. G. Zelevinsky, Z 48 Quantum physics: textbook. allowance / V. G. Zelevinsky; Novosibirsk: RIC NSU, 2015: T. 2. Central field. Atom in external fields.434 p.
[3] R.H. Dicke Phys. Rev., 1954, v. 93, p.99.
[4] V.G. Zelevinsky, V.V. Sokolov Materials of the Leningrad Nuclear Physics Winter School, Leningrad, 1989
[5] V.V. Sokolov, V.G. Zelevinsky Nucl. Phys. A 504 (1989) 562