International Journal of Theoretical Physics最新文献

{"title":"A Boundary-Corrected Analytical Approximation for the Large-Parameter Troesch Problem","authors":"Helmi Temimi,&nbsp;Marwan Alquran","doi":"10.1007/s10773-026-06455-6","DOIUrl":"10.1007/s10773-026-06455-6","url":null,"abstract":"<div><p>The Troesch boundary value problem is a highly sensitive nonlinear problem whose solution develops a sharp boundary layer near the right endpoint as the sensitivity parameter becomes large. This paper develops a simple explicit analytical approximation tailored to the large-parameter regime. The approximation is derived directly from the first integral of Troesch’s equation by exploiting the exponentially small initial slope and retaining the dominant boundary-layer balance. The resulting leading expression satisfies the nonlinear differential equation and the right boundary condition exactly, while the left boundary condition is violated only by an exponentially small amount. A simple affine correction is then introduced to enforce both Dirichlet boundary conditions exactly, producing a closed-form approximation that retains the dominant large-parameter boundary-layer behavior. The resulting formula is non-iterative and is intended as a practical approximation for sufficiently large values of the sensitivity parameter. Numerical simulations are reported for large values of the parameter and are compared with the average of the lower and upper analytical envelopes of Halic, Tajarod and Temimi and with the high-sensitivity numerical results of Ben-Romdhane and Temimi. The compu wted right-end derivative agrees with the available benchmark values to the displayed precision for parameters up to <span>(lambda =500)</span>. Pointwise comparisons and graphical results further demonstrate that the corrected approximation accurately reproduces the high-sensitivity Troesch solution in the large-parameter regime.</p></div>","PeriodicalId":597,"journal":{"name":"International Journal of Theoretical Physics","volume":"65 9","pages":""},"PeriodicalIF":2.3,"publicationDate":"2026-08-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148837424","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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}

{"title":"Complex-Ray Geometry and the Emergence of Projective Qubits","authors":"Kenneth A. Menard","doi":"10.1007/s10773-026-06456-5","DOIUrl":"10.1007/s10773-026-06456-5","url":null,"abstract":"<div><p>Building upon the complex-ray formulation of Gaussian quantum states, we show that the projective state geometry of a qubit arises as a compact sector of the underlying continuous symplectic phase space. In this framework, quantum states are represented by complex covariance coordinates in the Siegel upper half-space <span>(mathbb {H}_n)</span>, allowing continuous phase-space geometry to be projected onto the compact geometry of a qubit. We demonstrate that several fundamental geometric structures underlying qubit kinematics—the Bloch sphere, the compact <span>(mathfrak {su}(2))</span> Lie-Poisson algebra, and the spinorial double-cover structure—emerge naturally from the symplectic geometry of the covariance manifold together with the metaplectic group <span>(textrm{Mp}(2n,mathbb {R}))</span> under a canonical compactification. Within this complex-ray framework, the Bloch sphere arises as the projective reduction of the covariance hyperboloid associated with a non-compact <span>(mathfrak {sp}(2,mathbb {R})^*cong mathfrak {su}(1,1)^*)</span> moment map. We prove that among conformal rescalings of the projected Kirillov–Kostant–Souriau symplectic form on this hyperboloid, the factor <span>(w^2)</span> is uniquely singled out as the conformal rescaling within this class that reproduces the standard compact <span>(mathfrak {su}(2))</span> Lie-Poisson algebra. Invoking the Kirillov–Kostant orbit theorem, we identify the compactified orbit as an <span>(textrm{SU}(2))</span> coadjoint orbit, canonically diffeomorphic to <span>(textrm{SU}(2)/textrm{U}(1)cong S^2cong mathbb{C}mathbb{P}^1)</span>. Under Kähler polarization, geometric quantization of the minimal integral orbit yields a two-dimensional complex Hilbert space, recovering the fundamental spin-1/2 representation directly from continuous phase-space invariants. Furthermore, we show that the characteristic sign reversal under <span>(2pi )</span> rotations reproduces the same double-cover topology as the metaplectic holonomy generated by the zero-point energy of the quadratic Hamiltonian. Finally, we establish that the natural Kähler metric on <span>(mathbb {H}_n)</span> coincides with the quantum Fisher information metric, yielding a direct relation between geodesic distance and quantum fidelity along a squeezing trajectory.</p></div>","PeriodicalId":597,"journal":{"name":"International Journal of Theoretical Physics","volume":"65 9","pages":""},"PeriodicalIF":2.3,"publicationDate":"2026-08-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148837427","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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}

