Symmetry

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44 pages, 1757 KB

Open AccessArticle

First-Order Axial Perturbation of the Reissner–Nordström Metric Against a Possible Parity-Violating Gravity Background

by Abhishek Rout and Brett Altschul

Symmetry 2026, 18(4), 560; https://doi.org/10.3390/sym18040560 - 25 Mar 2026

Viewed by 627

We study axial perturbations of Reissner–Nordström black holes within the general framework of parity-violating modified gravity theories. We derive the governing equations for a class of frame-dragging perturbations, focusing on the symmetry structure and radial dependence of the perturbed metric component, describing its [...] Read more.

We study axial perturbations of Reissner–Nordström black holes within the general framework of parity-violating modified gravity theories. We derive the governing equations for a class of frame-dragging perturbations, focusing on the symmetry structure and radial dependence of the perturbed metric component, describing its behavior across three distinct regions: near the singularity (

r \to 0

), between the inner and outer Reissner–Nordström horizons (

r_{-} < r < r_{+}

), and in the asymptotic exterior regime (

r \to \infty

). Using a combination of analytical and numerical methods, we analyze the solutions for varying black hole charge-to-mass ratios (

Q / M

) and angular momentum parameters (l). Key findings include the suppression of perturbations by the electromagnetic field for higher

Q / M

; the emergence of radial resonance-like behavior for specific l values; and a high degree of symmetry for solutions in the extremal limit (

Q / M \sim 1

), attributed to the AdS₂

\times S^{2}

near-horizon geometry. The WKB approximation is employed to study the high-l regime, revealing quantized radial resonance modes and singular behavior in the extremal limit. Additionally, we explore the role of boundary conditions and the possibility of a Chern–Simons field

Θ

as the source of the parity violation, showing that consistency and the behavior of the perturbations under time reversal demand a constant field (and thus no actually observable Chern–Simons effects) at leading order. These results provide a basis for further analysis of the stability and dynamical properties of charged black holes in parity-violating theories, with potential experimental signatures in gravitational wave observations. Full article

(This article belongs to the Special Issue Feature Papers in 'Physics' Section 2025)

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27 pages, 486 KB

Open AccessArticle

Symmetry-Based Perspectives on Hamiltonian Quantum Search Algorithms and Schrödinger’s Dynamics Between Orthogonal States

by Carlo Cafaro and James Schneeloch

Symmetry 2026, 18(3), 422; https://doi.org/10.3390/sym18030422 - 28 Feb 2026

Viewed by 336

Abstract

It is known that the continuous-time variant of Grover’s search algorithm is characterized by quantum search frameworks that are governed by stationary Hamiltonians, which result in search trajectories confined to the two-dimensional subspace of the complete Hilbert space formed by the source and [...] Read more.

It is known that the continuous-time variant of Grover’s search algorithm is characterized by quantum search frameworks that are governed by stationary Hamiltonians, which result in search trajectories confined to the two-dimensional subspace of the complete Hilbert space formed by the source and target states. Specifically, the search approach is ineffective when the source and target states are orthogonal. In this paper, we employ normalization, orthogonality, and energy limitations to demonstrate that it is unfeasible to breach time-optimality between orthogonal states with constant Hamiltonians when the evolution is limited to the two-dimensional space spanned by the initial and final states. Deviations from time-optimality for unitary evolutions between orthogonal states can only occur with time-dependent Hamiltonian evolutions or, alternatively, with constant Hamiltonian evolutions in higher-dimensional subspaces of the entire Hilbert space. Ultimately, we employ our quantitative analysis to provide meaningful insights regarding the relationship between time-optimal evolutions and analog quantum search methods. We determine that the challenge of transitioning between orthogonal states with a constant Hamiltonian in a sub-optimal time is closely linked to the shortcomings of analog quantum search when the source and target states are orthogonal and not interconnected by the search Hamiltonian. In both scenarios, the fundamental cause of the failure lies in the existence of an inherent symmetry within the system. Full article

(This article belongs to the Special Issue Feature Papers in 'Physics' Section 2025)

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10 pages, 319 KB

Open AccessArticle

Timing and Signal Amplitude Measurements in a Small EAS Array

by Tadeusz Wibig

Symmetry 2026, 18(2), 229; https://doi.org/10.3390/sym18020229 - 28 Jan 2026

Viewed by 326

Abstract

Small detector arrays, which are designed to record relatively small EAS with energy in the ‘knee’ region, are often equipped with clocks that measure the time difference between fast signals from several detectors, as well as spectrometric channels that provide the amplitudes of [...] Read more.

