Pub Date : 2026-02-01Epub Date: 2025-12-03DOI: 10.1016/j.aop.2025.170292
S. Baid , A. Lahbas , M. Oulne
We extend our previously developed approach combining an energy-dependent Davidson potential with deformation-dependent mass formalism from -unstable to axially symmetric prolate-deformed nuclei within the Bohr Hamiltonian. The model is applied to analyze the collective properties of 62 nuclei (13 actinides and 49 rare earth nuclei). The theoretical framework employs four adjustable parameters that are optimized through least-squares fitting to experimental energy levels. Particular attention is given to the N = 90 isotones (150Nd, 152Sm, 154Gd, and 156Dy), which are considered the best candidates of X(5) critical point symmetry. Our results demonstrate significant improvements over previous approaches, particularly in addressing the overestimation of -band level spacings characteristic of the traditional Davidson potential. Analysis of effective potentials reveals distinctive signatures of criticality through deeper potential wells for 0 states and enhanced separation between the ground and band-head state minima. The model also provides satisfactory predictions for B(E2) transition ratios, though with a tendency to overestimate interband transitions. These results suggest that the combination of energy dependence and deformation-dependent mass offers a more comprehensive framework for describing nuclear collective properties in transitional regions.
{"title":"Vibrational and rotational excited states within a Bohr Hamiltonian with energy-dependent Davidson potential and deformation-dependent mass formalisms","authors":"S. Baid , A. Lahbas , M. Oulne","doi":"10.1016/j.aop.2025.170292","DOIUrl":"10.1016/j.aop.2025.170292","url":null,"abstract":"<div><div>We extend our previously developed approach combining an energy-dependent Davidson potential with deformation-dependent mass formalism from <span><math><mi>γ</mi></math></span>-unstable to axially symmetric prolate-deformed nuclei within the Bohr Hamiltonian. The model is applied to analyze the collective properties of 62 nuclei (13 actinides and 49 rare earth nuclei). The theoretical framework employs four adjustable parameters that are optimized through least-squares fitting to experimental energy levels. Particular attention is given to the N = 90 isotones (<sup>150</sup>Nd, <sup>152</sup>Sm, <sup>154</sup>Gd, and <sup>156</sup>Dy), which are considered the best candidates of X(5) critical point symmetry. Our results demonstrate significant improvements over previous approaches, particularly in addressing the overestimation of <span><math><mi>β</mi></math></span>-band level spacings characteristic of the traditional Davidson potential. Analysis of effective potentials reveals distinctive signatures of criticality through deeper potential wells for 0<span><math><msubsup><mrow></mrow><mrow><mi>β</mi></mrow><mrow><mo>+</mo></mrow></msubsup></math></span> states and enhanced separation between the ground and <span><math><mi>γ</mi></math></span> band-head state minima. The model also provides satisfactory predictions for B(E2) transition ratios, though with a tendency to overestimate interband transitions. These results suggest that the combination of energy dependence and deformation-dependent mass offers a more comprehensive framework for describing nuclear collective properties in transitional regions.</div></div>","PeriodicalId":8249,"journal":{"name":"Annals of Physics","volume":"485 ","pages":"Article 170292"},"PeriodicalIF":3.0,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145691988","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-02-01Epub Date: 2025-12-22DOI: 10.1016/j.aop.2025.170294
G.G.L. Nashed , A. Eid
We develop a model of Einstein gravity coupled to two scalar fields that admits exact analytical solutions representing a realistic compact stellar object. To this end, we derive the equations of motion describing a spherically symmetric spacetime within this framework. The resulting system consists of three equations involving eight unknown functions: three associated with the scalar field coefficients, three arising from the energy–momentum tensor components, and two corresponding to the metric potentials. It is shown that one scalar field coefficient vanishes identically, reducing the number of unknowns to seven. To close the system, four additional constraints are imposed, including two equations of state one radial and one tangential, and specified forms for the metric potentials. This approach yields explicit expressions for the energy density and the two scalar field coefficients. We then evaluate the model against physical requirements such as the regularity of the energy–momentum tensor components at the stellar center and verify that the mass function aligns with observations from the pulsar PSR J0740+6620. Finally, we analyze the mass–radius relation and apply best-fit techniques to the equations of state, confirming their consistency with the imposed assumptions.
