Research

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29 pages, 2758 KiB

Open AccessArticle

Vacuum Currents for a Scalar Field in Models with Compact Dimensions

by Aram A. Saharian

Symmetry 2024, 16(1), 92; https://doi.org/10.3390/sym16010092 - 11 Jan 2024

Viewed by 1037

This paper presents a review of investigations into the vacuum expectation value of the current density for a charged scalar field in spacetimes that hold toroidally compactified spatial dimensions. As background geometries, the locally Minkowskian (LM), locally de Sitter (LdS), and locally anti-de [...] Read more.

This paper presents a review of investigations into the vacuum expectation value of the current density for a charged scalar field in spacetimes that hold toroidally compactified spatial dimensions. As background geometries, the locally Minkowskian (LM), locally de Sitter (LdS), and locally anti-de Sitter (LAdS) spacetimes are considered. Along compact dimensions, quasi-periodicity conditions are imposed on the field operator and the presence of a constant gauge field is assumed. The vacuum current has nonzero components along the compact dimensions only. Those components are periodic functions of the magnetic flux enclosed in compact dimensions, with a period that is equal to the flux quantum. For LdS and LAdS geometries, and for small values of the length of a compact dimension, compared with the curvature radius, the leading term in the expansion of the the vacuum current along that dimension coincides with that for LM bulk. In this limit, the dominant contribution to the mode sum for the current density comes from the vacuum fluctuations with wavelengths smaller to those of the curvature radius; additionally, the influence of the gravitational field is weak. The effects of the gravitational field are essential for lengths of compact dimensions that are larger than the curvature radius. In particular, instead of the exponential suppression of the current density in LM bulk, one can obtain a power law decay in the LdS and LAdS spacetimes. Full article

(This article belongs to the Special Issue Physics and Symmetry Section: Feature Papers 2023)

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15 pages, 5176 KiB

Open AccessArticle

Asymmetries Caused by Nonparaxiality and Spin–Orbit Interaction during Light Propagation in a Graded-Index Medium

by Nikolai I. Petrov

Symmetry 2024, 16(1), 87; https://doi.org/10.3390/sym16010087 - 10 Jan 2024

Viewed by 638

Abstract

Spin–orbit coupling and nonparaxiality effects during the propagation of vortex vector light beams in a cylindrical graded-index waveguide are investigated by solving the full three-component field Maxwell’s equations. Symmetry-breaking effects for left- and right-handed circularly polarized vortex light beams propagating in a rotationally [...] Read more.

Spin–orbit coupling and nonparaxiality effects during the propagation of vortex vector light beams in a cylindrical graded-index waveguide are investigated by solving the full three-component field Maxwell’s equations. Symmetry-breaking effects for left- and right-handed circularly polarized vortex light beams propagating in a rotationally symmetric graded-index optical fiber are considered. The mode-group delay in a graded-index fiber due to spin–orbit interaction is demonstrated. A scheme for observing the temporal spin Hall effect is proposed. It is shown that the relative delay times between vortex pulses of opposite circular polarizations of the order of 10 ps/km can be observed in graded-index fibers for high-order topological charges. Full article

(This article belongs to the Special Issue Physics and Symmetry Section: Feature Papers 2023)

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17 pages, 550 KiB

Open AccessArticle

Spontaneous Emergence of a Causal Time Axis in Euclidean Space from a Gauged Rotational Symmetry Theory

by Michael Luke Walker

Symmetry 2024, 16(1), 4; https://doi.org/10.3390/sym16010004 - 19 Dec 2023

Viewed by 964

Abstract

We demonstrate the emergence of an effective “time” axis in the ground state of a gauged rotational symmetry theory in four-dimensional Euclidean space. In so doing, we remove the necessity of Wick rotation to Lorentz spacetime, an arbitrary and sometimes ill-defined procedure, especially [...] Read more.