Small detector arrays, which are designed to record relatively small EAS with energy in the ‘knee’ region, are often equipped with clocks that measure the time difference between fast signals from several detectors, as well as spectrometric channels that provide the amplitudes of these signals. When analyzing them to determine the angles of arrival and the size of the registered showers, it is important to take into account uncertainties, i.e., the dispersion of measured time differences and shower size relative to the ‘true’ values, which are unknown in the actual situation. Analyses of these spreads are essentially only possible on the basis of correctly performed simulation calculations that take into account all possible stochastic processes in the development of showers in the atmosphere. In this paper, we present a simulation-based analysis using the CORSIKA program of a small EAS array model consisting of four charged particle detectors. We demonstrate the potential offered by ideal timing and how we can infer the energy of the primary particle by analyzing signal amplitudes. The analysis shows that the costs, not only financial, of introducing timing and shower spectrometry are not worth the potential physical gains that we can achieve by using them to analyse small showers. Full article

(This article belongs to the Special Issue Feature Papers in 'Physics' Section 2025)

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16 pages, 412 KB

Open AccessArticle

Noether Symmetries of Time-Dependent Damped Dynamical Systems: A Geometric Approach

by Michael Tsamparlis

Symmetry 2026, 18(2), 219; https://doi.org/10.3390/sym18020219 - 24 Jan 2026

Viewed by 377

Abstract

Finding Noether symmetries for time-dependent damped dynamical systems remains a significant challenge. This paper introduces a complete geometric algorithm for determining all Noether point symmetries and first integrals for the general class of Lagrangians

L = A (t) L_{0}

, [...] Read more.

Finding Noether symmetries for time-dependent damped dynamical systems remains a significant challenge. This paper introduces a complete geometric algorithm for determining all Noether point symmetries and first integrals for the general class of Lagrangians

L = A (t) L_{0}

, which model motion with general linear damping in a Riemannian space. We derive and prove a central Theorem that systematically links these symmetries to the homothetic algebra of the kinetic metric defined by

L_{0}

. The power of this method is demonstrated through a comprehensive analysis of the damped Kepler problem. Beyond recovering known results for constant damping, we discover new quadratic first integrals for time-dependent damping

ϕ (t) = γ / t

with

γ = - 1

and

γ = - 1 / 3

. We also include preliminary results on the Noether symmetries of the damped harmonic oscillator. Finally, we clarify why a time reparameterization that removes damping yields a physically inequivalent system with different Noether symmetries. This work provides a unified geometric framework for analyzing dissipative systems and reveals new integrable cases. Full article

(This article belongs to the Special Issue Feature Papers in 'Physics' Section 2025)

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29 pages, 1102 KB

Open AccessArticle

Formal Equivalence Between Maxwell Equations and the de Broglie–Bohm Theory for Two-Dimensional Optical Microcavities

by Aurélien Drezet and Bernard Michael Nabet

Symmetry 2026, 18(1), 157; https://doi.org/10.3390/sym18010157 - 14 Jan 2026

Cited by 1 | Viewed by 380

Abstract

We analyze the formal equivalence between the electromagnetic energy conservation law derived from Maxwell’s equations in an optical microcavity and the conservation of a probability fluid associated with the de Broglie–Bohm theory for an effective massive particle describing a photon in this cavity. [...] Read more.

