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Symmetry
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Symmetry in Many-Body Physics
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Symmetry in Many-Body Physics

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

Deadline for manuscript submissions: closed (31 August 2022) | Viewed by 27674

Printed Edition Available!
A printed edition of this Special Issue is available here.

Special Issue Editors

Prof. V.I. Yukalov

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Guest Editor
Bogolubov Laboratory of Theoretical Physics,Joint Institute for Nuclear Research, 141980 Dubna, Russia
Interests: statistical physics; phase transitions; coherent phenomena; nonlinear processes; complex systems; mathematical methods
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. V. S. Bagnato

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Guest Editor
Instituto de Fisica de Sao Carlos, Universidade de Sao Paulo, CP 369, Sao Carlos 13560-970, SP, Brazil
Interests: Bose-Einstein condensation; trapped atoms; turbulence
Special Issues, Collections and Topics in MDPI journals
Dr. Rashid G. Nazmitdinov

E-Mail Website
Guest Editor
Bogolubov Laboratory of Theoretical Physics, Joint Institute for Nuclear Research, 141980 Dubna, Russia
Interests: transport in nanostructures; graphene; random matrix approach; nuclear structure
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear colleagues,

The harmony of nature is expressed through the implementation of symmetry providing optimal structures for complex systems from snowflakes to graphene lattices. Sometimes nature breaks symmetry, as it happens in a sugar molecule, in the case of the predominance of people with heart on the left side, or in various phase transitions. Symmetry plays a crucial role in many-body physics. For instance, chiral symmetry is important in unusual properties of graphene and in the theory of strong interactions. Symmetry breaking and restoration constantly happens in the world around us.

Usually, finding exact solutions to the problem of interacting particles presents a fundamental challenge. Therefore, we have to restrict ourselves to approximate solutions that reflect the essential features of the entire problem as a whole and contain an indication of the range of applicability of these solutions. An important role in finding approximate solutions is played by the knowledge of basic symmetries that determine the accuracy of the used approximations.

The purpose of this issue is to demonstrate the principal role of exact and approximate symmetries in solving various problems of many-particle physics, as well as in finding approximate solutions for the systems typical of condensed matter, trapped Fermi and Bose gases, nuclear matter, and field theory.

Prof. V.I. Yukalov
Prof. V. S. Bagnato
Dr. R.G. Nazmitdinov
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 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

  • graphene
  • nonlinear transport
  • symmetry in nuclei
  • chiral symmetry
  • gauge symmetry
  • scaling symmetry
  • fractals
  • symmetry breaking and restoration
  • local symmetry
  • coexistence of different symmetries
  • mesoscopic symmetry fluctuations

Published Papers (15 papers)

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Editorial

Jump to: Research, Review

5 pages, 192 KiB  
Editorial
Symmetry in Many-Body Physics
by Vanderlei S. Bagnato, Rashid G. Nazmitdinov and Vyacheslav I. Yukalov
Symmetry 2023, 15(1), 72; https://0-doi-org.brum.beds.ac.uk/10.3390/sym15010072 - 27 Dec 2022
Cited by 1 | Viewed by 1201
Abstract
The harmony of nature is expressed through the implementation of symmetry providing optimal structures for complex systems from snowflakes to graphene lattices [...] Full article
(This article belongs to the Special Issue Symmetry in Many-Body Physics)

