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Symmetry
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Symmetry and Asymmetry in Quantum Mechanics
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Symmetry and Asymmetry in Quantum Mechanics

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

Deadline for manuscript submissions: closed (31 July 2023) | Viewed by 15706

Special Issue Editor

Dr. Valeriy Sbitnev

E-Mail Website
Guest Editor
St. Petersburg B. P. Konstantinov Nuclear Physics Institute, NRC Kurchatov Institute, Leningrad District, Gatchina 188300, Russia
Interests: quantum mechanics; superfluidity; Bose-Einstein condensate; quantum ether; quaternion algebra of physical fields; edge of chaos; neurodynamics; consciousness
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Symmetries are significant links in any physical discipline. Their observation and quantitative description provide the key to understanding the manifestation of a physical phenomenon. It follows from the theorem proved by Emmy Noether, which connects each continuous symmetry of a physical system with some conservation law (for example, if processes in an isolated system of particles are invariant to the time shift, then the law of energy conservation is fulfilled in this system). Groups of translations, rotations, reflections such as U(1), O(3) SU(2), SU(3), and others have a crucial place in the problems of quantum mechanics, be it the internal organization of particles, their interaction, or their behavior in any external field. Additionally, one can remark on the CPT theorem (charge, parity, and time reversal symmetry) proving a strict correspondence between matter and antimatter.

With sufficiently strong cooling, mesoscopic and even macroscopic samples can go into a quantum state in which a huge number of particles begin to move synchronously. These coherent waves of matter are Bose-Einstein condensate. From the other side, symmetry breaking induced by decoherence processes due to thermodynamic reasons causes the asymmetry of time.

Dr. Valeriy Sbitnev
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

  • Noether theorem
  • CPT theorem
  • Bose–Einstein condensate
  • decoherence
  • energy conservation
  • dissipation

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Published Papers (9 papers)

