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Symmetry
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Cooperative Effects in Finite Systems
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Cooperative Effects in Finite Systems

A special issue of Symmetry (ISSN 2073-8994). This special issue belongs to the section "Physics".

Deadline for manuscript submissions: closed (31 December 2023) | Viewed by 7214

Special Issue Editors

Prof. Dr. Vyacheslav Yukalov

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Guest Editor
Bogolubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, 141980 Dubna, Russia
Interests: optimized perturbation theory; self-similar approximation theory; method of self-similar prediction; correlated iteration theory; theory of heterophase fluctuations
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. V. S. Bagnato

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Guest Editor
Instituto de Fisica de Sao Carlos, Universidade de Sao Paulo, CP 369, Sao Carlos 13560-970, SP, Brazil
Interests: Bose-Einstein condensation; trapped atoms; turbulence
Special Issues, Collections and Topics in MDPI journals
Dr. Rashid G. Nazmitdinov

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Guest Editor
Bogolubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, 141980 Dubna, Russia
Interests: transport in nanostructures; graphene; random matrix approach; nuclear structure
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Cooperative phenomena are at the basis of many-body physics. These phenomena are associated with particle interactions and correlations. For example, in condensed matter physics, such phenomena as sound, thermal conductivity, etc. are due to collective particle interactions. Cooperative phenomena are at the origin of phase transitions. The arising long-range, mid-range, or short-range orders are due to coherent action of many constituents. They lead to quantum effects, such as superfluidity and superconductivity. With the development of modern technologies, operating on a nanometer scale, a natural question arises about the manifestation of cooperative phenomena in mesoscopic systems. In these systems, the finite-size effects can become important, as can the influence of the surfaces and boundaries, whose role can be neglected for macroscopic systems. Understanding the peculiarities of these phenomena in a microscopic environment becomes a real challenge for science. Indeed, the study of physics phenomena in mesoscopic systems has grown into a wide field of interdisciplinary investigations involving various branches of natural sciences from physics to chemistry and biology to sociology. Thus, the importance of studying different aspects of cooperative phenomena that can break or preserve symmetries in their evolution between the macroscopic and microscopic world becomes obvious. The knowledge, gained in the study of mesoscopic systems, will deepen our understanding of cooperative phenomena in various branches of modern science and will be useful for the advancement of new technologies.

Prof. Dr. Vyacheslav Yukalov
Prof. Dr. V. S. Bagnato
Dr. Rashid G. Nazmitdinov
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Symmetry is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2400 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • nanoclusters and nanomolecules
  • trapped Bose and fermi atoms
  • graphene and magnetic graphene
  • quantum dots
  • spintronics in nanomaterials
  • gauge symmetry
  • translation symmetry
  • mesoscopic superfluidity
  • mesoscopic superconductivity
  • mesoscopic Bose condensation
  • turbulence of trapped atoms
  • local symmetry breaking
  • mesoscopic fluctuations

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Published Papers (5 papers)

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Research

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20 pages, 1129 KiB  
Article
Quantum Hall and Shubnikov-de Haas Effects in Graphene within Non-Markovian Langevin Approach
by Erkin Kh. Alpomishev, Gurgen G. Adamian and Nikolay V. Antonenko
Symmetry 2024, 16(1), 7; https://doi.org/10.3390/sym16010007 - 19 Dec 2023
Cited by 1 | Viewed by 1174
Abstract
The theory of open quantum systems is applied to study galvano-, thermo-magnetic, and magnetization phenomena in axial symmetric two-dimensional systems. Charge carriers are considered as quantum particles interacting with the environment through a one-body (mean-field) mechanism. The dynamics of charge carriers is affected [...] Read more.
The theory of open quantum systems is applied to study galvano-, thermo-magnetic, and magnetization phenomena in axial symmetric two-dimensional systems. Charge carriers are considered as quantum particles interacting with the environment through a one-body (mean-field) mechanism. The dynamics of charge carriers is affected by the average collision time that takes effectively into account two-body effects. The functional dependencies of the average collision time on the external uniform magnetic field, concentration and temperature are phenomenologically treated. Analytical expressions are obtained for the tensors of electric and thermal conductivity and/or resistivity. The developed theory is applied to describe the Shubnikov-de Haas oscillations and quantum Hall effect in graphene and GaAs/AlxGa1−xAs heterostructure. The dependencies of magnetization and thermal conductivity on the magnetic field are also predicted. Full article
(This article belongs to the Special Issue Cooperative Effects in Finite Systems)
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14 pages, 4870 KiB  
Article
Rippled Graphene as an Ideal Spin Inverter
by Ján Buša, Michal Pudlák and Rashid Nazmitdinov
Symmetry 2023, 15(8), 1593; https://doi.org/10.3390/sym15081593 - 16 Aug 2023
Cited by 2 | Viewed by 1175
Abstract
We analyze a ballistic electron transport through a corrugated (rippled) graphene system with a curvature-induced spin–orbit interaction. The corrugated system is connected from both sides to two flat graphene sheets. The rippled structure unit is modeled by upward and downward curved surfaces. The [...] Read more.
We analyze a ballistic electron transport through a corrugated (rippled) graphene system with a curvature-induced spin–orbit interaction. The corrugated system is connected from both sides to two flat graphene sheets. The rippled structure unit is modeled by upward and downward curved surfaces. The cooperative effect of N units connected together (the superlattice) on the transmission of electrons that incident at the arbitrary angles on the superlattice is considered. The set of optimal angles and corresponding numbers of N units that yield the robust spin inverter phenomenon are found. Full article
(This article belongs to the Special Issue Cooperative Effects in Finite Systems)
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12 pages, 371 KiB  
Article
Density of States for the Unitary Fermi Gas and the Schwarzschild Black Hole
by Luca Salasnich
Symmetry 2023, 15(2), 350; https://doi.org/10.3390/sym15020350 - 27 Jan 2023
Viewed by 1346
Abstract
The density of states of a quantum system can be calculated from its definition, but, in some cases, this approach is quite cumbersome. Alternatively, the density of states can be deduced from the microcanonical entropy or from the canonical partition function. After discussing [...] Read more.
The density of states of a quantum system can be calculated from its definition, but, in some cases, this approach is quite cumbersome. Alternatively, the density of states can be deduced from the microcanonical entropy or from the canonical partition function. After discussing the relationship among these procedures, we suggest a simple numerical method, which is equivalent in the thermodynamic limit to perform a Legendre transformation, to obtain the density of states from the Helmholtz free energy. We apply this method to determine the many-body density of states of the unitary Fermi gas, a very dilute system of identical fermions interacting with a divergent scattering length. The unitary Fermi gas is highly symmetric due to the absence of any internal scale except for the average distance between two particles and, for this reason, its equation of state is called universal. In the last part of the paper, by using the same thermodynamical techniques, we review some properties of the density of states of a Schwarzschild black hole, which shares the problem of finding the density of states directly from its definition with the unitary Fermi gas. Full article
(This article belongs to the Special Issue Cooperative Effects in Finite Systems)
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Review

