Special Issue "Symmetry in Quantum Systems"

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

Deadline for manuscript submissions: 31 October 2020.

Special Issue Editor

Dr. Alessandro Sergi
Website
Guest Editor
Dipartimento di Scienze Matematiche e Informatiche, Scienze Fisiche e Scienze della Terra, Università degli Studi di Messina, viale F. Stagno d'Alcontres 31, 98166 Messina, Italy
Interests: non-Hermitian quantum mechanics; quantum-classical hybrid systems; non-Hamiltonian systems; open quantum systems; superfluid vacuum theory; action-at-a-distance classical and quantum theories; emergent quantum gravity; dark energy; analogue gravity phenomenology
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Special Issue Information

Dear Colleagues,

There is an almost undisputed consensus about quantum theory providing algorithms to calculate probabilities associated with certain events and/or processes. Hence, it follows that invariants and quasi-invariants of the computed probabilities carry physical meaning and predictive power. In turn, invariants and quasi-invariants are linked to symmetries. The net result is that symmetries and symmetry breaking have a special role in quantum theory, which is far more potent and deeper than the one they have in classical theories.

Papers that emphasize the role of symmetries and symmetry breaking in the time evolution, parameter space, and/or boundary conditions of both quantum systems, including quantum fields and hybrid quantum–classical systems are welcome. Moreover, contributions investigating the interplay between symmetries and the quantum–classical limit are especially desired. The scope of this Special Issue is broad, and both experimental and theoretical contributions are invited.

Prof. Dr. Alessandro Sergi
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 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 1400 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

  • quantum systems
  • quantum fields
  • symmetry
  • symmetry breaking
  • time evolution
  • parameter space
  • boundary conditions
  • quantum–classical hybrid systems
  • quantum–classical limit

Published Papers (5 papers)

