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Symmetry
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PT-Symmetry in Physical Systems
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PT-Symmetry in Physical Systems

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

Deadline for manuscript submissions: closed (31 January 2021) | Viewed by 8145

Special Issue Editor

Prof. Dr. Wiesław Leonski

E-Mail Website
Guest Editor
Faculty of Physics and Astronomy, Univeristy of Zielona Góra, ul. Z. Szafrana 4a, 65-516 Zielona Góra, Poland
Interests: quantum and nonlinear optics; quantum information theory; deterministic chaos; quantum chaos; cellular automata
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Recently, most intriguing and promising topics in modern physics have become those related to the description of the physical systems by non-Hermitian Hamiltonians. Especially, the Hamiltonians, which exhibit the PT-symmetry (parity-inversion plus time-reversal symmetry), have gained particular interest. Starting from the end of the previous century, they have attracted considerable and still increasing attention in both theoretical and experimental research. They concern critical phenomena, PT -symmetry breaking, and other aspects related to such Hamiltonians, and were the subject of numerous works dedicated to various areas ranging from mechanics, acoustics, electronics, classical and quantum optics, to optomechanics, plasmonics, metamaterials, and photonic crystals. Such studies are particularly relevant in finding ways to describe the coexistence of excitation and damping phenomena. Besides their practical aspects, advances in the research related to the PT-symmetric Hamiltonians can lead to the alternative formulation of quantum mechanics.

This Special Issue is devoted to the broad range of the topics which are related to the ideas of PT-symmetric Hamiltonians in classical and quantum models. I would like to invite all Colleagues to submit their original research results, reviews, and short communication articles to the Issue. Both theoretical and experimental proposals are welcome.

Prof. Dr. Wiesław Leoński
Guest Editor

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

  • PT-symmetry
  • PT-symmetry braking
  • non-Hermitian Hamiltonian
  • exceptional points
  • critical phenomena

Published Papers (4 papers)

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Research

15 pages, 907 KiB  
Article
The Bipartite and Tripartite Entanglement in PT-Symmetric System
by Vinh Le Duc, Mateusz Nowotarski and Joanna K. Kalaga
Symmetry 2021, 13(2), 203; https://doi.org/10.3390/sym13020203 - 27 Jan 2021
Cited by 3 | Viewed by 1848
Abstract
We consider a PT-symmetric system that involves three optical resonant elements coupled together. We investigate the quantum correlations between subsystems by calculating bipartite and tripartite entanglement. We show that when PT-symmetry is maintained, the correlations between subsystems strongly depend on the [...] Read more.
We consider a PT-symmetric system that involves three optical resonant elements coupled together. We investigate the quantum correlations between subsystems by calculating bipartite and tripartite entanglement. We show that when PT-symmetry is maintained, the correlations between subsystems strongly depend on the parameters describing the interaction between them and characterizing the gain and loss of energy in the system’s active and passive elements. We estimate the range of interaction parameter values for which the strongest bipartite and tripartite entanglement can be produced. Additionally, we show that the discussed system can be a source of stable entangled states. Full article
(This article belongs to the Special Issue PT-Symmetry in Physical Systems)
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14 pages, 272 KiB  
Article
PT -Symmetric Qubit-System States in the Probability Representation of Quantum Mechanics
by Vladimir N. Chernega, Margarita A. Man’ko and Vladimir I. Man’ko
Symmetry 2020, 12(10), 1702; https://doi.org/10.3390/sym12101702 - 16 Oct 2020
Cited by 5 | Viewed by 1812
Abstract
PT-symmetric qubit-system states are considered in the probability representation of quantum mechanics. The new energy eigenvalue equation for probability distributions identified with qubit and qutrit states is presented in an explicit form. A possibility to test PT-symmetry and its violation by [...] Read more.
PT-symmetric qubit-system states are considered in the probability representation of quantum mechanics. The new energy eigenvalue equation for probability distributions identified with qubit and qutrit states is presented in an explicit form. A possibility to test PT-symmetry and its violation by measuring the probabilities of spin projections for qubits in three perpendicular directions is discussed. Full article
(This article belongs to the Special Issue PT-Symmetry in Physical Systems)
15 pages, 356 KiB  
Article
Uncertainty Relations: Curiosities and Inconsistencies
by Krzysztof Urbanowski
Symmetry 2020, 12(10), 1640; https://doi.org/10.3390/sym12101640 - 06 Oct 2020
Cited by 2 | Viewed by 1517
Abstract
Analyzing general uncertainty relations one can find that there can exist such pairs of non-commuting observables A and B and such vectors that the lower bound for the product of standard deviations ΔA and ΔB calculated for these vectors is zero: [...] Read more.
Analyzing general uncertainty relations one can find that there can exist such pairs of non-commuting observables A and B and such vectors that the lower bound for the product of standard deviations ΔA and ΔB calculated for these vectors is zero: ΔA·ΔB≥0. Here we discuss examples of such cases and some other inconsistencies which can be found performing a rigorous analysis of the uncertainty relations in some special cases. As an illustration of such cases matrices (2×2) and (3×3) and the position–momentum uncertainty relation for a quantum particle in the box are considered. The status of the uncertainty relation in PT–symmetric quantum theory and the problems associated with it are also studied. Full article
(This article belongs to the Special Issue PT-Symmetry in Physical Systems)
12 pages, 331 KiB  
Article
Deforming Gibbs Factor Using Tsallis q-Exponential with a Complex Parameter: An Ideal Bose Gas Case
by Andrij Rovenchak
Symmetry 2020, 12(5), 732; https://doi.org/10.3390/sym12050732 - 05 May 2020
Cited by 1 | Viewed by 2016
Abstract
The paper presents a study of a non-standard model of fractional statistics. The exponential of the Gibbs factor in the expression for the occupation numbers of ideal bosons is substituted with the Tsallis q-exponential and the parameter [...] Read more.
The paper presents a study of a non-standard model of fractional statistics. The exponential of the Gibbs factor in the expression for the occupation numbers of ideal bosons is substituted with the Tsallis q-exponential and the parameter q = 1 − α is considered complex. Such an approach predicts quantum critical phenomena, which might be associated with PT -symmetry breaking. Thermodynamic functions are calculated for this system. Analysis is made both numerically and analytically. Singularities in the temperature dependence of fugacity and specific heat are revealed. The critical temperature is defined by non-analyticities in the expressions for the occupation numbers. Due to essentially transcendental nature of the respective equations, only numerical estimations are reported for several values of parameters. In the limit of α → 0 some simplifications are obtained in equations defining the temperature dependence of fugacity and relations defining the critical temperature. Applications of the proposed model are expected in physical problems with energy dissipation and inderdisciplinarily in effective description of complex systems to describe phenomena with non-monotonic dependencies. Full article
(This article belongs to the Special Issue PT-Symmetry in Physical Systems)
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