{"title":"Two-scalar field stellar configurations in Einstein gravity","authors":"G.G.L. Nashed , A. Eid","doi":"10.1016/j.aop.2025.170294","DOIUrl":"10.1016/j.aop.2025.170294","url":null,"abstract":"<div><div>We develop a model of Einstein gravity coupled to two scalar fields that admits exact analytical solutions representing a realistic compact stellar object. To this end, we derive the equations of motion describing a spherically symmetric spacetime within this framework. The resulting system consists of three equations involving eight unknown functions: three associated with the scalar field coefficients, three arising from the energy–momentum tensor components, and two corresponding to the metric potentials. It is shown that one scalar field coefficient vanishes identically, reducing the number of unknowns to seven. To close the system, four additional constraints are imposed, including two equations of state one radial and one tangential, and specified forms for the metric potentials. This approach yields explicit expressions for the energy density and the two scalar field coefficients. We then evaluate the model against physical requirements such as the regularity of the energy–momentum tensor components at the stellar center and verify that the mass function aligns with observations from the pulsar PSR J0740+6620. Finally, we analyze the mass–radius relation and apply best-fit techniques to the equations of state, confirming their consistency with the imposed assumptions.</div></div>","PeriodicalId":8249,"journal":{"name":"Annals of Physics","volume":"485 ","pages":"Article 170294"},"PeriodicalIF":3.0,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145836664","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-02-01Epub Date: 2025-12-15DOI: 10.1016/j.aop.2025.170324
Faizuddin Ahmed , Abdelmalek Bouzenada
In this study, we investigate the dynamics of photons and the propagation of electromagnetic waves in a three-dimensional static wormhole geometry threaded by disclinations. Our primary focus is on photon trajectories and how they are influenced by key geometric parameters, including the wormhole throat radius, the curvature radius, and the disclinations parameter. We demonstrate that these parameters significantly affect the path of photons traversing the wormhole background. We find that the effective potential governing photon motion asymptotically approaches a constant value near the wormhole throat, forming a repulsive barrier that restricts inward propagation unless the photon possesses energy above a critical threshold. Furthermore, we analyze the wave-optical properties by solving the scalar Helmholtz wave equation in this wormhole background. Employing a suitable wave function ansatz, we transform the equation into a Schrödinger-like form, which allows us to identify the effective potential governing wave propagation. From this formulation, we derive a spatially and frequency-dependent effective refractive index. Our results show that the geometrical parameters-particularly the throat radius, the curvature radius, and the disclinations parameter have a substantial impact on the refractive index and overall wave-optical behavior of the system.
