Special Issue "The Importance of Being Symmetrical"

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

Deadline for manuscript submissions: closed (30 April 2021).

Special Issue Editors

Prof. Dr. Ignazio Licata
E-Mail Website
Guest Editor
1. ISEM Institute for Scientific Methodology, Via Ugo La Malfa, 153, 90146 Palermo, Italy
2. School of Advanced International Studies on Applied Theoretical and Non Linear Methodologies of Physics, 70121 Bari, Italy
Interests: foundation of quantum theories; quantum cosmology; de sitter holographic models; dissipative quantum field theories; physics of emergence and organization; fisher information; sub and super turing computation models
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Roberto Passante
E-Mail Website
Guest Editor
1. Dipartimento di Fisica e Chimica, Universita' degli Studi di Palermo, Via Archirafi 36, I-90123 Palermo, Italy
2. INFN, Laboratori Nazionali del Sud, Via S. Sofia 44, I-95123 Catania, Italy
Interests: casimir physics; quantum electrodynamics; quantum fluctuations; radiative processes in static and dynamical structured environments; quantum field theory in accelerated frames and in a curved space-time; PT symmetric non-Hermitian Hamiltonians in quantum mechanics; quantum optomechanics; resonances and dressed unstable states; microscopic origin of time asymmetry in quantum physics; cosmological axions and dark matter
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

In Strena seu de nive sexangula (1611), J. Kepler poses a mathematical problem on the packaging of spheres in an Euclidean space, but also anticipates a very modern style of reasoning in physics. In fact, by starting from the extraordinary symmetries of the snowflake, Keplero hypothesizes something about its "particle" structure, while ignoring the concept of a molecule. Like much of Kepler's work, this reflection is also in the balance between an ancient concept of symmetry, linked to "beauty", and a "dynamic" concept, connected instead to the interplay of interactions in a system. It is to the last one that the first modern considerations on symmetry in physics, due to Pierre Curie, must be referred (Sur la symetrie dans les phenomenes physiques. Symetrie d’un champ   ́electrique et d’un champ magnetique, Journal de Physique 3: 393-415), as follows:

1) When certain causes produce certain effects, the symmetry elements of the causes must be found in their effects.

2) When certain effects show a certain dissymmetry, this dissymmetry must be found in the causes that gave rise to them.

3) In practice, the converses of these two propositions are not true, that is, the effects can be more symmetric than their causes.

4) A phenomenon may exist in a medium having the same characteristic symmetry or the symmetry of a subgroup of its characteristic symmetry. In other words, certain elements of symmetry can coexist with certain phenomena, but they are not necessary. What is necessary, is that certain elements of symmetry do not exist. Dissymmetry is what creates the phenomenon.

Even today, one can still admire this synthesis, which foreshadows the powerful notion of symmetry breaking, at the base of unification programs in cosmology and particle physics. It is a sign of the high level of coherence of our theories on the nature that even the GR, in spite of physical differences, were later revealed to belong to the same "mathematical key bunch" of gauge theories.

The reason symmetries (and their breaks) work so well was highlighted in an exemplary way by Emmy Noether in 1915, which clarified the close relationship between symmetries, invariances, and conservation laws, indicating the ideal formalism in group structures. Almost everything we know about nature can be expressed in terms of symmetry, as follows: The universe after the big bang was in a hot phase that then lost its symmetries, like a drop of water when it freezes into ice, through a sequence of breaks that generated families of elementary particles by pairing with Higgs particles. The deep symmetries of the laws of nature are thus transformed into the richness of the observed world.

In the end, it is correct to say “That symmetry dictates interactions, that geometry is at the heart of physics” (Chen Non Yang, Einstein's impact on theoretical physics, Contemporary Physics, 1980).

The formidable questions posed by quantum gravity re-proposes the question from new points of view. Beyond the recent question within the Anti-de Sitter/conformal field theory correspondence (Daniel Harlow, Hirosi Ooguri, Constraints on Symmetries from Holography, PRL, 191601 (2019)), there is a wider front that tends to resolve symmetries according to an emergentist perspective, whose tutelary deities are Robert Laughlin and, recently, Edward Witten (Symmetry and emergence, Nature Physics volume 14, pages 116–119 (2018). Again, there are recurring questions in the history of physics, namely: are symmetries "written" in a background at the bottom of the world, or emerging from the constraints on this background? The closest suggestion comes from condensed matter and the numerous points of contact with QFTs.

Beyond these foundational questions, symmetry continues to be a solid guide for the exploration of the physical world, as demonstrated by the recent results of the PT symmetry in the study of dissipative systems and quantum computing (M. Naghiloo, M. Abbasi, Yogesh N. Joglekar, and K. W. Murch, Quantum state tomography across the exceptional point in a single dissipative qubit, Nature Physics, 2019).

This Special Issue is conceived both as a place to discuss about “Quantum Symmetries” in their philosophical and foundational aspects, and in the rich panorama of their applications.