We analyze the formal equivalence between the electromagnetic energy conservation law derived from Maxwell’s equations in an optical microcavity and the conservation of a probability fluid associated with the de Broglie–Bohm theory for an effective massive particle describing a photon in this cavity. This work is part of a critical analysis of recent experiments by Sharoglazova et al. carried out with a view to refuting the de Broglie–Bohm theory. Furthermore, the consequences of our analysis for microphotonics go far beyond these experiments. In particular, extensions that take into account photon spin and stochastic aspects associated with radiative or absorption losses are considered. From the point of view of symmetries and probability current, here the effective photon behaves like a spin-1/2 particle. Full article

(This article belongs to the Special Issue Feature Papers in 'Physics' Section 2025)

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8 pages, 740 KB

Open AccessArticle

Charged Particle Energization by Low-Amplitude Electrostatic Waves at Cyclotron Harmonics

by Fabio Sattin and Lorenzo Martinelli

Symmetry 2026, 18(1), 10; https://doi.org/10.3390/sym18010010 - 19 Dec 2025

Cited by 1 | Viewed by 408

Abstract

The system made by a charged particle interacting with a single electrostatic wave which propagates perpendicularly to the magnetic field, at a frequency larger than the cyclotron one, has been extensively studied in the literature due to its implications for ion heating in [...] Read more.

The system made by a charged particle interacting with a single electrostatic wave which propagates perpendicularly to the magnetic field, at a frequency larger than the cyclotron one, has been extensively studied in the literature due to its implications for ion heating in magnetized plasmas. It is known that a threshold in the electrostatic potential must be exceeded in order for stochastic particle motion and heating to occur. Regardless of its amplitude, however, the electrostatic wave induces a periodic oscillation in the particle motion. We show, by analytical and numerical arguments, that this dynamic is non-adiabatic, meaning that the particle does not land back in its initial state when the wave is slowly turned off. This way, particle energization (although not rigorous heating) occurs even under sub-threshold conditions. Full article

(This article belongs to the Special Issue Feature Papers in 'Physics' Section 2025)

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20 pages, 1554 KB

Open AccessArticle

Structure of Odd-A Ag Isotopes Studied via Algebraic Approaches

by Stanimir Kisyov and Stefan Lalkovski

Symmetry 2025, 17(8), 1276; https://doi.org/10.3390/sym17081276 - 8 Aug 2025

Viewed by 899

Abstract

The structure of the odd-A silver isotopes

{}^{103 - 115}{Ag}

is discussed within the frame of the interacting boson–fermion model (IBFM). An overview of their key properties is presented, with a particular attention paid to the “J-1 anomaly”, represented [...] Read more.

The structure of the odd-A silver isotopes

{}^{103 - 115}{Ag}

is discussed within the frame of the interacting boson–fermion model (IBFM). An overview of their key properties is presented, with a particular attention paid to the “J-1 anomaly”, represented by an abnormal ordering of the lowest

{7/2}^{+}

and

{9/2}^{+}

states. By examining previously published data and newly performed calculations, it is demonstrated that the experimentally known level schemes and electromagnetic properties of

{}^{103 - 115}{Ag}

can be reproduced well within IBFM-1 by using a consistent set of model parameters. The contribution of different single-particle orbitals to the structure of the lowest-lying excited nuclear states in

{}^{103 - 115}{Ag}

is discussed. Given that the J-1 anomaly brings down the

{7/2}^{+}

level from the

j^{- 3}

multiplet to energies, which can be thermally populated in hot stellar environments, the importance of low-lying excited states in odd-A silver isotopes for astrophysical processes is outlined. Full article

(This article belongs to the Special Issue Feature Papers in 'Physics' Section 2025)

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8 pages, 342 KB

Open AccessArticle

Should the Evolution of Our Universe Be Treated as an Initial Value Problem?

by Martin Tamm

Symmetry 2025, 17(8), 1258; https://doi.org/10.3390/sym17081258 - 7 Aug 2025

Cited by 1 | Viewed by 626

Abstract

In classical physics, the traditional way to handle dynamics is to work with initial value problems: Specifying all variables and their time-derivatives at a certain time will, together with the equations of motion, give the state of the system at any time. In [...] Read more.