We demonstrate the emergence of an effective “time” axis in the ground state of a gauged rotational symmetry theory in four-dimensional Euclidean space. In so doing, we remove the necessity of Wick rotation to Lorentz spacetime, an arbitrary and sometimes ill-defined procedure, especially for gravity-related theories. We begin by adapting the Cho-Duan-Ge decomposition to the gauge theory of the four-dimensional rotational symmetry group

S O (4)

, where it identifies the maximal Abelian subgroup

S O (2) \otimes S O (2)

in a gauge covariant manner. We then find the one-loop effective theory to have a stable condensate of monopoles corresponding to the reduction of

S O (4)

symmetry to

S O (2) \otimes S O (2)

. The construction of the condensate ensures that the four-dimensional spatial direction of its field strength must coincide with that of this embedding, and that a magnetic potential must be worked against to divert a trajectory away from this direction. Indeed, movement along this direction represents minimal potential energy. We take it to be the time direction. The gauge-dependent nature of the condensate is such that different gauge choices may lead to different time axes and we show on very general grounds that these different coordinate systems must be relatable by transformations of Lorentz form. Full article

(This article belongs to the Special Issue Physics and Symmetry Section: Feature Papers 2023)

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19 pages, 489 KiB

Open AccessArticle

Characterization of Quantum and Classical Critical Points for an Integrable Two-Qubit Spin–Boson Model

by Roberto Grimaudo, Antonino Messina, Hiromichi Nakazato, Alessandro Sergi and Davide Valenti

Symmetry 2023, 15(12), 2174; https://doi.org/10.3390/sym15122174 - 07 Dec 2023

Viewed by 1056

Abstract

The class of two-interacting-qubit spin–boson models with vanishing transverse fields on the spin-pair is studied. The model can be mapped exactly into two independent standard single-impurity spin–boson models where the role of the tunneling parameter is played by the spin–spin coupling. The dynamics [...] Read more.

The class of two-interacting-qubit spin–boson models with vanishing transverse fields on the spin-pair is studied. The model can be mapped exactly into two independent standard single-impurity spin–boson models where the role of the tunneling parameter is played by the spin–spin coupling. The dynamics of the magnetization are analyzed for different levels of (an)isotropy. The existence of a decoherence-free subspace, as well as of different classical regimes separated by a critical temperature, and symptoms of quantum (first-order and Kosterlitz–Thouless type) phase transitions in the Ohmic regime are brought to light. Full article

(This article belongs to the Special Issue Physics and Symmetry Section: Feature Papers 2023)

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40 pages, 611 KiB

Open AccessArticle

Covariant Cubic Interacting Vertices for Massless and Massive Integer Higher Spin Fields

by I. L. Buchbinder and A. A. Reshetnyak

Symmetry 2023, 15(12), 2124; https://doi.org/10.3390/sym15122124 - 28 Nov 2023

Cited by 8 | Viewed by 642

Abstract

We develop the BRST approach to construct the general off-shell local Lorentz covariant cubic interaction vertices for irreducible massless and massive higher spin fields on d-dimensional Minkowski space. We consider two different cases for interacting higher spin fields: with one massive and [...] Read more.

We develop the BRST approach to construct the general off-shell local Lorentz covariant cubic interaction vertices for irreducible massless and massive higher spin fields on d-dimensional Minkowski space. We consider two different cases for interacting higher spin fields: with one massive and two massless; two massive, both with coinciding and with different masses and one massless field of spins

s_{1}, s_{2}, s_{3}

. Unlike the previous results on cubic vertices we extend our earlier result in (Buchbinder, I.L.; et al. Phys. Lett. B 2021, 820, 136470) for massless fields and employ the complete BRST operator, including the trace constraints, which is used to formulate an irreducible representation with definite integer spin. We generalize the cubic vertices proposed for reducible higher spin fields in (Metsaev, R.R. Phys. Lett. B 2013, 720, 237) in the form of multiplicative and non-multiplicative BRST-closed constituents and calculate the new contributions to the vertex, which contains the additional terms with a smaller number of space-time derivatives. We prove that without traceless conditions for the cubic vertices in (Metsaev, R.R. Phys. Lett. B 2013, 720, 237) it is impossible to provide the noncontradictory Lagrangian dynamics and find explicit traceless solution for these vertices. As the examples, we explicitly construct the interacting Lagrangians for the massive spin of the s field and the massless scalars, both with and without auxiliary fields. The interacting models with different combinations of triples higher spin fields: massive spin s with massless scalar and vector fields and with two vector fields; massless helicity

λ

with massless scalar and massive vector fields; two massive fields of spins

s, 0

and massless scalar is also considered. Full article

(This article belongs to the Special Issue Physics and Symmetry Section: Feature Papers 2023)