Research

Jump to: Editorial, Review

9 pages, 536 KiB  
Article
Long-Time Bit Storage and Retrieval without Cold Atom Technology
by Richard Friedberg and Jamal T. Manassah
Symmetry 2022, 14(8), 1505; https://0-doi-org.brum.beds.ac.uk/10.3390/sym14081505 - 22 Jul 2022
Cited by 1 | Viewed by 967
Abstract
We report computer studies showing how the duration of memory for storage and retrieval of a classical bit can be increased to 100 times the decay time of an isolated atom, with no use of high-tech cold-atom preparations recently developed in the light-matter [...] Read more.
We report computer studies showing how the duration of memory for storage and retrieval of a classical bit can be increased to 100 times the decay time of an isolated atom, with no use of high-tech cold-atom preparations recently developed in the light-matter field. We suggest that our low-tech procedure can greatly enlarge the number of experimenters able to enter this field. The role of symmetry in this procedure arises in a careful interplay of incoherent and coherent excitations of a large collection of “two-level” atoms, the level separation being matched by the dominant frequency of the electromagnetic fields (short pulses and continuing field) applied to the system. Full article
(This article belongs to the Special Issue Symmetry in Many-Body Physics)
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11 pages, 343 KiB  
Article
Spin Interference Effects in a Ring with Rashba Spin-Orbit Interaction Subject to Strong Light–Matter Coupling in Magnetic Field
by Michal Pudlak and R. Nazmitdinov
Symmetry 2022, 14(6), 1194; https://0-doi-org.brum.beds.ac.uk/10.3390/sym14061194 - 09 Jun 2022
Cited by 2 | Viewed by 1354
Abstract
Electron transport through a one-dimensional quantum ring, subjected to Rashba spin–orbit interaction and connected with two external leads, is studied in the presence of external fields. They include the optical radiation, produced by an off-resonant high-frequency electric field, and a perpendicular magnetic field. [...] Read more.
Electron transport through a one-dimensional quantum ring, subjected to Rashba spin–orbit interaction and connected with two external leads, is studied in the presence of external fields. They include the optical radiation, produced by an off-resonant high-frequency electric field, and a perpendicular magnetic field. By means of the Floquet theory of periodically driven quantum systems the interference effects under these fields are described in detail. It is found analytically the specific conditions to reach the spin-filtering effect, caused by the interplay of the external fields and Rashba spin-orbit interaction. Full article
(This article belongs to the Special Issue Symmetry in Many-Body Physics)
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17 pages, 3548 KiB  
Article
Formation of Matter-Wave Droplet Lattices in Multi-Color Periodic Confinements
by Maitri R. Pathak and Ajay Nath
Symmetry 2022, 14(5), 963; https://0-doi-org.brum.beds.ac.uk/10.3390/sym14050963 - 09 May 2022
Cited by 2 | Viewed by 1392
Abstract
In the paper, we introduce a new model that addresses the generation of quantum droplets (QDs) in the binary Bose–Einstein condensate (BEC) mixture with mutually symmetric spinor components loaded in multi-color optical lattices (MOLs) of commensurate wavelengths and tunable intensities. The considered MOL [...] Read more.
In the paper, we introduce a new model that addresses the generation of quantum droplets (QDs) in the binary Bose–Einstein condensate (BEC) mixture with mutually symmetric spinor components loaded in multi-color optical lattices (MOLs) of commensurate wavelengths and tunable intensities. The considered MOL confinement is the combination of the four-color optical lattice with an exponential periodic trap, which includes the complete set of the Fourier harmonics. Employing the one-dimensional (1D) extended Gross–Pitäevskii equation (eGPE), we calculate the exact analytical form of the wavefunction, MF/BMF nonlinearities, and MOL trap parameters. Utilizing the exact solutions, the formation of supersolid-like spatially periodic matter-wave droplet lattices and superlattices is illustrated under the space-periodic nonlinearity management. The precise positioning of the density maxima/minima of the droplet patterns at the center of the trap and tunable Anderson-like localization are observed by tuning the symmetry and amplitude of the considered MOL trap. The stability of the obtained solution is confirmed using the Vakhitov–Kolokolov (VK) criterion. Full article
(This article belongs to the Special Issue Symmetry in Many-Body Physics)
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12 pages, 579 KiB  
Article
Josephson-like Oscillations in Toroidal Spinor Bose–Einstein Condensates: A Prospective Symmetry Probe
by Mário H. Figlioli Donato and Sérgio R. Muniz
Symmetry 2022, 14(5), 867; https://0-doi-org.brum.beds.ac.uk/10.3390/sym14050867 - 23 Apr 2022
Cited by 1 | Viewed by 3427
Abstract