{"title":"Relativistic Quantum Oscillators in the Yang Model of Noncommutative Geometry","authors":"A. Merad,&nbsp;S. Merad","doi":"10.1007/s10773-026-06444-9","DOIUrl":"10.1007/s10773-026-06444-9","url":null,"abstract":"<div><p>We investigate one-dimensional relativistic quantum oscillators within the framework of the Yang model of noncommutative geometry. Using a Hermitian realization of the deformed position and momentum operators, we derive the modified wave equations and solve them analytically to leading order in the deformation parameters <span>(alpha )</span> and <span>(beta )</span>. The energy spectrum of the system shows a dependence on <span>(n^2)</span>, which corresponds to the phenomenon of confinement. This quadratic dependence on <i>n</i> leads to spectral compression and the spectrum reaches its maximum at <span>(n_{peak} sim 2momega /gamma )</span>, reflecting the bounded nature of phase space inherent to the Yang algebra. The thermodynamic properties of the relativistic oscillators are analyzed in the high-temperature regime using the Euler-MacLaurin method. In the appropriate limits, we recover the standard relativistic oscillator spectra.</p></div>","PeriodicalId":597,"journal":{"name":"International Journal of Theoretical Physics","volume":"65 9","pages":""},"PeriodicalIF":2.3,"publicationDate":"2026-08-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148837426","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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}

{"title":"Bipartite States Entanglement for the (mathcal {A}_{kappa }) Weyl-Heisenberg Algebra and Their Geometrical Aspects","authors":"Ghayth Ouirdani,&nbsp;Bouchra Maroufi,&nbsp;Mohammed Daoud,&nbsp;M. W. Mansouri","doi":"10.1007/s10773-026-06451-w","DOIUrl":"10.1007/s10773-026-06451-w","url":null,"abstract":"<div><p>We investigate the entanglement of bipartite states arising from the Barut-Girardello coherent states of the <span>(mathcal {A}_{kappa })</span> Weyl-Heisenberg algebra. The geometric aspects of entanglement of our bipartite quantum system were investigated into account by calculating the Berry connection, the Berry phase and the Berry curvature in addition to determining the roots of the Majorana polynomial.</p></div>","PeriodicalId":597,"journal":{"name":"International Journal of Theoretical Physics","volume":"65 9","pages":""},"PeriodicalIF":2.3,"publicationDate":"2026-08-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148783111","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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}

{"title":"Noncommutative Scalar Quasinormal Modes in Static de Sitter Spacetime","authors":"Soulaf Kirat,&nbsp;Salah Haouat","doi":"10.1007/s10773-026-06450-x","DOIUrl":"10.1007/s10773-026-06450-x","url":null,"abstract":"<div><p>In this paper, we investigate the quasinormal modes (QNMs) of a scalar field in a static de Sitter spacetime within the framework of noncommutative geometry. Using the Moyal star-product and the Seiberg-Witten map to first order in the noncommutativity parameter <span>(theta )</span>, the corresponding equation of motion is reduced to a Schrödinger-type equation with an effective Pöschl-Teller potential. Then, the QNM spectrum is obtained analytically. We have shown that the noncommutativity breaks rotational symmetry and lifts the degeneracy with respect to the magnetic quantum number <i>m</i>. Moreover, we have studied the temporal evolution of scalar perturbations. It is shown how the noncommutativity modifies the amplitude of the signal leading to either enhanced or suppressed damping, depending on the sign of <span>(mtheta H)</span>.</p></div>","PeriodicalId":597,"journal":{"name":"International Journal of Theoretical Physics","volume":"65 9","pages":""},"PeriodicalIF":2.3,"publicationDate":"2026-08-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148783153","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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}

{"title":"On Ricci Vector Fields and Almost Product Structures in Three-Dimensional Walker Manifolds","authors":"Aydin Gezer,&nbsp;Buşra Aktaş,&nbsp;Uday Chand De","doi":"10.1007/s10773-026-06445-8","DOIUrl":"10.1007/s10773-026-06445-8","url":null,"abstract":"<div><p>Motivated by the vector fields <span>(varphi (textrm{Ric}) )</span> defined through the condition <span>(nabla varphi = mu textrm{Ric} )</span>, where <span>(mu )</span> is a real constant and <span>(varphi )</span> denotes a vector field on the underlying manifold, this paper investigates the existence problem of Ricci vector fields <span>(( mu = 1 ))</span> on three-dimensional Lorentzian Walker manifolds <span>((M^3, g_f) )</span>. A theorem is established providing the necessary and sufficient conditions for their existence, followed by several propositions offering a local classification of the component functions of Ricci vector fields and of the functions <i>f</i> determining the Walker metric under specific geometric constraints. Further results characterize the existence of spacelike and timelike Ricci vector fields. Introducing a product structure <i>J</i> on the Walker manifold, we show that the metric <span>(g_f )</span> is pure with respect to <i>J</i>, and we construct the associated twin metric <span>(G_f )</span>, whose index exhibits a particularly noteworthy behavior when <span>(f &gt; 0 )</span>. Finally, a theorem is presented giving the necessary and sufficient conditions for the existence of Ricci vector fields with respect to the twin metric <span>(G_f )</span> on the almost product Walker manifold <span>((M^3, J, g_f) )</span>.</p></div>","PeriodicalId":597,"journal":{"name":"International Journal of Theoretical Physics","volume":"65 9","pages":""},"PeriodicalIF":2.3,"publicationDate":"2026-08-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148783152","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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}