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21 pages, 8222 KiB

Open AccessArticle

Ionospheric Global and Regional Electron Contents in Solar Cycles 23–25

by Yury Yasyukevich, Artem Padokhin, Artem Vesnin, Alexei Bykov, Alexander Kiselev, Alexander Ivanov and Anna Yasyukevich

Symmetry 2023, 15(10), 1940; https://doi.org/10.3390/sym15101940 - 19 Oct 2023

Cited by 1 | Viewed by 994

Abstract

The Earth’s ionosphere experiences forcing from above and below and varies in different periods. We analyzed the dynamics of the ionospheric global and regional electron contents (GEC and REC) in solar cycles 23/24 (SC23/SC24) and the first part of solar cycle 25 (SC25). [...] Read more.

The Earth’s ionosphere experiences forcing from above and below and varies in different periods. We analyzed the dynamics of the ionospheric global and regional electron contents (GEC and REC) in solar cycles 23/24 (SC23/SC24) and the first part of solar cycle 25 (SC25). We considered several methodological issues for GEC calculations and created a tool to compute GEC and made it available through SIMuRG (System for Ionosphere Monitoring and Research from GNSS). The paper shows the asymmetry of GEC dynamics in different solar cycles. The mid-latitude summer evening anomaly disrupted the diurnal REC variation in the Siberian region under solar minima. The mean GEC showed similar dependence on the F10.7 index in SC25 and SC23/SC24. The difference in solar cycles could prevent reliable forecasting for GEC for the next solar cycle. Our model, based on a neural network, could predict GEC dynamics in SC25 accurately when we input the F10.7 index. Full article

(This article belongs to the Special Issue Physics and Symmetry Section: Feature Papers 2023)

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10 pages, 309 KiB

Open AccessArticle

Kinetic Axion f(R) Gravity Phase Space

by Vasilis K. Oikonomou, Fotis P. Fronimos, Olga Razina and Pyotr Tsyba

Symmetry 2023, 15(10), 1897; https://doi.org/10.3390/sym15101897 - 10 Oct 2023

Viewed by 591

Abstract

In this work, we studied the phase space of

f (R)

gravity in the presence of a misalignment axion, including parity violating Chern–Simons terms. We construct the autonomous dynamical system by using appropriate dimensionless variables and find the cosmological attractors of [...] Read more.

In this work, we studied the phase space of

f (R)

gravity in the presence of a misalignment axion, including parity violating Chern–Simons terms. We construct the autonomous dynamical system by using appropriate dimensionless variables and find the cosmological attractors of the phase space, which are basically the fixed points of the autonomous dynamical system. We focus on the

R^{2}

model and the misalignment axion potential near the minimum. We demonstrate that the Chern–Simons terms have no effect on the phase space. We found four distinct, possibly unstable fixed points with physical significance. Specifically, we found two identical de Sitter fixed points, one radiation domination fixed point, and one dark matter dominated fixed point. Thus, in the presence of a kinetic misalignment axion, the vacuum

f (R)

gravity contains all of the cosmological fixed points that can characterize all of the known evolution eras of our universe. Full article

(This article belongs to the Special Issue Physics and Symmetry Section: Feature Papers 2023)

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16 pages, 14087 KiB

Open AccessArticle

A Novel Four-Dimensional Memristive Hyperchaotic Map Based on a Three-Dimensional Parabolic Chaotic Map with a Discrete Memristor

by Mengjiao Wang, Luyao Tong, Chunlai Li, Xinan Zhang, Herbert Ho-Ching Iu and Zhijun Li

Symmetry 2023, 15(10), 1879; https://doi.org/10.3390/sym15101879 - 06 Oct 2023

Cited by 1 | Viewed by 783

Abstract

Recently, the application of memristors in chaotic systems has been extensively studied. Unfortunately, there is limited literature on the introduction of discrete memristors into chaotic maps, especially into non-classical multidimensional maps. For this reason, this paper establishes a new three-dimensional parabolic chaotic map [...] Read more.