In classical physics, the traditional way to handle dynamics is to work with initial value problems: Specifying all variables and their time-derivatives at a certain time will, together with the equations of motion, give the state of the system at any time. In this paper, it is questioned whether this is the right way to treat cosmology. The main reason is that cosmology, as opposed to almost all other parts of physics, deals with genuinely global problems. The main example in this paper will be the accelerating expansion. It is not claimed that the model studied here gives any kind of final explanation of this phenomenon. Nevertheless, it shows that what is commonly interpreted as the result of some dark energy, could instead be the result of a global condition for the universe. This model cannot be treated as a classical initial value problem. But an interesting additional property is that it can explain why the rate of acceleration now seems to be decreasing with time. Full article

(This article belongs to the Special Issue Feature Papers in 'Physics' Section 2025)

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13 pages, 302 KB

Open AccessArticle

Unveiling the Role of Vector Potential in the Aharonov–Bohm Effect

by Masashi Wakamatsu

Symmetry 2025, 17(6), 935; https://doi.org/10.3390/sym17060935 - 12 Jun 2025

Viewed by 2497

Abstract

The most popular interpretation of the Aharonov–Bohm (AB) effect is that the electromagnetic potential locally affects the complex phase of a charged particle’s wave function in the magnetic field free region. However, since the vector potential is a gauge-variant quantity, multiple researchers suspect [...] Read more.

The most popular interpretation of the Aharonov–Bohm (AB) effect is that the electromagnetic potential locally affects the complex phase of a charged particle’s wave function in the magnetic field free region. However, since the vector potential is a gauge-variant quantity, multiple researchers suspect that it is just a convenient tool for calculating the force field. This motivates them to explain the AB effect without using the vector potential, which inevitably leads to some sort of non-locality. This frustrating situation is shortly summarized by the statement by Aharonov et al. that the AB effect may be due to a local gauge potential or due to non-local gauge-invariant fields. In the present paper, we shall give several convincing arguments which support the viewpoint that the vector potential is not just a convenient mathematical tool with little physical entity. Despite its gauge arbitrariness, the vector potential certainly contains a gauge-invariant piece, which solely explains the observed AB phase shift. Importantly, this component has a property such that it is basically unique and cannot be eliminated by any regular gauge transformations. To complete the discussion, we also discuss the role of remaining gauge arbitrariness still contained in the entire vector potential. Full article

(This article belongs to the Special Issue Feature Papers in 'Physics' Section 2025)

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19 pages, 3412 KB

Open AccessArticle

Neutron Stars in the Theory of Gravity with Non-Minimal Derivative Coupling and Realistic Equations of State

by Pavel E. Kashargin, Alexander A. Lebedev and Sergey V. Sushkov

Symmetry 2025, 17(6), 910; https://doi.org/10.3390/sym17060910 - 9 Jun 2025

Viewed by 1820

Abstract

We numerically construct compact stars in the scalar–tensor theory of gravity with non-minimal derivative coupling of a scalar field to the curvature and nonzero cosmological constant. There are two free parameters in this model of gravity: the non-minimal derivative coupling parameter ℓ and [...] Read more.

We numerically construct compact stars in the scalar–tensor theory of gravity with non-minimal derivative coupling of a scalar field to the curvature and nonzero cosmological constant. There are two free parameters in this model of gravity: the non-minimal derivative coupling parameter ℓ and the cosmological constant parameter

ξ

. We study the relationship between the model parameters and characteristic of the neutron star, which allowed us to limit the permissible range of

ξ

and ℓ. In particular, in the case

ξ = - 1

, the external geometry of the neutron star coincides with the Schwarzschild–anti-de Sitter geometry, while the internal geometry of the star differs from the case of the standard gravity theory. Many realistic equations of the state of neutron star matter were considered. In general, the neutron star model in the theory of gravity with a non-minimal derivative coupling does not contradict astronomical data and is viable. Full article

(This article belongs to the Special Issue Feature Papers in 'Physics' Section 2025)

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