{"title":"Parity-Dependent Single-Particle Structure in Odd-A Nuclei from a Dunkl Shell Model","authors":"Omid Hamidi,&nbsp;Vahid Mirzaei Mahmoud Abadi","doi":"10.1007/s10773-026-06443-w","DOIUrl":"10.1007/s10773-026-06443-w","url":null,"abstract":"<div><p>Conventional shell-model and mean-field approaches provide a highly successful framework for describing nuclear single-particle spectra. In nuclei with strong octupole correlations or reflection-asymmetric intrinsic shapes, however, effective single-particle spectra may display parity-dependent shifts, parity doublet structures, and parity-dependent average energy shifts that are commonly described through deformation-dependent mean fields, particle-vibration coupling, or beyond-mean-field methods. In this work we explore an effective Dunkl-modified single-particle framework in which the angular part of the kinetic energy is generalized through a Dunkl-type reflection operator. The resulting Hamiltonian contains a control parameter μ that introduces parity-dependent modifications of the effective centrifugal term while recovering the conventional Woods–Saxon limit as the parameter μ tends to zero. The parameter μ is not interpreted as a fundamental deformation variable, but as an effective measure of parity-sensitive correlations within a reduced single-particle description. Calculations are performed for representative nuclei, including near-spherical benchmarks and nuclei known to exhibit octupole correlations. The results show smooth <span>(mu)</span>-dependent spectral evolution, state-dependent energy shifts, and enhanced sensitivity of low-<span>({ell})</span> orbitals. Moderate reductions of the spectroscopic RMSE are obtained in selected reflection-asymmetric systems, while the conventional limit is recovered for the reflection-symmetric benchmark. The proposed Dunkl Shell Model should therefore be regarded as a phenomenological and symmetry-guided extension of single-particle dynamics, complementary to conventional shell-model, mean-field, and particle-vibration approaches. Its limitations, including the absence of explicit parity projection and collective phonon degrees of freedom, are discussed.</p></div>","PeriodicalId":597,"journal":{"name":"International Journal of Theoretical Physics","volume":"65 9","pages":""},"PeriodicalIF":2.3,"publicationDate":"2026-08-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148752407","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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}

{"title":"Regularization in Scattering from Dirac Delta Potential with Minimal Length","authors":"N. Ferkous,&nbsp;M. S. Zidi,&nbsp;F. Feltane","doi":"10.1007/s10773-026-06449-4","DOIUrl":"10.1007/s10773-026-06449-4","url":null,"abstract":"<div><p>The scattering of a quantum particle by a two or three-dimensional Dirac delta potential leads to divergent integrals, rendering the cross section ill-defined and requiring an ad hoc regularization scheme. We demonstrate that this problem is naturally resolved by invoking a minimal length scale, as predicted by models of quantum gravity and encoded in a generalized uncertainty principle (GUP). This cutoff regularizes the theory and yields finite s-wave scattering amplitudes and cross sections without the introduction of any external regulator or additional parameters. Moreover, we derive an upper bound on the minimal length based on the resonance energy in proton–proton scattering.</p></div>","PeriodicalId":597,"journal":{"name":"International Journal of Theoretical Physics","volume":"65 9","pages":""},"PeriodicalIF":2.3,"publicationDate":"2026-08-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148782697","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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}

{"title":"Exact Solutions for Compactly Supported Parabolic and Landau Quantum Barriers","authors":"Peter Collas,&nbsp;David Klein","doi":"10.1007/s10773-026-06448-5","DOIUrl":"10.1007/s10773-026-06448-5","url":null,"abstract":"<div><p>We derive exact solutions to the one-dimensional Schrödinger equation for compactly supported parabolic and hyperbolic secant potential barriers, along with combinations of these types of potential barriers. We give the expressions for transmission and reflection coefficients and calculate some dwell times of interest.</p></div>","PeriodicalId":597,"journal":{"name":"International Journal of Theoretical Physics","volume":"65 9","pages":""},"PeriodicalIF":2.3,"publicationDate":"2026-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148752401","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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}

{"title":"Effective-Potential Formulation of Schrödinger–Newton Dynamics and the (m^{11}) Stiffness Scaling","authors":"Kenneth A. Menard","doi":"10.1007/s10773-026-06403-4","DOIUrl":"10.1007/s10773-026-06403-4","url":null,"abstract":"<div><p>The Schrödinger–Newton (SN) equation is the foundational model of semiclassical gravity. In this work, we develop a Gaussian variational reduction that makes the intrinsic scale-invariant structure of the SN equation analytically explicit, yielding a compact and accurate one-dimensional effective Hamiltonian. This framework maps the phase-space geometry of the SN dynamics and reveals that the dimensionally required <span>(m^{11})</span> stiffness scaling produces a strongly mass-dependent restoring force against wave-packet deformation. Applying this self-gravitational stiffness to levitated optomechanics, we identify a concrete and falsifiable laboratory signature: a mass-dependent, nonlinear upward shift in the mechanical frequency of a trapped nanoparticle.</p></div>","PeriodicalId":597,"journal":{"name":"International Journal of Theoretical Physics","volume":"65 8","pages":""},"PeriodicalIF":2.3,"publicationDate":"2026-08-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"148782162","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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}