arXiv subjects

Boubakeur Khantoul

Publications and source records attributed to Boubakeur Khantoul.

7 recordsLinked to original sources

arXiv2026

Dunkl--Pauli Oscillator in an Aharonov--Bohm Flux: Restriction of Admissible Angular Sectors and Thermodynamic Signatures

We study a two-dimensional Dunkl--Pauli oscillator in the presence of an Aharonov--Bohm (AB) flux. The combination of reflection symmetry (via Dunkl operators) and a topological gauge field imposes a nontrivial constraint on the admissible quantum states: the regularity condition on radial wave functions, together with the matching conditions at the flux tube, leads to a compatibility relation $ν_1+\varepsilonν_2=0$ and forces the emergence of a lowest angular quantum number~$\ell_0$. As a result, the admissible angular sectors are restricted rather than the spectrum being merely shifted in energy. Using the exact spectrum, we construct the canonical partition function and derive closed-form expressions for the internal energy, entropy, and heat capacity. The thermodynamic quantities directly reflect this spectral constraint: the low-temperature behaviour is governed by~$\ell_0$, and the heat capacity exhibits a flux-controlled Schottky-like peak. The Dunkl parameter~$ν$ plays a dual role: within a fixed sector it shifts the energy scale, while globally it controls the flux threshold that determines which sectors are admissible. At high temperatures the classical two-dimensional oscillator limit is recovered. Our results demonstrate that the interplay between Dunkl symmetry and AB flux qualitatively modifies the set of admissible states, with observable thermodynamic signatures.

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arXiv2026

Time-Dependent Dunkl-Pauli Oscillator in the Presence of the Aharonov-Bohm Effect

We present an exact, time-dependent solution for a two-dimensional Pauli oscillator deformed by Dunkl operators in the presence of an Aharonov--Bohm (AB) flux. By replacing conventional momenta with Dunkl momenta and allowing arbitrary time dependence in both, mass and frequency, we derive a deformed Pauli Hamiltonian that encodes reflection symmetries and topological gauge phases. Employing the Lewis-Riesenfeld invariant method, we derive exact expressions for the eigenvalues and spinor eigenfunctions of the system. Crucially, the AB flux imposes symmetry constraints on the Dunkl parameters of the form $ν_1 = \mp ν_2 $, linking the reflection symmetry ($ε= \pm 1 $) to the quantization of angular momentum. These constraints modify the energy spectrum and wavefunctions of the angular operator and the invariant operator. Our framework reveals novel spectral characteristics arising from the interplay between topology and Dunkl symmetry, with potential implications for quantum simulation in engineered systems such as cold atoms and quantum dots.

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arXiv2025

Uncertainty Relation for Pseudo-Hermitian Quantum Systems

This study investigates pseudo-Hermitian quantum mechanics, where the Hamiltonian satisfies a modified Hermiticity condition. We extend the uncertainty relation for such systems, demonstrating its equivalence to the standard Hermitian case within a pseudo-Hermitian inner product. Analytical solutions to the time-dependent Schrödinger equation with a linearly evolving potential are derived. Furthermore, we show that the uncertainty relation for position and momentum remains real and greater than 1/2, highlighting the significance of non-Hermitian systems in quantum mechanics.

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arXiv2023

Exact solutions for time-dependent complex symmetric potential well

Using the pseudo-invariant operator method, we investigate the model of a particle with a time-dependent mass in a complex time-dependent symmetric potential well $V\left( x,t\right) =if\left(t\right) \left\vert x\right\vert$. The problem is exactly solvable and the analytic expressions of the Schrödinger wavefunctions are given in terms of the Airy function. Indeed, with an appropriate choice of the time-dependent metric operators and the unitary transformations, for each region, the two corresponding pseudo-Hermitian invariants transform into a well-known time-independent Hermitian invariant which is the Hamiltonian of a particle confined in a symmetric linear potential well. The eigenfunctions of the last invariant are the Airy functions. Then, the phases obtained are real for both regions and the general solution to the problem is deduced.

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arXiv2017

On the invariant method for the time-dependent non-Hermitian Hamiltonians

We propose a scheme to deal with certain time-dependent non-Hermitian Hamiltonian operators $H(t)$ that generate a real phase in their time-evolution. This involves the use of invariant operators $I_{PH}(t)$ that are pseudo-Hermitian with respect to the time-dependent metric operator, which implies that the dynamics is governed by unitary time evolution. Furthermore, $H(t)$ is not generally quasi-Hermitian and does not define an observable of the system but $I_{PH}(t)$ obeys a quasi-hermiticity transformation as in the completely time-independent Hamiltonian systems case. The harmonic oscillator with a time-dependent frequency under the action of a complex time-dependent linear potential is considered as an illustrative example.

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arXiv2015

Time-dependent massless Dirac fermions in graphene

Using the Lewis-Riesenfeld method of invariants we construct explicit analytical solutions for the massless Dirac equation in 2+1 dimensions describing quasi-particles in graphene. The Hamiltonian of the system considered contains some explicit time-dependence in addition to one resulting from being minimally coupled to a time-dependent magnetic field. The eigenvalue equations for the two spinor components of the Lewis-Riesenfeld invariant are found to decouple into a pair of supersymmetric invariants in a similar fashion as the known decoupling for the time-independent Dirac Hamiltonians.

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arXiv2013

Hermitian versus non-Hermitian representations for minimal length uncertainty relations

We investigate four different types of representations of deformed canonical variables leading to generalized versions of Heisenberg's uncertainty relations resulting from noncommutative spacetime structures. We demonstrate explicitly how the representations are related to each other and study three characteristically different solvable models on these spaces, the harmonic oscillator, the manifestly non-Hermitian Swanson model and an intrinsically noncommutative model with Poeschl-Teller type potential. We provide an analytical expression for the metric in terms of quantities specific to the generic solution procedure and show that when it is appropriately implemented expectation values are independent of the particular representation. A recently proposed inequivalent representation resulting from Jordan twists is shown to lead to unphysical models. We suggest an anti-PT-symmetric modification to overcome this shortcoming.

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