{"title":"Null geodesic and Helmholtz wave equation in (1+2)-dimensional static wormhole with disclinations","authors":"Faizuddin Ahmed , Abdelmalek Bouzenada","doi":"10.1016/j.aop.2025.170324","DOIUrl":"10.1016/j.aop.2025.170324","url":null,"abstract":"<div><div>In this study, we investigate the dynamics of photons and the propagation of electromagnetic waves in a three-dimensional static wormhole geometry threaded by disclinations. Our primary focus is on photon trajectories and how they are influenced by key geometric parameters, including the wormhole throat radius, the curvature radius, and the disclinations parameter. We demonstrate that these parameters significantly affect the path of photons traversing the wormhole background. We find that the effective potential governing photon motion asymptotically approaches a constant value near the wormhole throat, forming a repulsive barrier that restricts inward propagation unless the photon possesses energy above a critical threshold. Furthermore, we analyze the wave-optical properties by solving the scalar Helmholtz wave equation in this wormhole background. Employing a suitable wave function ansatz, we transform the equation into a Schrödinger-like form, which allows us to identify the effective potential governing wave propagation. From this formulation, we derive a spatially and frequency-dependent effective refractive index. Our results show that the geometrical parameters-particularly the throat radius, the curvature radius, and the disclinations parameter have a substantial impact on the refractive index and overall wave-optical behavior of the system.</div></div>","PeriodicalId":8249,"journal":{"name":"Annals of Physics","volume":"485 ","pages":"Article 170324"},"PeriodicalIF":3.0,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145797570","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-02-01Epub Date: 2025-11-29DOI: 10.1016/j.aop.2025.170313
Farhang Loran , Ali Mostafazadeh
Stationary potential scattering admits a formulation in terms of the quantum dynamics generated by a non-Hermitian effective Hamiltonian. We use this formulation to give a proof of the reciprocity theorem in two and three dimensions that does not rely on the properties of the scattering operator, Green’s functions, or Green’s identities. In particular, we identify reciprocity with an operator identity satisfied by an integral operator , called the fundamental transfer matrix. This is a multi-dimensional generalization of the transfer matrix of potential scattering in one dimension that stores the information about the scattering amplitude of the potential. We use the property of that is responsible for reciprocity to identify the analog of the relation, , in two and three dimensions, and establish a generic anti-pseudo-Hermiticity of the scattering operator. Our results apply for both real and complex potentials.
{"title":"Reciprocity theorem and fundamental transfer matrix","authors":"Farhang Loran , Ali Mostafazadeh","doi":"10.1016/j.aop.2025.170313","DOIUrl":"10.1016/j.aop.2025.170313","url":null,"abstract":"<div><div>Stationary potential scattering admits a formulation in terms of the quantum dynamics generated by a non-Hermitian effective Hamiltonian. We use this formulation to give a proof of the reciprocity theorem in two and three dimensions that does not rely on the properties of the scattering operator, Green’s functions, or Green’s identities. In particular, we identify reciprocity with an operator identity satisfied by an integral operator <span><math><mover><mrow><mi>M</mi></mrow><mrow><mo>̂</mo></mrow></mover></math></span>, called the fundamental transfer matrix. This is a multi-dimensional generalization of the transfer matrix <span><math><mi>M</mi></math></span> of potential scattering in one dimension that stores the information about the scattering amplitude of the potential. We use the property of <span><math><mover><mrow><mi>M</mi></mrow><mrow><mo>̂</mo></mrow></mover></math></span> that is responsible for reciprocity to identify the analog of the relation, <span><math><mrow><mo>det</mo><mi>M</mi><mo>=</mo><mn>1</mn></mrow></math></span>, in two and three dimensions, and establish a generic anti-pseudo-Hermiticity of the scattering operator. Our results apply for both real and complex potentials.</div></div>","PeriodicalId":8249,"journal":{"name":"Annals of Physics","volume":"485 ","pages":"Article 170313"},"PeriodicalIF":3.0,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145691987","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-02-01Epub Date: 2025-11-24DOI: 10.1016/j.aop.2025.170302
Shahid Chaudhary , Muhammad Danish Sultan , Talha Anwar , Atif Mossad Ali EI-Rehim , Farruh Atamurotov , Ali M. Mubaraki , Muhammad Hadi , M.A. Sayed
We study the gravitational lensing, shadow structure, and accretion dynamics of black holes modified by dark photon interactions arising from a hidden gauge symmetry. The metric incorporates Yukawa-type and magnetic dipole potentials sourced by dark photons. Using the Gauss–Bonnet theorem, we derive the weak deflection angle and show that the dark photon coupling , mass , and magnetic dipole ratio produce measurable deviations from general relativity. We further analyze light propagation in a plasma medium, where chromatic dispersion enhances the influence of the dark sector on the deflection angle. Extending the analysis to massive particles through the Jacobi metric approach, we demonstrate that velocity-dependent corrections cause slower particles to experience stronger deflection. The optical appearance of thin accretion disks is modeled using the Novikov–Thorne formalism and relativistic ray tracing, revealing that dark photon effects alter disk brightness and secondary image formation. Finally, static spherical accretion and shadow imaging analyses show that variations in and significantly modify the shadow boundary and ring luminosity, offering potential observational signatures of hidden-sector physics.
