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Symmetry
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Symmetry and Chaos in Quantum Mechanics
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Symmetry and Chaos in Quantum Mechanics

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

Deadline for manuscript submissions: 31 December 2024 | Viewed by 8927

Special Issue Editor

Dr. Cheng Peng

E-Mail Website
Guest Editor
Kavli Institute for Theoretical Sciences (KITS), University of Chinese Academy of Sciences, Beijing 100190, China
Interests: quantum field theory; holographic principles; solvable models; gravity; string theory

Special Issue Information

Dear Colleagues,

Twentieth-century physics witnessed the fundamental role played by symmetries. Indeed, symmetry has long been a guiding principle in the study of quantum mechanical systems. Today, cutting-edge research in the field is pushed forward by various extensions of the traditional symmetries. For example, supersymmetry has proved successful in extracting the fundamental properties of many complex systems. Additionally, our understanding of symmetry in quantum systems has deepened recently due to the exciting progress in generalizations of traditional symmetries to higher-form symmetry and higher-categorical symmetries. Their relations to topological defects and other fascinating phenomena have attracted significant attention in both the condensed matter community and the high energy theory community. In addition, chaos and disorder, which in some sense reflect the lack of symmetry, have also emerged as important diagnoses of quantum systems. In this Special Issue, we aim to collect original research and topical reviews on the aforementioned aspects as well as other related topics.

Dr. Cheng Peng
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

  • supersymmetry
  • higher-spin symmetry
  • discrete symmetry
  • higher form symmetry
  • higher categorical symmetry
  • algebraic structures in quantum systems
  • quantum phase transition
  • disorder and quantum chaos
  • integrability
  • bootstrap

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Published Papers (6 papers)

