Symmetry Principles in Quantum Systems II

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

Deadline for manuscript submissions: closed (20 July 2022) | Viewed by 4602

Special Issue Editor

Special Issue Information

Dear Colleagues,

In 1931, Herman published the famous monograph “The Theory of Groups and Quantum Mechanics”. From that moment, symmetry has been one of the most important principles for describing quantum phenomena. This Special Issue invites you to contribute your original research work and review articles on “Symmetry in Quantum Systems” that either advances theoretical and mathematical methods or extends the bounds of existing methodologies and other challenges in quantum theory. Symmetry is usually associated with theory, but we also expect articles discussing the experimental aspects of symmetry.

We hope that this Special Issue will provide an overall picture of the discussed problems and up-to-date findings for both researchers and students, and that readers will ultimately benefit from reading the contributions.

Scope: Potential topics dealing with but not limited to the following subheadings are deemed suitable for publication:

  • Group theoretical methods;
  • Many body quantum systems;
  • Low-dimensional systems;
  • Symmetries of differential equations proposed as mathematical models;
  • Quantum selection rules;
  • Symmetry in quantum information processing;
  • Supersymmetry in quantum systems;
  • Symmetry in soft matter physics;
  • Symmetry in condensed matter physics;
  • Approximate symmetry and symmetry breaking;
  • The gauge principle;
  • Green’s functions and propagators.

Prof. Dr. Jan Sładkowski
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

  • symmetry principles
  • representations of groups
  • many body systems
  • quantum theory
  • supersymmetry
  • symmetry breaking
  • molecular symmetry

Published Papers (3 papers)

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Research

15 pages, 329 KiB  
Article
Big Bang and Topology
Symmetry 2022, 14(9), 1887; https://doi.org/10.3390/sym14091887 - 09 Sep 2022
Cited by 1 | Viewed by 1221
Abstract
In this paper, we discuss the initial state of the universe at the Big Bang. By using the ideas of Freedman in the proof of the disk embedding theorem for 4-manifolds, we describe the corresponding spacetime as a gravitational instanton. The spatial space [...] Read more.
In this paper, we discuss the initial state of the universe at the Big Bang. By using the ideas of Freedman in the proof of the disk embedding theorem for 4-manifolds, we describe the corresponding spacetime as a gravitational instanton. The spatial space is a fractal space (wild embedded 3-sphere). Then, we construct the quantum state from this fractal space. This quantum state is part of the string algebra of Ocneanu. There is a link between the Jones polynomial and Witten’s topological field theory. Using this link, we are able to determine the physical theory (action) as the Chern–Simons functional. The gauge fixing of this action determines the foliation of the spacetime and the smoothness properties. Finally, we determine the quantum symmetry of the quantum state to be the enveloped Lie algebra Uq(sl2(C)), where q is the fourth root of unity. Full article
(This article belongs to the Special Issue Symmetry Principles in Quantum Systems II)
10 pages, 286 KiB  
Article
Kantian Equilibria in Classical and Quantum Symmetric Games
Symmetry 2022, 14(3), 546; https://doi.org/10.3390/sym14030546 - 08 Mar 2022
Cited by 1 | Viewed by 1506
Abstract
The aim of the paper is to examine the notion of simple Kantian equilibrium in 2×2 symmetric games and their quantum counterparts. We focus on finding the Kantian equilibrium strategies in the general form of the games. As a result, we [...] Read more.
The aim of the paper is to examine the notion of simple Kantian equilibrium in 2×2 symmetric games and their quantum counterparts. We focus on finding the Kantian equilibrium strategies in the general form of the games. As a result, we derive a formula that determines the reasonable strategies for any payoffs in the bimatrix game. This allowed us to compare the payoff results for classical and quantum way of playing the game. We showed that a very large part of 2×2 symmetric games, in which the arithmetic mean of the off-diagonal payoffs is greater than the other payoffs, have more beneficial Kantian equilibria when they are played with the use of quantum strategies. In that case, both players always obtain higher payoffs than when they use the classical strategies. Full article
(This article belongs to the Special Issue Symmetry Principles in Quantum Systems II)
15 pages, 2175 KiB  
Article
Quantum Behavior of a Nonextensive Oscillatory Dissipative System in the Coherent State
Symmetry 2021, 13(7), 1178; https://doi.org/10.3390/sym13071178 - 29 Jun 2021
Cited by 1 | Viewed by 1181
Abstract
We investigate the nonextensivity of a generalized dissipative oscillatory system in the Glauber coherent state. We introduce a parameter q as a measure of the nonextensivity of the system. Considering the characteristic of nonextensivity, the system is described by a deformed Caldirola–Kanai oscillator, [...] Read more.
We investigate the nonextensivity of a generalized dissipative oscillatory system in the Glauber coherent state. We introduce a parameter q as a measure of the nonextensivity of the system. Considering the characteristic of nonextensivity, the system is described by a deformed Caldirola–Kanai oscillator, which is represented in terms of q. We manage the system by describing the associated Hamiltonian in terms of the harmonic oscillator ladder operators. The time evolutions of the canonical variables, the Hamiltonian expectation value, the quantum energy, and the symmetry-breaking in the evolution of the system, are analyzed in detail regarding their dependence on q, damping factor, and the external driving force. The amplitude of the oscillator is slightly quenched as q becomes large, whereas the amplitude of the canonical momentum is enhanced in response to the growth in q. As q increases, the dissipation of the quantum energy becomes a little faster as a manifestation of the nonextensivity of the system. Our results are compared to the classical results, as well as to those in the previous research performed on the basis of the SU(1,1) coherent states. The coherent states, including the Glauber coherent states, can be convenient resources for carrying information, which is crucial in quantum information processing. Full article
(This article belongs to the Special Issue Symmetry Principles in Quantum Systems II)
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