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20 pages, 528 KiB  
Review
Transport Properties of Strongly Correlated Fermi Systems
by Vasily R. Shaginyan, Alfred Z. Msezane and Mikhail V. Zverev
Symmetry 2023, 15(11), 2055; https://doi.org/10.3390/sym15112055 - 13 Nov 2023
Cited by 1 | Viewed by 1118
Abstract
Physicists are actively debating the nature of the quantum critical phase transition that determines the low-temperature properties of metals with heavy fermions. Important experimental observations of their transport properties incisively probe the nature of the quantum critical phase transition. In our short review, [...] Read more.
Physicists are actively debating the nature of the quantum critical phase transition that determines the low-temperature properties of metals with heavy fermions. Important experimental observations of their transport properties incisively probe the nature of the quantum critical phase transition. In our short review, we consider the transport properties of strongly correlated Fermi systems like heavy fermion metals and high—Tc superconductors. Their transport properties are defined by strong inter-particle interactions, forming flat bands in these compounds. These properties do not coincide with those of conventional metals. Indeed, in contrast to the behavior of the transport properties of conventional metals, the strongly correlated compounds exhibit linear temperature resistivity ρ(T)∝T. We analyze the magnetoresistance and show that under the application of the magnetic field, it becomes negative. It is shown that near a quantum phase transition, when the density of the electronic states diverges, semiclassical physics remains applicable to describe the resistivity ρ of strongly correlated metals due to the presence of a transverse zero-sound collective mode, representing the phonon mode in solids. We demonstrate that when T exceeds the extremely low Debye temperature TD, the resistivity ρ(T) changes linearly with T since the mechanism of formation of the T-dependence ρ(T) is a similar electron-phonon mechanism, which predominates at high temperatures in ordinary metals. Thus, in the region of T-linear resistance, electron-phonon scattering leads to a lifetime of τ quasiparticles practically independent of the material, which is expressed as the ratio of the Planck constant ℏ to the Boltzmann constant kB, Tτ∼ℏ/kB. We explain that due to the non-Fermi-liquid behavior, the real part of the frequency-dependent optical conductivity σoptR(ω) exhibits a scaling behavior and demonstrates the unusual power law behavior σoptR(ω)∝ω−1, rather than the well-known one shown by conventional metals, σoptR(ω)∝ω−2. All our theoretical considerations are illustrated and compared with the corresponding experimental facts. Our results are in a good agreement with experimental observations. Full article
(This article belongs to the Special Issue Cooperative Effects in Finite Systems)
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39 pages, 1844 KiB  
Review
Approximate Calculation of Functional Integrals Generated by Nonrelativistic and Relativistic Hamiltonians
by Edik Ayryan, Michal Hnatic, Juha Honkonen and Victor Malyutin
Symmetry 2023, 15(9), 1785; https://doi.org/10.3390/sym15091785 - 18 Sep 2023
Viewed by 1390
Abstract
The discussion revolves around the most recent outcomes in the realm of approximating functional integrals through calculations. Review of works devoted to the application of functional integrals in quantum mechanics and quantum field theory, nuclear physics and in other areas is presented. Methods [...] Read more.
The discussion revolves around the most recent outcomes in the realm of approximating functional integrals through calculations. Review of works devoted to the application of functional integrals in quantum mechanics and quantum field theory, nuclear physics and in other areas is presented. Methods obtained by the authors for approximate calculation of functional integrals generated by nonrelativistic Hamiltonians are given. One of the methods is based on the expansion in eigenfunctions of the Hamiltonian. In an alternate approach, the functional integrals are tackled using the semiclassical approximation. Methods for approximate evaluation of functional integrals generated by relativistic Hamiltonians are presented. These are the methods using functional polynomial approximation (analogue of formulas of a given degree of accuracy) and methods based on the expansion in eigenfunctions of the Hamiltonian, generating a functional integral. Full article
(This article belongs to the Special Issue Cooperative Effects in Finite Systems)
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