Josephson junctions are essential ingredients in the superconducting circuits used in many existing quantum technologies. Additionally, ultracold atomic quantum gases have also become essential platforms to study superfluidity. Here, we explore the analogy between superconductivity and superfluidity to present an intriguing effect caused [...] Read more.
Josephson junctions are essential ingredients in the superconducting circuits used in many existing quantum technologies. Additionally, ultracold atomic quantum gases have also become essential platforms to study superfluidity. Here, we explore the analogy between superconductivity and superfluidity to present an intriguing effect caused by a thin finite barrier in a quasi-one-dimensional toroidal spinor Bose–Einstein condensate (BEC). In this system, the atomic current density flowing through the edges of the barrier oscillates, such as the electrical current through a Josephson junction in a superconductor, but in our case, there is no current circulation through the barrier. We also show how the nontrivial broken-symmetry states of spinor BECs change the structure of this Josephson-like current, creating the possibility to probe the spinor symmetry, solely using measurements of this superfluid current. Full article
(This article belongs to the Special Issue Symmetry in Many-Body Physics)
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13 pages, 3277 KiB  
Article
Spontaneous Symmetry Breaking: The Case of Crazy Clock and Beyond
by Maja C. Pagnacco, Jelena P. Maksimović, Marko Daković, Bojana Bokic, Sébastien R. Mouchet, Thierry Verbiest, Yves Caudano and Branko Kolaric
Symmetry 2022, 14(2), 413; https://0-doi-org.brum.beds.ac.uk/10.3390/sym14020413 - 19 Feb 2022
Cited by 4 | Viewed by 2147
Abstract
In this work, we describe the crazy-clock phenomenon involving the state I (low iodide and iodine concentration) to state II (high iodide and iodine concentration with new iodine phase) transition after a Briggs–Rauscher (BR) oscillatory process. While the BR crazy-clock phenomenon is known, [...] Read more.
In this work, we describe the crazy-clock phenomenon involving the state I (low iodide and iodine concentration) to state II (high iodide and iodine concentration with new iodine phase) transition after a Briggs–Rauscher (BR) oscillatory process. While the BR crazy-clock phenomenon is known, this is the first time that crazy-clock behavior is linked and explained with the symmetry-breaking phenomenon, highlighting the entire process in a novel way. The presented phenomenon has been thoroughly investigated by running more than 60 experiments, and evaluated by using statistical cluster K-means analysis. The mixing rate, as well as the magnetic bar shape and dimensions, have a strong influence on the transition appearance. Although the transition for both mixing and no-mixing conditions are taking place completely randomly, by using statistical cluster analysis we obtain different numbers of clusters (showing the time-domains where the transition is more likely to occur). In the case of stirring, clusters are more compact and separated, revealed new hidden details regarding the chemical dynamics of nonlinear processes. The significance of the presented results is beyond oscillatory reaction kinetics since the described example belongs to the small class of chemical systems that shows intrinsic randomness in their response and it might be considered as a real example of a classical liquid random number generator. Full article
(This article belongs to the Special Issue Symmetry in Many-Body Physics)
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9 pages, 1158 KiB  
Article
Exact Solutions for Solitary Waves in a Bose-Einstein Condensate under the Action of a Four-Color Optical Lattice
by Barun Halder, Suranjana Ghosh, Pradosh Basu, Jayanta Bera, Boris Malomed and Utpal Roy
Symmetry 2022, 14(1), 49; https://0-doi-org.brum.beds.ac.uk/10.3390/sym14010049 - 31 Dec 2021
Cited by 11 | Viewed by 1700
Abstract
We address dynamics of Bose-Einstein condensates (BECs) loaded into a one-dimensional four-color optical lattice (FOL) potential with commensurate wavelengths and tunable intensities. This configuration lends system-specific symmetry properties. The analysis identifies specific multi-parameter forms of the FOL potential which admits exact solitary-wave solutions. [...] Read more.
We address dynamics of Bose-Einstein condensates (BECs) loaded into a one-dimensional four-color optical lattice (FOL) potential with commensurate wavelengths and tunable intensities. This configuration lends system-specific symmetry properties. The analysis identifies specific multi-parameter forms of the FOL potential which admits exact solitary-wave solutions. This newly found class of potentials includes more particular species, such as frustrated double-well superlattices, and bichromatic and three-color lattices, which are subject to respective symmetry constraints. Our exact solutions provide options for controllable positioning of density maxima of the localized patterns, and tunable Anderson-like localization in the frustrated potential. A numerical analysis is performed to establish dynamical stability and structural stability of the obtained solutions, which makes them relevant for experimental realization. The newly found solutions offer applications to the design of schemes for quantum simulations and processing quantum information. Full article