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Research

Jump to: Review

23 pages, 365 KiB  
Article
Is the Wavefunction Already an Object on Space?
by Ovidiu Cristinel Stoica
Symmetry 2024, 16(10), 1379; https://doi.org/10.3390/sym16101379 - 16 Oct 2024
Cited by 4 | Viewed by 1002
Abstract
Since the discovery of quantum mechanics, the fact that the wavefunction is defined on the 3n-dimensional configuration space rather than on the 3-dimensional space has seemed uncanny to many, including Schrödinger, Lorentz, and Einstein. Even today, this continues to be seen [...] Read more.
Since the discovery of quantum mechanics, the fact that the wavefunction is defined on the 3n-dimensional configuration space rather than on the 3-dimensional space has seemed uncanny to many, including Schrödinger, Lorentz, and Einstein. Even today, this continues to be seen as a significant issue in the foundations of quantum mechanics. In this article, it will be shown that the wavefunction is, in fact, a genuine object on space. While this may seem surprising, the wavefunction does not possess qualitatively new features that were not previously encountered in objects known from Euclidean geometry and classical physics. The methodology used involves finding equivalent reinterpretations of the wavefunction exclusively in terms of objects from the geometry of space. The result is that we will find the wavefunction to be equivalent to geometric objects on space in the same way as was always the case in geometry and physics. This will be demonstrated to hold true from the perspective of Euclidean geometry, but also within Felix Klein’s Erlangen Program, which naturally fits into the classification of quantum particles by the representations of spacetime isometries, as realized by Wigner and Bargmann, adding another layer of confirmation. These results lead to clarifications in the debates about the ontology of the wavefunction. From an empirical perspective, we already take for granted that all quantum experiments take place in space. I suggest that the reason why this works is that they can be interpreted naturally and consistently with the results presented here, showing that the wavefunction is an object on space. Full article
(This article belongs to the Special Issue Symmetry and Chaos in Quantum Mechanics)
14 pages, 1201 KiB  
Article
TT¯ Deformation: A Lattice Approach
by Yunfeng Jiang
Symmetry 2023, 15(12), 2212; https://doi.org/10.3390/sym15122212 - 18 Dec 2023
Cited by 1 | Viewed by 1209
Abstract
Integrable quantum field theories can be regularized on the lattice while preserving integrability. The resulting theories on the lattice are integrable lattice models. A prototype of such a regularization is the correspondence between a sine-Gordon model and a six-vertex model on a light-cone [...] Read more.
Integrable quantum field theories can be regularized on the lattice while preserving integrability. The resulting theories on the lattice are integrable lattice models. A prototype of such a regularization is the correspondence between a sine-Gordon model and a six-vertex model on a light-cone lattice. We propose an integrable deformation of the light-cone lattice model such that in the continuum limit we obtain the TT¯-deformed sine-Gordon model. Under this deformation, the cut-off momentum becomes energy dependent and the underlying Yang–Baxter integrability is preserved. Therefore, this deformation is integrable but non-local: similar to the TT¯ deformation of quantum field theory. Full article
(This article belongs to the Special Issue Symmetry and Chaos in Quantum Mechanics)
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17 pages, 1801 KiB  
Article
Control of Strongly Nonequilibrium Coherently Correlated States and Superconducting Transition Temperature
by Sergei P. Kruchinin, Roberts I. Eglitis, Valery E. Novikov, Andrzej M. Oleś and Steffen Wirth
Symmetry 2023, 15(9), 1732; https://doi.org/10.3390/sym15091732 - 9 Sep 2023
Viewed by 2689
Abstract
Our paper considers the possibility of the emergence and control of non-equilibrium states of a quasi-homogenous condensed medium with energy and particle flows in the phase space, which, first of all, manifest themselves in the explosive development of the asymmetry in the initially [...] Read more.
Our paper considers the possibility of the emergence and control of non-equilibrium states of a quasi-homogenous condensed medium with energy and particle flows in the phase space, which, first of all, manifest themselves in the explosive development of the asymmetry in the initially symmetric equilibrium system. This symmetry breaking and the appearance of non-equilibrium in the system are controlled by the coherent acceleration of the system. Dependencies of thermodynamic parameters of a strong nonequilibrium system on the indices of disequilibrium in coherently correlated states are given, and the estimates of the dielectric permittivity in a non-equilibrium system and modes of plasma acoustic oscillations are made. An estimate of the superconducting transition temperature under nonequilibrium conditions has been made. It is demonstrated that the superconducting transition temperature can approach the limiting value, corresponding to a quantum with its plasma frequency of the medium. Full article
(This article belongs to the Special Issue Symmetry and Chaos in Quantum Mechanics)
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9 pages, 255 KiB  
Article
Anisotropic Scaling Non-Relativistic Holography: A Symmetry Perspective
by Hong Lü, Pujian Mao and Junbao Wu
Symmetry 2023, 15(8), 1579; https://doi.org/10.3390/sym15081579 - 13 Aug 2023
Viewed by 1145
Abstract
We study the holographic dual of the two-dimensional non-relativistic field theory with anisotropic scaling from a symmetry perspective. We construct a new four-dimensional metric with two-dimensional global anisotropic scaling isometry. The four-dimensional spacetime is homogeneous and is a solution of Einstein gravity with [...] Read more.
We study the holographic dual of the two-dimensional non-relativistic field theory with anisotropic scaling from a symmetry perspective. We construct a new four-dimensional metric with two-dimensional global anisotropic scaling isometry. The four-dimensional spacetime is homogeneous and is a solution of Einstein gravity with quadratic-curvature extension. We consider this spacetime dual to the vacuum of the boundary field theory. By introducing a proper solution phase space, we find that the asymptotic symmetry of the gravity theory is the two-dimensional local anisotropic conformal symmetry, which recovers precisely the results from the dual non-relativistic field theory side. Full article
(This article belongs to the Special Issue Symmetry and Chaos in Quantum Mechanics)
23 pages, 347 KiB  
Article
Islands in Generalized Dilaton Theories
by Jia Tian
Symmetry 2023, 15(7), 1402; https://doi.org/10.3390/sym15071402 - 11 Jul 2023
Cited by 15 | Viewed by 1062
Abstract
This work systematically studies the island formula in the general asymptotically flat eternal black holes in generalized dilaton gravity theories or higher-dimensional spherical black holes. Under some reasonable and mild assumptions, we prove that (the boundary of) the island always appears barely outside [...] Read more.
This work systematically studies the island formula in the general asymptotically flat eternal black holes in generalized dilaton gravity theories or higher-dimensional spherical black holes. Under some reasonable and mild assumptions, we prove that (the boundary of) the island always appears barely outside the horizon in the late time of Hawking radiation, so the information paradox is resolved. In particular, we find a proper island in the Liouville black hole that solves the previous the puzzle. Full article
(This article belongs to the Special Issue Symmetry and Chaos in Quantum Mechanics)

Review

Jump to: Research

18 pages, 3448 KiB  
Review
A Mini-Review of the Kinetic Energy Partition Method in Quantum Mechanics
by Yu-Hsin Chen, I-Huan Wu and Sheng D. Chao
Symmetry 2024, 16(3), 290; https://doi.org/10.3390/sym16030290 - 1 Mar 2024
Viewed by 1038
Abstract
Based on the idea of adiabatic symmetry, we present a novel basis set expansion method—the kinetic energy partition (KEP) method—for solving quantum eigenvalue problems. Broken symmetry is responsible for quantum entanglement in many-body systems via parametric non-adiabatic corrections. Starting from simple one-particle-in-one-dimension problems, [...] Read more.
Based on the idea of adiabatic symmetry, we present a novel basis set expansion method—the kinetic energy partition (KEP) method—for solving quantum eigenvalue problems. Broken symmetry is responsible for quantum entanglement in many-body systems via parametric non-adiabatic corrections. Starting from simple one-particle-in-one-dimension problems, we gradually increase the complexity in the number of particles and the interaction patterns. Our goal in the mini-review is to advocate for the utility of the KEP method in front-line research, in particular for research beginners in quantum many-body problems. Full article
(This article belongs to the Special Issue Symmetry and Chaos in Quantum Mechanics)
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