{"title":"Gravitational lensing, shadow images and accretion dynamics of dark photon corrected black holes","authors":"Shahid Chaudhary , Muhammad Danish Sultan , Talha Anwar , Atif Mossad Ali EI-Rehim , Farruh Atamurotov , Ali M. Mubaraki , Muhammad Hadi , M.A. Sayed","doi":"10.1016/j.aop.2025.170302","DOIUrl":"10.1016/j.aop.2025.170302","url":null,"abstract":"<div><div>We study the gravitational lensing, shadow structure, and accretion dynamics of black holes modified by dark photon interactions arising from a hidden <span><math><mrow><mi>U</mi><mrow><mo>(</mo><mn>1</mn><mo>)</mo></mrow></mrow></math></span> gauge symmetry. The metric incorporates Yukawa-type and magnetic dipole potentials sourced by dark photons. Using the Gauss–Bonnet theorem, we derive the weak deflection angle and show that the dark photon coupling <span><math><msub><mrow><mi>g</mi></mrow><mrow><mi>D</mi></mrow></msub></math></span>, mass <span><math><msub><mrow><mi>m</mi></mrow><mrow><msup><mrow><mi>A</mi></mrow><mrow><mo>′</mo></mrow></msup></mrow></msub></math></span>, and magnetic dipole ratio <span><math><mrow><msub><mrow><mi>μ</mi></mrow><mrow><mi>f</mi></mrow></msub><mo>/</mo><mi>Λ</mi></mrow></math></span> produce measurable deviations from general relativity. We further analyze light propagation in a plasma medium, where chromatic dispersion enhances the influence of the dark sector on the deflection angle. Extending the analysis to massive particles through the Jacobi metric approach, we demonstrate that velocity-dependent corrections cause slower particles to experience stronger deflection. The optical appearance of thin accretion disks is modeled using the Novikov–Thorne formalism and relativistic ray tracing, revealing that dark photon effects alter disk brightness and secondary image formation. Finally, static spherical accretion and shadow imaging analyses show that variations in <span><math><msub><mrow><mi>g</mi></mrow><mrow><mi>D</mi></mrow></msub></math></span> and <span><math><msub><mrow><mi>m</mi></mrow><mrow><msup><mrow><mi>A</mi></mrow><mrow><mo>′</mo></mrow></msup></mrow></msub></math></span> significantly modify the shadow boundary and ring luminosity, offering potential observational signatures of hidden-sector physics.</div></div>","PeriodicalId":8249,"journal":{"name":"Annals of Physics","volume":"485 ","pages":"Article 170302"},"PeriodicalIF":3.0,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145692357","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-02-01Epub Date: 2025-11-27DOI: 10.1016/j.aop.2025.170300
G. Abellán , N. Bolívar , I. Vasilev
We construct and analyse a class of static spherically symmetric spacetimes in general relativity sourced exclusively by classical electrostatic configurations. Using a spherically symmetric Painlevé–Gullstrand-like metric with unit lapse and a radial shift function, we develop piecewise-defined solutions where the interior geometry is flat and the exterior is supported by several sources inspired by electromagnetic distributions. These include point-charge-like fields, Yukawa-screened electric fields, dielectric layers, and Hulthén-type field. The Einstein equations naturally impose a relation between the energy density and radial pressure, while the tangential pressure is derived from the metric. We systematically evaluate the classical energy conditions in each model and study the appearance of singular behaviour using Israel junction conditions. This framework offers an analytically tractable setting to explore the gravitational effects of physically simple, well-understood sources without resorting to exotic matter.