(This article belongs to the Special Issue Symmetry in Many-Body Physics)
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18 pages, 991 KiB  
Article
Zeroth-Order Nucleation Transition under Nanoscale Phase Separation
by Vyacheslav I. Yukalov and Elizaveta P. Yukalova
Symmetry 2021, 13(12), 2379; https://0-doi-org.brum.beds.ac.uk/10.3390/sym13122379 - 09 Dec 2021
Cited by 3 | Viewed by 1800
Abstract
Materials with nanoscale phase separation are considered. A system representing a heterophase mixture of ferromagnetic and paramagnetic phases is studied. After averaging over phase configurations, a renormalized Hamiltonian is derived describing the coexisting phases. The system is characterized by direct and exchange interactions [...] Read more.
Materials with nanoscale phase separation are considered. A system representing a heterophase mixture of ferromagnetic and paramagnetic phases is studied. After averaging over phase configurations, a renormalized Hamiltonian is derived describing the coexisting phases. The system is characterized by direct and exchange interactions and an external magnetic field. The properties of the system are studied numerically. The stability conditions define the stable state of the system. At a temperature of zero, the system is in a pure ferromagnetic state. However, at finite temperature, for some interaction parameters, the system can exhibit a zeroth-order nucleation transition between the pure ferromagnetic phase and the mixed state with coexisting ferromagnetic and paramagnetic phases. At the nucleation transition, the finite concentration of the paramagnetic phase appears via a jump. Full article
(This article belongs to the Special Issue Symmetry in Many-Body Physics)
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11 pages, 12617 KiB  
Article
Small-Angle Scattering from Fractional Brownian Surfaces
by Eugen Mircea Anitas
Symmetry 2021, 13(11), 2042; https://0-doi-org.brum.beds.ac.uk/10.3390/sym13112042 - 30 Oct 2021
Cited by 1 | Viewed by 1122
Abstract
Recent developments in nanotechnology have allowed the fabrication of a new generation of advanced materials with various fractal-like geometries. Fractional Brownian surfaces (fBs) are often used as models to simulate and characterize these complex geometries, such as the surface of particles in dilute [...] Read more.
Recent developments in nanotechnology have allowed the fabrication of a new generation of advanced materials with various fractal-like geometries. Fractional Brownian surfaces (fBs) are often used as models to simulate and characterize these complex geometries, such as the surface of particles in dilute particulate systems (e.g., colloids) or the interfaces in non-particulate two-phase systems (e.g., semicrystalline polymers with crystalline and amorphous phases). However, for such systems, a realistic simulation involves parameters averaged over a macroscopic volume. Here, a method based on small-angle scattering technique is proposed to extract the main structural parameters of surfaces/interfaces from experimental data. It involves the analysis of scattering intensities and the corresponding pair distance distribution functions. This allows the extraction of information with respect to the overall size, fractal dimension, Hurst and spectral exponents. The method is applied to several classes of fBs, and it is shown that the obtained numerical values of the structural parameters are in very good agreement with theoretical ones. Full article
(This article belongs to the Special Issue Symmetry in Many-Body Physics)
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12 pages, 3390 KiB  
Article
Characteristic Length Scale during the Time Evolution of a Turbulent Bose-Einstein Condensate
by Lucas Madeira, Arnol D. García-Orozco, Michelle A. Moreno-Armijos, Francisco Ednilson Alves dos Santos and Vanderlei S. Bagnato
Symmetry 2021, 13(10), 1865; https://0-doi-org.brum.beds.ac.uk/10.3390/sym13101865 - 03 Oct 2021
Cited by 1 | Viewed by 1569
Abstract
Quantum turbulence is characterized by many degrees of freedom interacting non-linearly to produce disordered states, both in space and in time. In this work, we investigate the decaying regime of quantum turbulence in a trapped Bose-Einstein condensate. We present an alternative way of [...] Read more.