-  The role of symmetry in physics: historical and philosophical aspects

-   Local and global symmetries

-   Continuous and discrete symmetries

-   Lorentz and de Sitter group

-   Unitary group in QFT

-   CPT symmetry in particles physics and cosmology

-   PT symmetry, dissipative systems, and quantum computing

-   Renormalization group

-   Dynamical symmetries and chaotic behavior in physical systems

-   Symmetry Breaking in Condensed Matter, Particle Physics and Cosmology

-   Irreversibility and time-symmetry breaking

Prof. Dr. Ignazio Licata
Prof. Dr. Roberto Passante
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 papers will be 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 1800 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

  • The role of symmetry in physics: historical and philosophical aspects
  • Local and global symmetries
  • Continuous and discrete symmetries
  • Lorentz and de Sitter group
  • Unitary group in QFT
  • CPT symmetry in particles physics and cosmology
  • PT symmetry, dissipative systems, and quantum computing
  • Renormalization group
  • Dynamical symmetries and chaotic behavior in physical systems
  • Irreversibility and time-symmetry breaking

Published Papers (4 papers)

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Research

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Article
Anomalous Diffusion with an Apparently Negative Diffusion Coefficient in a One-Dimensional Quantum Molecular Chain Model
Symmetry 2021, 13(3), 506; https://0-doi-org.brum.beds.ac.uk/10.3390/sym13030506 - 19 Mar 2021
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Abstract
An interesting anomaly in the diffusion process with an apparently negative diffusion coefficient defined through the mean-square displacement in a one-dimensional quantum molecular chain model is shown. Nevertheless, the system satisfies the H-theorem so that the second law of thermodynamics is satisfied. The [...] Read more.
An interesting anomaly in the diffusion process with an apparently negative diffusion coefficient defined through the mean-square displacement in a one-dimensional quantum molecular chain model is shown. Nevertheless, the system satisfies the H-theorem so that the second law of thermodynamics is satisfied. The reason why the “diffusion constant” becomes negative is due to the effect of the phase mixing process, which is a characteristic result of the one-dimensionality of the system. We illustrate the situation where this negative “diffusion constant” appears. Full article
(This article belongs to the Special Issue The Importance of Being Symmetrical)
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Article
A Knot Theoretic Extension of the Bloch Sphere Representation for Qubits in Hilbert Space and Its Application to Contextuality and Many-Worlds Theories
Symmetry 2020, 12(7), 1135; https://0-doi-org.brum.beds.ac.uk/10.3390/sym12071135 - 07 Jul 2020
Cited by 1 | Viewed by 901
Abstract
We argue that the usual Bloch sphere is insufficient in various aspects for the representation of qubits in quantum information theory. For example, spin flip operations with the quaternions I J K = e 2 π i 2 = 1 and [...] Read more.
We argue that the usual Bloch sphere is insufficient in various aspects for the representation of qubits in quantum information theory. For example, spin flip operations with the quaternions I J K = e 2 π i 2 = 1 and J I K = + 1 cannot be distinguished on the Bloch sphere. We show that a simple knot theoretic extension of the Bloch sphere representation is sufficient to track all unitary operations for single qubits. Next, we extend the Bloch sphere representation to entangled states using knot theory. As applications, we first discuss contextuality in quantum physics—in particular the Kochen-Specker theorem. Finally, we discuss some arguments against many-worlds theories within our knot theoretic model of entanglement. The key ingredients of our approach are symmetries and geometric properties of the unitary group. Full article
(This article belongs to the Special Issue The Importance of Being Symmetrical)
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Article
The Emergence of Chaos in Quantum Mechanics
Symmetry 2020, 12(5), 785; https://0-doi-org.brum.beds.ac.uk/10.3390/sym12050785 - 08 May 2020
Cited by 2 | Viewed by 778
Abstract
Nonlinearity in Quantum Mechanics may have extrinsic or intrinsic origins and is a liable route to a chaotic behaviour that can be of difficult observations. In this paper, we propose two forms of nonlinear Hamiltonian, which explicitly depend upon the phase of the [...] Read more.
Nonlinearity in Quantum Mechanics may have extrinsic or intrinsic origins and is a liable route to a chaotic behaviour that can be of difficult observations. In this paper, we propose two forms of nonlinear Hamiltonian, which explicitly depend upon the phase of the wave function and produce chaotic behaviour. To speed up the slow manifestation of chaotic effects, a resonant laser field assisting the time evolution of the systems causes cumulative effects that might be revealed, at least in principle. The nonlinear Schrödinger equation is solved within the two-state approximation; the solution displays features with characteristics similar to those found in chaotic Classical Mechanics: sensitivity on the initial state, dense power spectrum, irregular filling of the Poincaré map and exponential separation of the trajectories of the Bloch vector σ in the Bloch sphere. Full article
(This article belongs to the Special Issue The Importance of Being Symmetrical)
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Review

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Review
Symmetries and Metamorphoses
Symmetry 2020, 12(6), 907; https://0-doi-org.brum.beds.ac.uk/10.3390/sym12060907 - 01 Jun 2020
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Abstract
In quantum field theory with spontaneous breakdown of symmetry, the invariance of the dynamics under continuous symmetry transformations manifests itself in observable ordered patterns with different symmetry properties. Such a dynamical rearrangement of symmetry describes, in well definite formal terms, metamorphosis processes. The [...] Read more.
In quantum field theory with spontaneous breakdown of symmetry, the invariance of the dynamics under continuous symmetry transformations manifests itself in observable ordered patterns with different symmetry properties. Such a dynamical rearrangement of symmetry describes, in well definite formal terms, metamorphosis processes. The coherence of the correlations generating order and self-similar fractal patterns plays a crucial role. The metamorphosis phenomenon is generated by the loss of infrared contributions in physical states and observables due to their localized nature. The dissipative dynamics and evolution, the arising of the arrow of time and entanglement are also discussed. The conclusions may be extended to biology and neuroscience and to some aspects of linguistics in the transition from syntax to semantics (generation of meanings). Full article
(This article belongs to the Special Issue The Importance of Being Symmetrical)
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