Special Issue "Symmetry in Quantum Systems"

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

Deadline for manuscript submissions: 31 July 2021.

Special Issue Editor

Dr. Alessandro Sergi
E-Mail 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-adiabatic dynamics; non-Hamiltonian systems; open quantum systems
Special Issues and Collections in MDPI journals

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 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

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

Published Papers (8 papers)

Order results
Result details
Select all
Export citation of selected articles as:

Research

Jump to: Review

Article
Electron Symmetry Breaking during Attosecond Charge Migration Induced by Laser Pulses: Point Group Analyses for Quantum Dynamics
Symmetry 2021, 13(2), 205; https://doi.org/10.3390/sym13020205 - 27 Jan 2021
Cited by 2 | Viewed by 661
Abstract
Quantum simulations of the electron dynamics of oriented benzene and Mg-porphyrin driven by short (<10 fs) laser pulses yield electron symmetry breaking during attosecond charge migration. Nuclear motions are negligible on this time domain, i.e., the point group symmetries G = D6h [...] Read more.
Quantum simulations of the electron dynamics of oriented benzene and Mg-porphyrin driven by short (<10 fs) laser pulses yield electron symmetry breaking during attosecond charge migration. Nuclear motions are negligible on this time domain, i.e., the point group symmetries G = D6h and D4h of the nuclear scaffolds are conserved. At the same time, the symmetries of the one-electron densities are broken, however, to specific subgroups of G for the excited superposition states. These subgroups depend on the polarization and on the electric fields of the laser pulses. They can be determined either by inspection of the symmetry elements of the one-electron density which represents charge migration after the laser pulse, or by a new and more efficient group-theoretical approach. The results agree perfectly with each other. They suggest laser control of symmetry breaking. The choice of the target subgroup is restricted, however, by a new theorem, i.e., it must contain the symmetry group of the time-dependent electronic Hamiltonian of the oriented molecule interacting with the laser pulse(s). This theorem can also be applied to confirm or to falsify complementary suggestions of electron symmetry breaking by laser pulses. Full article
(This article belongs to the Special Issue Symmetry in Quantum Systems)
Show Figures

Graphical abstract

Article
On Functional Hamilton–Jacobi and Schrödinger Equations and Functional Renormalization Group
Symmetry 2020, 12(10), 1657; https://doi.org/10.3390/sym12101657 - 10 Oct 2020
Viewed by 984
Abstract
We consider the functional Hamilton–Jacobi (HJ) equation, which is the central equation of the holographic renormalization group (HRG), functional Schrödinger equation, and generalized Wilson–Polchinski (WP) equation, which is the central equation of the functional renormalization group (FRG). These equations are formulated in D [...] Read more.
We consider the functional Hamilton–Jacobi (HJ) equation, which is the central equation of the holographic renormalization group (HRG), functional Schrödinger equation, and generalized Wilson–Polchinski (WP) equation, which is the central equation of the functional renormalization group (FRG). These equations are formulated in D-dimensional coordinate and abstract (formal) spaces. Instead of extra coordinates or an FRG scale, a “holographic” scalar field Λ is introduced. The extra coordinate (or scale) is obtained as the amplitude of delta-field or constant-field configurations of Λ. For all the functional equations above a rigorous derivation of corresponding integro-differential equation hierarchies for Green functions (GFs) as well as the integration formula for functionals are given. An advantage of the HJ hierarchy compared to Schrödinger or WP hierarchies is that the HJ hierarchy splits into independent equations. Using the integration formula, the functional (arbitrary configuration of Λ) solution for the translation-invariant two-particle GF is obtained. For the delta-field and the constant-field configurations of Λ, this solution is studied in detail. A separable solution for a two-particle GF is briefly discussed. Then, rigorous derivation of the quantum HJ and the continuity functional equations from the functional Schrödinger equation as well as the semiclassical approximation are given. An iterative procedure for solving the functional Schrödinger equation is suggested. Translation-invariant solutions for various GFs (both hierarchies) on delta-field configuration of Λ are obtained. In context of the continuity equation and open quantum field systems, an optical potential is briefly discussed. The mode coarse-graining growth functional for the WP action (WP functional) is analyzed. Based on this analysis, an approximation scheme is proposed for the generalized WP equation. With an optimized (Litim) regulator translation-invariant solutions for two-particle and four-particle amputated GFs from approximated WP hierarchy are found analytically. For Λ=0 these solutions are monotonic in each of the momentum variables. Full article
(This article belongs to the Special Issue Symmetry in Quantum Systems)
Article
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
Viewed by 660
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)
Show Figures

Figure 1

Article
The Spinor-Tensor Gravity of the Classical Dirac Field
Symmetry 2020, 12(7), 1124; https://doi.org/10.3390/sym12071124 - 06 Jul 2020
Cited by 1 | Viewed by 474
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)
Article
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
Cited by 8 | Viewed by 619
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 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)
Article
Representing Measurement as a Thermodynamic Symmetry Breaking
Symmetry 2020, 12(5), 810; https://doi.org/10.3390/sym12050810 - 13 May 2020
Cited by 5 | Viewed by 651
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)
Show Figures

Figure 1

Article
Quantum Computation and Measurements from an Exotic Space-Time R4
Symmetry 2020, 12(5), 736; https://doi.org/10.3390/sym12050736 - 05 May 2020
Cited by 1 | Viewed by 747
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-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)
Show Figures

Figure 1

Review

Jump to: Research

Review
Violation of the Time-Reversal and Particle-Hole Symmetries in Strongly Correlated Fermi Systems: A Review
Symmetry 2020, 12(10), 1596; https://doi.org/10.3390/sym12101596 - 25 Sep 2020
Viewed by 812
Abstract
In this review, we consider the time reversal T and particle-antiparticle C symmetries that, being most fundamental, can be violated at microscopic level by a weak interaction. The notable example here is from condensed matter, where strongly correlated Fermi systems like heavy-fermion metals [...] Read more.
In this review, we consider the time reversal T and particle-antiparticle C symmetries that, being most fundamental, can be violated at microscopic level by a weak interaction. The notable example here is from condensed matter, where strongly correlated Fermi systems like heavy-fermion metals and high Tc superconductors exhibit C and T symmetries violation due to so-called non-Fermi liquid (NFL) behavior. In these systems, tunneling differential conductivity (or resistivity) is a very sensitive tool to experimentally test the above symmetry break. When a strongly correlated Fermi system turns out to be near the topological fermion condensation quantum phase transition (FCQPT), it exhibits the NFL properties, so that the C symmetry breaks down, making the differential tunneling conductivity to be an asymmetric function of the bias voltage V. This asymmetry does not take place in normal metals, where Landau Fermi liquid (LFL) theory holds. Under the application of magnetic field, a heavy fermion metal transits to the LFL state, and σ(V) becomes symmetric function of V. These findings are in good agreement with experimental observations. We suggest that the same topological FCQPT underlies the baryon asymmetry in the Universe. We demonstrate that the most fundamental features of the nature are defined by its topological and symmetry properties. Full article
(This article belongs to the Special Issue Symmetry in Quantum Systems)
Show Figures

Figure 1

Back to TopTop