Quantum turbulence is characterized by many degrees of freedom interacting non-linearly to produce disordered states, both in space and in time. In this work, we investigate the decaying regime of quantum turbulence in a trapped Bose-Einstein condensate. We present an alternative way of exploring this phenomenon by defining and computing a characteristic length scale, which possesses relevant characteristics to study the establishment of the quantum turbulent regime. We reconstruct the three-dimensional momentum distributions with the inverse Abel transform, as we have done successfully in other works. We present our analysis with both the two- and three-dimensional momentum distributions, discussing their similarities and differences. We argue that the characteristic length allows us to intuitively visualize the time evolution of the turbulent state. Full article
(This article belongs to the Special Issue Symmetry in Many-Body Physics)
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10 pages, 389 KiB  
Article
Probing Many-Body Systems near Spectral Degeneracies
by Klaus Ziegler
Symmetry 2021, 13(10), 1796; https://0-doi-org.brum.beds.ac.uk/10.3390/sym13101796 - 26 Sep 2021
Cited by 2 | Viewed by 1226
Abstract
The diagonal elements of the time correlation matrix are used to probe closed quantum systems that are measured at random times. This enables us to extract two distinct parts of the quantum evolution, a recurrent part and an exponentially decaying part. This separation [...] Read more.
The diagonal elements of the time correlation matrix are used to probe closed quantum systems that are measured at random times. This enables us to extract two distinct parts of the quantum evolution, a recurrent part and an exponentially decaying part. This separation is strongly affected when spectral degeneracies occur, for instance, in the presence of spontaneous symmetry breaking. Moreover, the slowest decay rate is determined by the smallest energy level spacing, and this decay rate diverges at the spectral degeneracies. Probing the quantum evolution with the diagonal elements of the time correlation matrix is discussed as a general concept and tested in the case of a bosonic Josephson junction. It reveals for the latter characteristic properties at the transition to Hilbert-space localization. Full article
(This article belongs to the Special Issue Symmetry in Many-Body Physics)
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16 pages, 1472 KiB  
Article
Morphology of an Interacting Three-Dimensional Trapped Bose–Einstein Condensate from Many-Particle Variance Anisotropy
by Ofir E. Alon
Symmetry 2021, 13(7), 1237; https://0-doi-org.brum.beds.ac.uk/10.3390/sym13071237 - 09 Jul 2021
Cited by 2 | Viewed by 2630
Abstract
The variance of the position operator is associated with how wide or narrow a wave-packet is, the momentum variance is similarly correlated with the size of a wave-packet in momentum space, and the angular-momentum variance quantifies to what extent a wave-packet is non-spherically [...] Read more.
The variance of the position operator is associated with how wide or narrow a wave-packet is, the momentum variance is similarly correlated with the size of a wave-packet in momentum space, and the angular-momentum variance quantifies to what extent a wave-packet is non-spherically symmetric. We examine an interacting three-dimensional trapped Bose–Einstein condensate at the limit of an infinite number of particles, and investigate its position, momentum, and angular-momentum anisotropies. Computing the variances of the three Cartesian components of the position, momentum, and angular-momentum operators we present simple scenarios where the anisotropy of a Bose–Einstein condensate is different at the many-body and mean-field levels of theory, despite having the same many-body and mean-field densities per particle. This suggests a way to classify correlations via the morphology of 100% condensed bosons in a three-dimensional trap at the limit of an infinite number of particles. Implications are briefly discussed. Full article
(This article belongs to the Special Issue Symmetry in Many-Body Physics)
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5 pages, 207 KiB  
Article
Acoustic Plasmons in Graphene Sandwiched between Two Metallic Slabs
by Luca Salasnich
Symmetry 2021, 13(4), 684; https://0-doi-org.brum.beds.ac.uk/10.3390/sym13040684 - 15 Apr 2021
Cited by 2 | Viewed by 1280
Abstract
We study the effect of two metallic slabs on the collective dynamics of electrons in graphene positioned between the two slabs. We show that if the slabs are perfect conductors, the plasmons of graphene display a linear dispersion relation. The velocity of these [...] Read more.
We study the effect of two metallic slabs on the collective dynamics of electrons in graphene positioned between the two slabs. We show that if the slabs are perfect conductors, the plasmons of graphene display a linear dispersion relation. The velocity of these acoustic plasmons crucially depends on the distance between the two metal gates and the graphene sheet. In the case of generic slabs, the dispersion relation of graphene plasmons is much more complicated, but we find that acoustic plasmons can still be obtained under specific conditions. Full article
(This article belongs to the Special Issue Symmetry in Many-Body Physics)