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Research

Open AccessArticle
Neutrino Oscillations in the Presence of Matter and Continuous Non-Selective Measurement
Symmetry 2020, 12(8), 1296; https://doi.org/10.3390/sym12081296 - 04 Aug 2020
Abstract
We investigate three-flavor neutrino oscillation affected by an environment mimicking a continuous non-selective measurement. We show that such a coupling that is given by a measured observable affects probability of inter-flavor neutrino transition and a steady-state correlation function of the neutrino’s flavor. We [...] Read more.
We investigate three-flavor neutrino oscillation affected by an environment mimicking a continuous non-selective measurement. We show that such a coupling that is given by a measured observable affects probability of inter-flavor neutrino transition and a steady-state correlation function of the neutrino’s flavor. We juxtapose and compare our predictions influenced by matter’s scattering and CP-violation. Full article
(This article belongs to the Special Issue Symmetry in Quantum Systems)
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Open AccessArticle
The Spinor-Tensor Gravity of the Classical Dirac Field
Symmetry 2020, 12(7), 1124; https://doi.org/10.3390/sym12071124 - 06 Jul 2020
Abstract
In this work, with the help of the quantum hydrodynamic formalism, the gravitational equation associated with the classical Dirac field is derived. The hydrodynamic representation of the Dirac equation described by the evolution of four mass densities, subject to the theory-defined quantum potential, [...] Read more.
In this work, with the help of the quantum hydrodynamic formalism, the gravitational equation associated with the classical Dirac field is derived. The hydrodynamic representation of the Dirac equation described by the evolution of four mass densities, subject to the theory-defined quantum potential, has been generalized to the curved space-time in the covariant form. Thence, the metric of space-time has been defined by imposing the minimum action principle. The derived gravity shows the spontaneous emergence of the “cosmological” gravity tensor (CGT), a generalization of the classical cosmological constant (CC), as a part of the energy-impulse tensor density (EITD). Even if the classical cosmological constant is set to zero, the CGT is non-zero, allowing a stable quantum vacuum (out of the collapsed branched polymer phase). The theory shows that in the classical macroscopic limit, the general relativity equation is recovered. In the perturbative approach, the CGT leads to a second-order correction to Newtonian gravity that takes contribution from the space where the mass is localized (and the space-time is curvilinear), while it tends to zero as the space-time approaches the flat vacuum, leading, as a means, to an overall cosmological constant that may possibly be compatible with the astronomical observations. The Dirac field gravity shows analogies with the modified Brans–Dicke gravity, where each spinor term brings an effective gravity constant G divided by its field squared. The work shows that in order to obtain the classical minimum action principle and the general relativity limit of the macroscopic classical scale, quantum decoherence is necessary. Full article
(This article belongs to the Special Issue Symmetry in Quantum Systems)
Open AccessArticle
SU(2) Symmetry of Qubit States and Heisenberg–Weyl Symmetry of Systems with Continuous Variables in the Probability Representation of Quantum Mechanics
Symmetry 2020, 12(7), 1099; https://doi.org/10.3390/sym12071099 - 02 Jul 2020
Abstract
In view of the probabilistic quantizer–dequantizer operators introduced, the qubit states (spin-1/2 particle states, two-level atom states) realizing the irreducible representation of the SU(2) symmetry group are identified with probability distributions (including the conditional ones) of classical-like dichotomic random [...] Read more.
In view of the probabilistic quantizer–dequantizer operators introduced, the qubit states (spin-1/2 particle states, two-level atom states) realizing the irreducible representation of the S U ( 2 ) symmetry group are identified with probability distributions (including the conditional ones) of classical-like dichotomic random variables. The dichotomic random variables are spin-1/2 particle projections m = ± 1 / 2 onto three perpendicular directions in the space. The invertible maps of qubit density operators onto fair probability distributions are constructed. In the suggested probability representation of quantum states, the Schrödinger and von Neumann equations for the state vectors and density operators are presented in explicit forms of the linear classical-like kinetic equations for the probability distributions of random variables. The star-product and quantizer–dequantizer formalisms are used to study the qubit properties; such formalisms are discussed for photon tomographic probability distribution and its correspondence to the Heisenberg–Weyl symmetry properties. Full article
(This article belongs to the Special Issue Symmetry in Quantum Systems)
Open AccessArticle
Representing Measurement as a Thermodynamic Symmetry Breaking
Symmetry 2020, 12(5), 810; https://doi.org/10.3390/sym12050810 - 13 May 2020
Cited by 2
Abstract
Descriptions of measurement typically neglect the observations required to identify the apparatus employed to either prepare or register the final state of the “system of interest.” Here, we employ category-theoretic methods, particularly the theory of classifiers, to characterize the full interaction between observer [...] Read more.
Descriptions of measurement typically neglect the observations required to identify the apparatus employed to either prepare or register the final state of the “system of interest.” Here, we employ category-theoretic methods, particularly the theory of classifiers, to characterize the full interaction between observer and world in terms of information and resource flows. Allocating a subset of the received bits to system identification imposes two separability constraints and hence breaks two symmetries: first, between observational outcomes held constant and those allowed to vary; and, second, between observational outcomes regarded as “informative” and those relegated to purely thermodynamic functions of free-energy acquisition and waste heat dissipation. We show that breaking these symmetries induces decoherence, contextuality, and measurement-associated disturbance of the system of interest. Full article
(This article belongs to the Special Issue Symmetry in Quantum Systems)
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Open AccessArticle
Quantum Computation and Measurements from an Exotic Space-Time R4
Symmetry 2020, 12(5), 736; https://doi.org/10.3390/sym12050736 - 05 May 2020
Abstract
The authors previously found a model of universal quantum computation by making use of the coset structure of subgroups of a free group G with relations. A valid subgroup H of index d in G leads to a ‘magic’ state ψ in d [...] Read more.
The authors previously found a model of universal quantum computation by making use of the coset structure of subgroups of a free group G with relations. A valid subgroup H of index d in G leads to a ‘magic’ state ψ in d-dimensional Hilbert space that encodes a minimal informationally complete quantum measurement (or MIC), possibly carrying a finite ‘contextual’ geometry. In the present work, we choose G as the fundamental group π 1 ( V ) of an exotic 4-manifold V, more precisely a ‘small exotic’ (space-time) R 4 (that is homeomorphic and isometric, but not diffeomorphic to the Euclidean R 4 ). Our selected example, due to S. Akbulut and R. E. Gompf, has two remarkable properties: (a) it shows the occurrence of standard contextual geometries such as the Fano plane (at index 7), Mermin’s pentagram (at index 10), the two-qubit commutation picture G Q ( 2 , 2 ) (at index 15), and the combinatorial Grassmannian Gr ( 2 , 8 ) (at index 28); and (b) it allows the interpretation of MICs measurements as arising from such exotic (space-time) R 4 s. Our new picture relating a topological quantum computing and exotic space-time is also intended to become an approach of ‘quantum gravity’. Full article
(This article belongs to the Special Issue Symmetry in Quantum Systems)
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Planned Papers

The below list represents only planned manuscripts. Some of these manuscripts have not been received by the Editorial Office yet. Papers submitted to MDPI journals are subject to peer-review.

Title: Electron Symmetry Breaking versus Nuclear Symmetry Conservation During Attosecond Charge Migration: Quantum Dynamics and Point Group Analyses
Authors: Dietrich Haase; Joern Manz; Jean Christophe Tremblay

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