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Research

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13 pages, 1464 KiB  
Article
Single-Photon Superradiance and Subradiance as Collective Emission from Symmetric and Anti-Symmetric States
by Nicola Piovella and Stefano Olivares
Symmetry 2023, 15(10), 1817; https://doi.org/10.3390/sym15101817 - 25 Sep 2023
Viewed by 1161
Abstract
Recent works have shown that collective single-photon spontaneous emission from an ensemble of N resonant two-level atoms is a rich field of study. Superradiance describes the emission from a completely symmetric state of N atoms, with a single excited atom prepared with a [...] Read more.
Recent works have shown that collective single-photon spontaneous emission from an ensemble of N resonant two-level atoms is a rich field of study. Superradiance describes the emission from a completely symmetric state of N atoms, with a single excited atom prepared with a given phase, for instance, imprinted by an external laser. Instead, subradiance is associated with the emission from the remaining N−1 asymmetric states, with a collective decay rate less than the single-atom value. Here, we discuss the properties of the orthonormal basis of symmetric and asymmetric states and the entanglement properties of superradiant and subradiant states. On the one hand, by separating the symmetric superradiant state from the subradiant ones, we are able to determine the subradiant fraction induced in the system by the laser. On the other hand, we show that, as the external laser is switched off and the atomic excitation decays, entanglement in the atomic ensemble appears when the superradiant fraction falls below the threshold 1/N. Full article
(This article belongs to the Special Issue Symmetry and Asymmetry in Quantum Mechanics)
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23 pages, 760 KiB  
Article
Quaternion Quantum Mechanics II: Resolving the Problems of Gravity and Imaginary Numbers
by Marek Danielewski, Lucjan Sapa and Chantal Roth
Symmetry 2023, 15(9), 1672; https://doi.org/10.3390/sym15091672 - 30 Aug 2023
Cited by 1 | Viewed by 1640
Abstract
We present a quaternion representation of quantum mechanics that allows its ontological interpretation. The correspondence between classical and quaternion quantum equations permits one to consider the universe (vacuum) as an ideal elastic solid. Elementary particles would have to be standing or soliton-like waves. [...] Read more.
We present a quaternion representation of quantum mechanics that allows its ontological interpretation. The correspondence between classical and quaternion quantum equations permits one to consider the universe (vacuum) as an ideal elastic solid. Elementary particles would have to be standing or soliton-like waves. Tension induced by the compression and twisting of the elastic medium would increase energy density, and as a result, generate gravity forcing and affect the wave speed. Consequently, gravity could be described by an index of refraction. Full article
(This article belongs to the Special Issue Symmetry and Asymmetry in Quantum Mechanics)
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13 pages, 309 KiB  
Article
A Relationship between the Schrödinger and Klein–Gordon Theories and Continuity Conditions for Scattering Problems
by Markus Scholle and Marcel Mellmann
Symmetry 2023, 15(9), 1667; https://doi.org/10.3390/sym15091667 - 29 Aug 2023
Viewed by 1026
Abstract
A rigorous analysis is undertaken based on the analysis of both Galilean and Lorentz (Poincaré) invariance in field theories in general in order to (i) identify a unique analytical scheme for canonical pairs of Lagrangians, one of them having Galilean, the other one [...] Read more.
A rigorous analysis is undertaken based on the analysis of both Galilean and Lorentz (Poincaré) invariance in field theories in general in order to (i) identify a unique analytical scheme for canonical pairs of Lagrangians, one of them having Galilean, the other one Poincaré invariance; and (ii) to obtain transition conditions for the state function purely from Hamilton’s principle and extended Noether’s theorem applied to the aforementioned symmetries. The general analysis is applied on Schrödinger and Klein–Gordon theory, identifying them as a canonical pair in the sense of (i) and exemplified for the scattering problem for both theories for a particle beam against a potential step in order to show that the transition conditions that result according to (ii) in a ‘natural’ way reproduce the well-known ‘methodical’ continuity conditions commonly found in the literature, at least in relevant cases, closing a relevant argumentation gap in quantum mechanical scattering problems. Full article
(This article belongs to the Special Issue Symmetry and Asymmetry in Quantum Mechanics)
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8 pages, 277 KiB  
Article
Two-Dimensional Symmetry Breaking at the Event Horizon of Black Holes
by Timothy Ganesan
Symmetry 2023, 15(3), 728; https://doi.org/10.3390/sym15030728 - 15 Mar 2023
Viewed by 1636
Abstract
This work investigates the combined dynamics of the Yang–Mills and Liouville gravity fields at the event horizon of black holes. To analyze quantum dynamics at the event horizon of black holes existing in a three-dimensional (spatial) universe, a two-dimensional formulation is introduced. The [...] Read more.
This work investigates the combined dynamics of the Yang–Mills and Liouville gravity fields at the event horizon of black holes. To analyze quantum dynamics at the event horizon of black holes existing in a three-dimensional (spatial) universe, a two-dimensional formulation is introduced. The following hypothesis is proposed in this work: there exists a two-dimensional analogue to the Higgs field at the event horizon. This field is then considered as a two-dimensional Yang–Mills field. The interaction and symmetry breaking of the combined two-dimensional Yang–Mills and Liouville gravitational fields are then discussed. The resulting gravitational scalar boson and its implications to the quantum dynamics occurring at the event horizon are presented. Full article
(This article belongs to the Special Issue Symmetry and Asymmetry in Quantum Mechanics)
20 pages, 704 KiB  
Article
Circuit Complexity in Interacting Quenched Quantum Field Theory
by Sayantan Choudhury, Rakshit Mandish Gharat, Saptarshi Mandal and Nilesh Pandey
Symmetry 2023, 15(3), 655; https://doi.org/10.3390/sym15030655 - 5 Mar 2023
Cited by 10 | Viewed by 1989
Abstract
In this work, we explore the effects of quantum quenching on the circuit complexity of quenched quantum field theory with weakly coupled quartic interactions. We use the invariant operator method under a perturbative framework to compute the ground state of this system. We [...] Read more.
In this work, we explore the effects of quantum quenching on the circuit complexity of quenched quantum field theory with weakly coupled quartic interactions. We use the invariant operator method under a perturbative framework to compute the ground state of this system. We give the analytical expressions for specific reference and target states using the ground state of the system. Using a particular cost functional, we show the analytical computation of circuit complexity for the quenched and interacting field theory. Furthermore, we give a numerical estimate of circuit complexity with respect to the quench rate, δt, for two coupled oscillators. The parametric variation in the unambiguous contribution of the circuit complexity for an arbitrary number of oscillators has been studied with respect to the dimensionless parameter (t/δt). We comment on the variation in the circuit complexity for different values of coupling strength, different numbers of oscillators and even in different dimensions. Full article
(This article belongs to the Special Issue Symmetry and Asymmetry in Quantum Mechanics)
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22 pages, 594 KiB  
Article
Relativistic Fermion and Boson Fields: Bose-Einstein Condensate as a Time Crystal
by Valeriy Sbitnev
Symmetry 2023, 15(2), 275; https://doi.org/10.3390/sym15020275 - 18 Jan 2023
Cited by 2 | Viewed by 2454
Abstract
In a basis of the space-time coordinate frame four quaternions discovered by Hamilton can be used. For subsequent reproduction of the coordinate frame these four quaternions are expanded to four 4 × 4 matrices with real-valued matrix coefficients −0 and 1. This group [...] Read more.
In a basis of the space-time coordinate frame four quaternions discovered by Hamilton can be used. For subsequent reproduction of the coordinate frame these four quaternions are expanded to four 4 × 4 matrices with real-valued matrix coefficients −0 and 1. This group set is isomorphic to the SU(2) group. Such a matrix basis introduces extra six degrees of freedom of matter motion in space-time. There are three rotations about three space axes and three boosts along these axes. Next one declares the differential generating operators acting on the energy-momentum density tensor written in the above quaternion basis. The subsequent actions of this operator together with its transposed one on the above tensor lead to the emergence of the gravitomagnetic equations that are like the Maxwell equations. Wave equations extracted from the gravitomagnetic ones describe the propagation of energy density waves and their vortices through space. The Dirac equations and their reduction to two equations with real-valued functions, the quantum Hamilton-Jacobi equations and the continuity equations, are considered. The Klein-Gordon equations arising on the mass shell hints to the alternation of the paired fermion fields and boson ones. As an example, a Feynman diagram of an electron–positron time crystal is illustrated. Full article
(This article belongs to the Special Issue Symmetry and Asymmetry in Quantum Mechanics)
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12 pages, 322 KiB  
Article
Time-Dependent 4D Quantum Harmonic Oscillator and Reacting Hydrogen Atom
by Ashot S. Gevorkyan and Aleksander V. Bogdanov
Symmetry 2023, 15(1), 252; https://doi.org/10.3390/sym15010252 - 16 Jan 2023
Cited by 1 | Viewed by 1617
Abstract
With the help of low-dimensional reference equations (ordinary differential equations) and the corresponding coordinate transformations, the non-stationary 4D quantum oscillator in an external field is reduced to an autonomous form. The latter, in particular, reflects the existence of a new type of [...] Read more.
With the help of low-dimensional reference equations (ordinary differential equations) and the corresponding coordinate transformations, the non-stationary 4D quantum oscillator in an external field is reduced to an autonomous form. The latter, in particular, reflects the existence of a new type of dynamical symmetry that reduces the equation of motion of a non-stationary oscillator to an autonomous form that does not change with time. By imposing an additional constraint on the wave function of the isotropic oscillator, we have obtained the total wave functions of the reacting hydrogen atom in two different cases: (a) when the non-stationary frequency has two asymptotic values and there is no external field; and (b) when, in addition to the non-stationary frequency, an external force acts on the hydrogen atom. The transition S-matrix elements of various elementary atomic–molecular processes are constructed. The probabilities of quantum transitions of the hydrogen atom to others, including new bound states, are studied in detail, taking into account the influence of external forces. Full article
(This article belongs to the Special Issue Symmetry and Asymmetry in Quantum Mechanics)
12 pages, 363 KiB  
Article
Quantifying Complementarity via Robustness of Asymmetry
by Xin Lü
Symmetry 2022, 14(8), 1738; https://doi.org/10.3390/sym14081738 - 20 Aug 2022
Viewed by 1581
Abstract
Complementarity plays a central role in the conceptual development of quantum mechanics, and also provides practical applications in quantum information technologies. How to properly quantify it is an important problem in quantum foundations, and there exists different types of complementarity relations. In this [...] Read more.
Complementarity plays a central role in the conceptual development of quantum mechanics, and also provides practical applications in quantum information technologies. How to properly quantify it is an important problem in quantum foundations, and there exists different types of complementarity relations. In this paper, a complementarity relation is established with the robustness of asymmetry. Specifically, the two complementary aspects are quantified by applying the robustness of asymmetry corresponding to two cyclic groups whose generators are linked by the Fourier matrix. This complementarity relation is compared with known results and considered in other perspectives, especially its operational meaning regarding quantum state discrimination. We conclude that the internal asymmetry of quantum states is closely related to other fundamental concepts, such as complementarity and coherence, and it is possible to quantitatively investigate complementarity and quantum state discrimination using the robustness of asymmetry. Full article
(This article belongs to the Special Issue Symmetry and Asymmetry in Quantum Mechanics)
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Review