Review

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11 pages, 1137 KiB  
Review
Non-Thermal Fixed Points in Bose Gas Experiments
by Lucas Madeira and Vanderlei S. Bagnato
Symmetry 2022, 14(4), 678; https://0-doi-org.brum.beds.ac.uk/10.3390/sym14040678 - 25 Mar 2022
Cited by 2 | Viewed by 1879
Abstract
One of the most challenging tasks in physics has been understanding the route an out-of-equilibrium system takes to its thermalized state. This problem can be particularly overwhelming when one considers a many-body quantum system. However, several recent theoretical and experimental studies have indicated [...] Read more.
One of the most challenging tasks in physics has been understanding the route an out-of-equilibrium system takes to its thermalized state. This problem can be particularly overwhelming when one considers a many-body quantum system. However, several recent theoretical and experimental studies have indicated that some far-from-equilibrium systems display universal dynamics when close to a so-called non-thermal fixed point (NTFP), following a rescaling of both space and time. This opens up the possibility of a general framework for studying and categorizing out-of-equilibrium phenomena into well-defined universality classes. This paper reviews the recent advances in observing NTFPs in experiments involving Bose gases. We provide a brief introduction to the theory behind this universal scaling, focusing on experimental observations of NTFPs. We present the benefits of NTFP universality classes by analogy with renormalization group theory in equilibrium critical phenomena. Full article
(This article belongs to the Special Issue Symmetry in Many-Body Physics)
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18 pages, 2114 KiB  
Review
A Review of Many-Body Interactions in Linear and Nonlinear Plasmonic Nanohybrids
by Mahi R. Singh
Symmetry 2021, 13(3), 445; https://0-doi-org.brum.beds.ac.uk/10.3390/sym13030445 - 09 Mar 2021
Cited by 5 | Viewed by 1695
Abstract
In this review article, we discuss the many-body interactions in plasmonic nanohybrids made of an ensemble of quantum emitters and metallic nanoparticles. A theory of the linear and nonlinear optical emission intensity was developed by using the many-body quantum mechanical density matrix method. [...] Read more.
In this review article, we discuss the many-body interactions in plasmonic nanohybrids made of an ensemble of quantum emitters and metallic nanoparticles. A theory of the linear and nonlinear optical emission intensity was developed by using the many-body quantum mechanical density matrix method. The ensemble of quantum emitters and metallic nanoparticles interact with each other via the dipole-dipole interaction. Surfaces plasmon polaritons are located near to the surface of the metallic nanoparticles. We showed that the nonlinear Kerr intensity enhances due to the weak dipole-dipole coupling limits. On the other hand, in the strong dipole-dipole coupling limit, the single peak in the Kerr intensity splits into two peaks. The splitting of the Kerr spectrum is due to the creation of dressed states in the plasmonic nanohybrids within the strong dipole-dipole interaction. Further, we found that the Kerr nonlinearity is also enhanced due to the interaction between the surface plasmon polaritons and excitons of the quantum emitters. Next, we predicted the spontaneous decay rates are enhanced due to the dipole-dipole coupling. The enhancement of the Kerr intensity due to the surface plasmon polaritons can be used to fabricate nanosensors. The splitting of one peak (ON) two peaks (OFF) can be used to fabricate the nanoswitches for nanotechnology and nanomedical applications. Full article
(This article belongs to the Special Issue Symmetry in Many-Body Physics)
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