{"title":"Gravitational effects of sources inspired by ideal electromagnetic fields in spherical Painlevé–Gullstrand coordinates","authors":"G. Abellán , N. Bolívar , I. Vasilev","doi":"10.1016/j.aop.2025.170300","DOIUrl":"10.1016/j.aop.2025.170300","url":null,"abstract":"<div><div>We construct and analyse a class of static spherically symmetric spacetimes in general relativity sourced exclusively by classical electrostatic configurations. Using a spherically symmetric Painlevé–Gullstrand-like metric with unit lapse and a radial shift function, we develop piecewise-defined solutions where the interior geometry is flat and the exterior is supported by several sources inspired by electromagnetic distributions. These include point-charge-like fields, Yukawa-screened electric fields, dielectric layers, and Hulthén-type field. The Einstein equations naturally impose a relation between the energy density and radial pressure, while the tangential pressure is derived from the metric. We systematically evaluate the classical energy conditions in each model and study the appearance of singular behaviour using Israel junction conditions. This framework offers an analytically tractable setting to explore the gravitational effects of physically simple, well-understood sources without resorting to exotic matter.</div></div>","PeriodicalId":8249,"journal":{"name":"Annals of Physics","volume":"485 ","pages":"Article 170300"},"PeriodicalIF":3.0,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145622793","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-02-01Epub Date: 2025-11-22DOI: 10.1016/j.aop.2025.170299
Alexey Dubinsky
We study axial gravitational perturbations of the Dymnikova regular black hole, an asymptotically flat spacetime in which the Schwarzschild singularity is replaced by a de Sitter core. Using the WKB method with Padé approximants, we compute grey-body factors, and absorption cross-sections, and test the recently proposed correspondence between quasinormal frequencies and transmission coefficients. We find that variations of the quantum parameter affect the effective potential only near the horizon, leading to minor deviations of grey-body factors and absorption cross-sections from the Schwarzschild case. As a result, the Hawking radiation spectrum is governed mainly by the modified Hawking temperature, with grey-body factors providing only subleading corrections. Unlike higher quasinormal overtones, which are highly sensitive to near-horizon deformations, the grey-body factors remain robust, a feature explicitly confirmed for the Dymnikova geometry. The correspondence between quasinormal modes and grey-body factors holds in our case with high accuracy for multipoles .
{"title":"Gravitational perturbations of Dymnikova black holes: Grey-body factors and absorption cross-sections","authors":"Alexey Dubinsky","doi":"10.1016/j.aop.2025.170299","DOIUrl":"10.1016/j.aop.2025.170299","url":null,"abstract":"<div><div>We study axial gravitational perturbations of the Dymnikova regular black hole, an asymptotically flat spacetime in which the Schwarzschild singularity is replaced by a de Sitter core. Using the WKB method with Padé approximants, we compute grey-body factors, and absorption cross-sections, and test the recently proposed correspondence between quasinormal frequencies and transmission coefficients. We find that variations of the quantum parameter <span><math><msub><mrow><mi>l</mi></mrow><mrow><mi>cr</mi></mrow></msub></math></span> affect the effective potential only near the horizon, leading to minor deviations of grey-body factors and absorption cross-sections from the Schwarzschild case. As a result, the Hawking radiation spectrum is governed mainly by the modified Hawking temperature, with grey-body factors providing only subleading corrections. Unlike higher quasinormal overtones, which are highly sensitive to near-horizon deformations, the grey-body factors remain robust, a feature explicitly confirmed for the Dymnikova geometry. The correspondence between quasinormal modes and grey-body factors holds in our case with high accuracy for multipoles <span><math><mrow><mi>ℓ</mi><mo>≥</mo><mn>2</mn></mrow></math></span>.</div></div>","PeriodicalId":8249,"journal":{"name":"Annals of Physics","volume":"485 ","pages":"Article 170299"},"PeriodicalIF":3.0,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145600383","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The supermultiplet model, based on the reduction chain , is revisited through the lens of commutants within universal enveloping algebras of Lie algebras. From this analysis, a collection of twenty polynomials up to degree nine emerges from the commutant associated with the subalgebra. This study is conducted in the Poisson (commutative) framework using the Lie-Poisson bracket associated with the dual of the Lie algebra under consideration. As the main result, we obtain the polynomial Poisson algebra generated by these twenty linearly independent and indecomposable polynomials, with five elements being central. This incorporates polynomial expansions up to degree seventeen in the Lie algebra generators. We further discuss additional algebraic relations among these polynomials, explicitly detailing some of the lower-order ones. As a byproduct of these results, we also show that the recently introduced ‘grading method’ turns out to be essential for deriving the Poisson bracket relations when the degree of the expansions becomes so high that standard approaches are no longer applicable due to computational limitations. These findings represent a further step toward the systematic exploration of polynomial algebras relevant to nuclear models.