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13 pages, 2146 KiB  
Review
Symmetry and Electronic Properties of Metallic Nanoclusters
by Emil Roduner
Symmetry 2023, 15(8), 1491; https://doi.org/10.3390/sym15081491 - 27 Jul 2023
Cited by 1 | Viewed by 1114
Abstract
Spherical nanoclusters with countable member atoms and delocalized valence orbitals are superatoms with properties analogous to those of simple atoms. This is reflected, in particular, in their optical spectra and magnetic properties, in a similar sense to transition metal ions and complexes. Clusters [...] Read more.
Spherical nanoclusters with countable member atoms and delocalized valence orbitals are superatoms with properties analogous to those of simple atoms. This is reflected, in particular, in their optical spectra and magnetic properties, in a similar sense to transition metal ions and complexes. Clusters can be of low-spin or high-spin with considerable contributions to magnetism by the large cluster orbital magnetic moment. Due to the large radius of the clusters, they can be diamagnetic with an unusually high diamagnetic susceptibility. Gold and platinum, which in the bulk are non-magnetic, show pronounced superparamagnetism associated with their high-spin nature, and the magnetic moment can be trapped in symmetry-breaking environments so that hysteresis pertains far beyond room temperature. A significant deviation from hydrogen-like orbitals results from the shape of the confining potential, which has the effect that the orbital quantum number ℓ is not limited to values less than the principal quantum number n. Full article
(This article belongs to the Special Issue Symmetry and Asymmetry in Quantum Mechanics)
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