Recently, the application of memristors in chaotic systems has been extensively studied. Unfortunately, there is limited literature on the introduction of discrete memristors into chaotic maps, especially into non-classical multidimensional maps. For this reason, this paper establishes a new three-dimensional parabolic chaotic map model; in order to improve the complexity and randomness of the map, it is coupled with a square-charge-controlled discrete memristor to design a new four-dimensional memristive hyperchaotic map. Firstly, the stability of the two maps is discussed. And their dynamical properties are compared using Lyapunov exponential spectra and bifurcation diagrams. Then, the phase diagram and iteration sequence of the 4D memristive hyperchaotic map are obtained. Meanwhile, we investigate the hyperchaotic states, the transient chaos, state transfer and attractor coexistence phenomena of the four-dimensional memristive map. In particular, the special state transfer phenomenon of switching from a periodic attractor to a quasi-periodic attractor and the special coexistence phenomenon of a quasi-periodic attractor coexisting with a quasi-periodic attractor around fixed points are found, which have not been observed in other systems. Finally, the phase-track diagrams and iterative sequence diagrams of the four-dimensional memristive map are verified on a digital experimental platform, revealing its potential for practical applications. Full article

(This article belongs to the Special Issue Physics and Symmetry Section: Feature Papers 2023)

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17 pages, 2243 KiB

Open AccessArticle

Exact Solutions of the Oberbeck–Boussinesq Equations for the Description of Shear Thermal Diffusion of Newtonian Fluid Flows

by Sergey Ershkov, Natalya Burmasheva, Dmytro D. Leshchenko and Evgeniy Yu. Prosviryakov

Symmetry 2023, 15(9), 1730; https://doi.org/10.3390/sym15091730 - 08 Sep 2023

Cited by 4 | Viewed by 827

Abstract

We present a new exact solution of the thermal diffusion equations for steady-state shear flows of a binary fluid. Shear fluid flows are used in modeling and simulating large-scale currents of the world ocean, motions in thin layers of fluid, fluid flows in [...] Read more.

We present a new exact solution of the thermal diffusion equations for steady-state shear flows of a binary fluid. Shear fluid flows are used in modeling and simulating large-scale currents of the world ocean, motions in thin layers of fluid, fluid flows in processes, and apparatuses of chemical technology. To describe the steady shear flows of an incompressible fluid, the system of Navier–Stokes equations in the Boussinesq approximation is redefined, so the construction of exact and numerical solutions to the equations of hydrodynamics is a very difficult and urgent task. A non-trivial exact solution is constructed in the Lin-Sidorov-Aristov class. For this class of exact solutions, the hydrodynamic fields (velocity field, pressure field, temperature field, and solute concentration field) were considered as linear forms in the x and y coordinates. The coefficients of linear forms depend on the third coordinate z. Thus, when considering a shear flow, the two-dimensional velocity field depends on three coordinates. It is worth noting that the solvability condition given in the article imposes a condition (relation) only between the velocity gradients. A theorem on the uniqueness of the exact solution in the Lin–Sidorov–Aristov class is formulated. The remaining coefficients of linear forms for hydrodynamic fields have functional arbitrariness. To illustrate the exact solution of the overdetermined system of Oberbeck–Boussinesq equations, a boundary value problem was solved to describe the complex convection of a vertical swirling fluid without its preliminary rotation. It was shown that the velocity field is highly stratified. Complex countercurrents are recorded in the fluid. Full article

(This article belongs to the Special Issue Physics and Symmetry Section: Feature Papers 2023)

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Review

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29 pages, 396 KiB

Open AccessFeature PaperReview

Baryogenesis: A Symmetry Breaking in the Primordial Universe Revisited

by David S. Pereira, João Ferraz, Francisco S. N. Lobo and José P. Mimoso

Symmetry 2024, 16(1), 13; https://doi.org/10.3390/sym16010013 - 21 Dec 2023

Viewed by 1375

Abstract

In this review article, we revisit the topic of baryogenesis, which is the physical process that generated the observed baryon asymmetry during the first stages of the primordial Universe. A viable theoretical explanation to understand and investigate the mechanisms underlying baryogenesis must always [...] Read more.