{"title":"Polynomial algebra from the Lie algebra reduction chain su(4)⊃su(2)×su(2): The supermultiplet model","authors":"Rutwig Campoamor-Stursberg , Danilo Latini , Ian Marquette , Junze Zhang , Yao-Zhong Zhang","doi":"10.1016/j.aop.2025.170322","DOIUrl":"10.1016/j.aop.2025.170322","url":null,"abstract":"<div><div>The supermultiplet model, based on the reduction chain <span><math><mrow><mi>su</mi><mrow><mo>(</mo><mn>4</mn><mo>)</mo></mrow><mo>⊃</mo><mi>su</mi><mrow><mo>(</mo><mn>2</mn><mo>)</mo></mrow><mo>×</mo><mi>su</mi><mrow><mo>(</mo><mn>2</mn><mo>)</mo></mrow></mrow></math></span>, is revisited through the lens of commutants within universal enveloping algebras of Lie algebras. From this analysis, a collection of twenty polynomials up to degree nine emerges from the commutant associated with the <span><math><mrow><mi>su</mi><mrow><mo>(</mo><mn>2</mn><mo>)</mo></mrow><mo>×</mo><mi>su</mi><mrow><mo>(</mo><mn>2</mn><mo>)</mo></mrow></mrow></math></span> subalgebra. This study is conducted in the Poisson (commutative) framework using the Lie-Poisson bracket associated with the dual of the Lie algebra under consideration. As the main result, we obtain the polynomial Poisson algebra generated by these twenty linearly independent and indecomposable polynomials, with five elements being central. This incorporates polynomial expansions up to degree seventeen in the Lie algebra generators. We further discuss additional algebraic relations among these polynomials, explicitly detailing some of the lower-order ones. As a byproduct of these results, we also show that the recently introduced ‘grading method’ turns out to be essential for deriving the Poisson bracket relations when the degree of the expansions becomes so high that standard approaches are no longer applicable due to computational limitations. These findings represent a further step toward the systematic exploration of polynomial algebras relevant to nuclear models.</div></div>","PeriodicalId":8249,"journal":{"name":"Annals of Physics","volume":"485 ","pages":"Article 170322"},"PeriodicalIF":3.0,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145836663","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2026-02-01Epub Date: 2025-12-12DOI: 10.1016/j.aop.2025.170316
L.C.N. Santos , H. Aounallah , L.G. Barbosa
In this work, we investigate the behavior of scalar bosons governed by the Klein–Gordon equation in a spacetime modified by both a cosmic string and a global monopole, under the framework of gravity’s rainbow. Two interaction types are considered: a Klein–Gordon oscillator and a Coulomb-like potential. The presence of topological defects introduces effective angular momentum modifications, while the rainbow functions and incorporate an energy dependence into the spacetime geometry. Analytical and numerical solutions are obtained for the bound states, and the resulting energy spectra are analyzed for different choices of rainbow functions. The results demonstrate that both the topological parameters , and the rainbow parameter significantly influence the energy levels, introducing shifts and asymmetries that are sensitive to the functional form of the rainbow modifications.
