arXiv subjects

Saber Zarrinkamar

Publications and source records attributed to Saber Zarrinkamar.

6 recordsLinked to original sources

arXiv2026

$\cal{PT}$-Symmetric GUP-Modified Single- and Double-Well Quartic Oscillators

We study the GUP-deformed quartic oscillator $H_η=p^2+ηp^4+x^4$ and distinguish its real-axis realization from complex-contour realizations. A contour chosen to remain in the decay sectors compatible with the undeformed quartic oscillator gives low-lying eigenvalues that approach the ordinary quartic spectrum as $η\to0^+$. This limiting-compatible contour does not, by itself, produce a low-level $\PT$-symmetry-breaking transition. To investigate exceptional points while retaining the same quartic leading behavior, we then introduce the explicitly $\PT$-symmetric extension $H_{η,a,g}=p^2+ηp^4+x^4-a x^2+\ii g x^3$ and fix $a=4$, for which the real part of the potential has a double-well form. Harmonic-oscillator-basis diagonalization with basis dimensions up to $N=100$ yields a converged exceptional-point branch: the critical coupling increases from $g_{\mathrm{EP}}\simeq0.10222364$ at $η=0$ to $g_{\mathrm{EP}}\simeq0.15603309$ at $η=0.1$. Across the transition, the two lowest real eigenvalues coalesce and continue as a complex-conjugate pair. The exceptional-point results belong to this stated double-well extension, not to the original single-well Hamiltonian alone.

physics.gen-ph↗

arXiv2026

Neutrino Spin--Flavor Dynamics and Quantum Rabi Model: Spectral Correspondence and QRM Benchmarks

We formulate a two-state neutrino spin--flavor system coupled through a transition magnetic moment to a single quantized electromagnetic mode and establish its operator-level correspondence with the quantum Rabi model (QRM). For the sector $\{\lvertν_{iL}\rangle,\lvertν_{jR}\rangle\}$, the diagonal splitting is $Δ_s=(m_i^2-m_j^2)/(2E)+V_{iL}-V_{jR}$, while quantization of a transverse electromagnetic mode gives a coupling $g_ν=μ_{ij}B_{\rm zpf}$. The effective Hamiltonian consequently has the QRM form $H_ν=Δ_sσ_z/2+ω_c a^\dagger a+g_νσ_x(a+a^\dagger)$. We then formulate the correspondence at the level of the exact QRM spectrum, focusing on its exceptional (Juddian) states, and transfer the QRM constraint polynomials directly to neutrino variables. This yields explicit algebraic conditions on the neutrino mass splitting, energy, transition magnetic moment, zero-point magnetic field, and mode frequency. We also identify QRM phenomena that would become conditional predictions of the quantized-field neutrino model---including counter-rotating corrections, parity structure, spin--field entanglement, and occupation-dependent dynamics. The trapped-ion QRM experiments provide benchmarks for the operator family, while none of these QRM phenomena is presented as an already observed neutrino effect.

physics.gen-ph↗

arXiv2026

A Braak-Inspired Spectral Determinant Approach to a Dirac Bound-State Problem

We develop a parity-resolved spectral-connection construction for a one-dimensional Dirac particle in an attractive soft-core Coulomb potential. The square-root dependence of the potential produces algebraic branch points in the coordinate plane. We uniformize these branch points by introducing $t=\sqrt{x^2+β^2}$, while retaining the full-line $Z_2$ symmetry generated by $Π=σ_z P_x$. In each parity sector the resulting problem is formulated as a global connection problem between a solution selected at the physical origin and the decaying solution at infinity. This defines parity-resolved spectral connection functions whose zeros determine bound-state energies. We further construct a quasi-exact Bethe-ansatz sector directly from the same Dirac equations and use its polynomial solutions as independent benchmarks of the spectral condition. The comparison clarifies the distinction between local quasi-exact solvability and the global spectral determinant. The construction is inspired by the role of discrete symmetry and global analyticity in the quantum Rabi model, without identifying the present spectral function with Braak's $G$-function.

physics.gen-ph↗

arXiv2026

One-dimensional Coulomb Problem in GUP Formalism

We investigate the one-dimensional Coulomb problem on the positive half-line for a fourth-order Schrödinger equation generated by a commonly used realization of the Generalized Uncertainty Principle (GUP). The problem is treated directly in position space by a higher-order Bethe--Ansatz construction, with the wave function represented as a polynomial multiplied by an exponential factor. The resulting residue conditions yield an analytic quantization condition and explicit polynomial solutions for the first three bound states. We identify the branch that is continuously connected to the ordinary Coulomb problem and show that its energies, decay constants, polynomial factors, and Bethe--Ansatz roots recover the ordinary half-line Coulomb results in the vanishing-deformation limit. On this Coulomb-connected branch, the deformation produces a lower admissibility bound on the principal quantum number, while arbitrarily high quantum numbers remain admissible. We also discuss the physical interpretation of the deformation strength: for ordinary microscopic systems, the weak-GUP regime is the conservative expectation in Planck-scale motivated models, whereas intermediate and strong regimes are primarily theoretical regimes in the present analysis. Since the differential equation is truncated at first order in the GUP parameter, quantitative predictions outside the weak-deformation regime should be interpreted with care.

physics.gen-ph↗

arXiv2026

Algebraic solutions for propagation of elastic SH-waves through an isotropic inhomogeneous geometry

The algebraic structure of the equation governing the propagation of an elastic SHwave through an isotropic inhomogeneous layer surrounded by two homogeneous half-spaces is revisited. It is shown that the problem under a quartic variation has a hidden sl(2) symmetry based on which quasi-exact solutions are available via a completely analytical approach. This is of particular interest as the approach proposed for the corresponding tri-confluent Heun equation can be generalized to some other classes of geometries as well and the complicated considerations in case of Heun equations are absent.

physics.gen-ph↗

arXiv2014

Harmonic Oscillator in Relativistic Minimal Length Quantum Mechanics

We consider the Dirac equation with a generalized uncertainty principle in the presence of the Harmonic interaction and an external magnetic field. By doing the study in the momentum space, the problem solved in an exact analytical manner and the eigenfucntions reported in terms of the hypergeometric functions.

quant-ph↗