In this review article, we revisit the topic of baryogenesis, which is the physical process that generated the observed baryon asymmetry during the first stages of the primordial Universe. A viable theoretical explanation to understand and investigate the mechanisms underlying baryogenesis must always ensure that the Sakharov criteria are fulfilled. These essentially state the following: (i) baryon number violation; (ii) the violation of both C (charge conjugation symmetry) and CP (the composition of parity and C); (iii) and the departure from equilibrium. Throughout the years, various mechanisms have been proposed to address this issue, and here we review two of the most important, namely, electroweak baryogenesis (EWB) and Grand Unification Theories (GUTs) baryogenesis. Furthermore, we briefly explore how a change in the theory of gravity affects the EWB and GUT baryogenesis by considering Scalar–Tensor Theories (STT), where the inclusion of a scalar field mediates the gravitational interaction, in addition to the metric tensor field. We consider specific STT toy models and show that a modification of the underlying gravitational theory implies a change in the time–temperature relation of the evolving cosmological model, thus altering the conditions that govern the interplay between the rates of the interactions generating baryon asymmetry, and the expansion rate of the Universe. Therefore, the equilibrium of the former does not exactly occur as in the general relativistic standard model, and there are consequences for the baryogenesis mechanisms that have been devised. This is representative of the type of modifications of the baryogenesis processes that are to be found when considering extended theories of gravity. Full article

(This article belongs to the Special Issue Physics and Symmetry Section: Feature Papers 2023)

18 pages, 6159 KiB

Open AccessReview

Systematically Constructing Mesoscopic Quantum States Relevant to Periodic Orbits in Integrable Billiards from Directionally Resolved Level Distributions

by Yung-Fu Chen, Song-Qing Lin, Ru-Wei Chang, Yan-Ting Yu and Hsing-Chih Liang

Symmetry 2023, 15(10), 1809; https://doi.org/10.3390/sym15101809 - 22 Sep 2023

Cited by 1 | Viewed by 843

Abstract

Two-dimensional quantum billiards are one of the most important paradigms for exploring the connection between quantum and classical worlds. Researchers are mainly focused on nonintegrable and irregular shapes to understand the quantum characteristics of chaotic billiards. The emergence of the scarred modes relevant [...] Read more.

Two-dimensional quantum billiards are one of the most important paradigms for exploring the connection between quantum and classical worlds. Researchers are mainly focused on nonintegrable and irregular shapes to understand the quantum characteristics of chaotic billiards. The emergence of the scarred modes relevant to unstable periodic orbits (POs) is one intriguing finding in nonintegrable quantum billiards. On the other hand, stable POs are abundant in integrable billiards. The quantum wavefunctions associated with stable POs have been shown to play a key role in ballistic transport. A variety of physical systems, such as microwave cavities, optical fibers, optical resonators, vibrating plates, acoustic waves, and liquid surface waves, are used to analogously simulate the wave properties of quantum billiards. This article gives a comprehensive review for the subtle connection between the quantum level clustering and the classical POs for three integrable billiards including square, equilateral triangle, and circular billiards. Full article

(This article belongs to the Special Issue Physics and Symmetry Section: Feature Papers 2023)

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69 pages, 819 KiB

Open AccessFeature PaperReview

Recent Advances in Inflation

by Sergei D. Odintsov, Vasilis K. Oikonomou, Ifigeneia Giannakoudi, Fotis P. Fronimos and Eirini C. Lymperiadou

Symmetry 2023, 15(9), 1701; https://doi.org/10.3390/sym15091701 - 05 Sep 2023

Cited by 66 | Viewed by 3354

Abstract

We review recent trends in inflationary dynamics in the context of viable modified gravity theories. After providing a general overview of the inflationary paradigm emphasizing on what problems hot Big Bang theory inflation solves, and a somewhat introductory presentation of single-field inflationary theories [...] Read more.

We review recent trends in inflationary dynamics in the context of viable modified gravity theories. After providing a general overview of the inflationary paradigm emphasizing on what problems hot Big Bang theory inflation solves, and a somewhat introductory presentation of single-field inflationary theories with minimal and non-minimal couplings, we review how inflation can be realized in terms of several string-motivated models of inflation, which involve Gauss–Bonnet couplings of the scalar field, higher-order derivatives of the scalar field, and some subclasses of viable Horndeski theories. We also present and analyze inflation in the context of Chern–Simons theories of gravity, including various subcases and generalizations of string-corrected modified gravities, which also contain Chern–Simons correction terms, with the scalar field being identified with the invisible axion, which is the most viable to date dark matter candidate. We also provide a detailed account of vacuum

f (R)

gravity inflation, and also inflation in

f (R, ϕ)

and kinetic-corrected

f (R, ϕ)

theories of gravity. At the end of the review, we discuss the technique for calculating the overall effect of modified gravity on the waveform of the standard general relativistic gravitational wave form. Full article

(This article belongs to the Special Issue Physics and Symmetry Section: Feature Papers 2023)

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