{"title":"Scalar bosons in the context of gravity’s rainbow in the double defect spacetime","authors":"L.C.N. Santos , H. Aounallah , L.G. Barbosa","doi":"10.1016/j.aop.2025.170316","DOIUrl":"10.1016/j.aop.2025.170316","url":null,"abstract":"<div><div>In this work, we investigate the behavior of scalar bosons governed by the Klein–Gordon equation in a spacetime modified by both a cosmic string and a global monopole, under the framework of gravity’s rainbow. Two interaction types are considered: a Klein–Gordon oscillator and a Coulomb-like potential. The presence of topological defects introduces effective angular momentum modifications, while the rainbow functions <span><math><mrow><mi>f</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mrow></math></span> and <span><math><mrow><mi>g</mi><mrow><mo>(</mo><mi>x</mi><mo>)</mo></mrow></mrow></math></span> incorporate an energy dependence into the spacetime geometry. Analytical and numerical solutions are obtained for the bound states, and the resulting energy spectra are analyzed for different choices of rainbow functions. The results demonstrate that both the topological parameters <span><math><mi>α</mi></math></span>, <span><math><mi>β</mi></math></span> and the rainbow parameter <span><math><mi>ξ</mi></math></span> significantly influence the energy levels, introducing shifts and asymmetries that are sensitive to the functional form of the rainbow modifications.</div></div>","PeriodicalId":8249,"journal":{"name":"Annals of Physics","volume":"485 ","pages":"Article 170316"},"PeriodicalIF":3.0,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145747819","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We investigate the Galileon scalar field model by considering the lowest order Galileon term in the Lagrangian, through the introduction of a field potential. We explore the late-time cosmological development of light mass Galileon utilizing two different forms for , specifically the double exponential and Quintessence-Driven Slow-Contraction CDM potentials. We identify the critical points and assess their stability for these models. Our findings indicate that the light mass Galileon with double exponential potential facilitates the attainment of a stable attractor solution, while a stable solution is unattainable in the scenario of light mass Galileon with Quintessence-Driven Slow-Contraction CDM potential. Furthermore, in the former case, we derive a phase portrait in which all trajectories converge towards the stable attractor point.
{"title":"Light mass Galileon: Phase space analysis and its late time cosmic relevance","authors":"Yerlan Myrzakulov , Mohd Shahalam , Shynaray Myrzakul , Koblandy Yerzhanov","doi":"10.1016/j.aop.2025.170315","DOIUrl":"10.1016/j.aop.2025.170315","url":null,"abstract":"<div><div>We investigate the Galileon scalar field model by considering the lowest order Galileon term in the Lagrangian, <span><math><mrow><msup><mrow><mrow><mo>(</mo><msub><mrow><mi>∂</mi></mrow><mrow><mi>μ</mi></mrow></msub><mi>ϕ</mi><mo>)</mo></mrow></mrow><mrow><mn>2</mn></mrow></msup><mo>□</mo><mi>ϕ</mi></mrow></math></span> through the introduction of a field potential. We explore the late-time cosmological development of light mass Galileon utilizing two different forms for <span><math><mrow><mi>V</mi><mrow><mo>(</mo><mi>ϕ</mi><mo>)</mo></mrow></mrow></math></span>, specifically the double exponential and Quintessence-Driven Slow-Contraction CDM potentials. We identify the critical points and assess their stability for these models. Our findings indicate that the light mass Galileon with double exponential potential facilitates the attainment of a stable attractor solution, while a stable solution is unattainable in the scenario of light mass Galileon with Quintessence-Driven Slow-Contraction CDM potential. Furthermore, in the former case, we derive a phase portrait in which all trajectories converge towards the stable attractor point.</div></div>","PeriodicalId":8249,"journal":{"name":"Annals of Physics","volume":"485 ","pages":"Article 170315"},"PeriodicalIF":3.0,"publicationDate":"2026-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"145692355","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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