Searcharxiv⌕ Search

arXiv subjects

Mahouton Norbert Hounkonnou

Publications and source records attributed to Mahouton Norbert Hounkonnou.

At least 19 recordsLinked to original sources
arXiv2026

Confinement-Tunable Synthetic Gauge Fields and Floquet Topological Phenomena in a Driven Quantum Wire Qubit

Theoretical analysis indicates that a spin qubit in a parabolic quantum wire, when driven by a bichromatic field, generates a confinement-tunable non-Abelian synthetic gauge field that gives rise to novel Floquet topological phenomena. In the low-confinement regime, the system exhibits topological Landau-Zener (LZ) transitions, chiral Landau-Zener-St$\ddot{u}$ckelberg-Majorana (LZSM) interference, and non-Abelian geometric phases around diabolical points. These features enable holonomic quantum computation, as well as unconventional Floquet Bloch oscillations and fractal spectra. In contrast, in the strong confinement regime, narrow avoided crossings significantly suppress cross-coupling, thereby insulating the qubit from multi-photon LZSM interference. Quantitative Floquet-Lindblad analysis shows that the optimized gate times, determined by the biharmonic driving period and non-Abelian parameter-space loops, are sufficiently short to surpass primary environmental decoherence channels. When applied to high-mobility $\text{GaAs/AlGaAs}$ core-shell nanowires, this approach converts spatial drives into robust non-Abelian gauge fields, positioning quantum wire systems as a versatile and scalable platform for fault-tolerant quantum information processing.

cond-mat.mes-hall↗
arXiv2026

Complete Factorial Asymptotics and Integrable Structure of Generalized Charlier Recurrence Coefficients

We study the monic recurrence coefficients of the generalized Charlier polynomials associated with the discrete weight \[ ρ_μ(k) = \frac{μ^k}{(k!)^2}, \qquad k\in\mathbb N_0, \qquad μ>0. \] We establish complete factorial asymptotics for the deviations $β_n-n$ and $μ-γ_n$, proving that they are beyond all algebraic orders and appear at the scale $μ^{n}/(n!)^2$. The key step is a parametrization $β_n-n=\sqrtμ\,c_nc_{n+1}$, $γ_n=μ(1-c_n^2)$, which reduces the problem to a positive sequence $(c_n)$ satisfying a discrete Painlevé II equation. Linearization around $c_n=0$ yields a discrete Bessel equation whose recessive solution is $J_n(2\sqrtμ)$. We prove that the ratio $c_n/J_n(2\sqrtμ)$ converges to a finite limit $L(μ)$, which we identify exactly as $L(μ)=1$ by combining Bessel comparison with a global analysis based on the sector decomposition of the associated Hankel determinant. This yields the exact connection formula \[ c_n \sim J_n(2\sqrtμ), \qquad n\to\infty, \] and consequently the precise asymptotics \[ β_n-n\sim \frac{μ^{n+1}}{n!(n+1)!}, \qquad μ-γ_n\sim \frac{μ^{n+1}}{(n!)^2}. \] We further develop a complementary approach based on Hankel determinants interpreted as a discrete logarithmic gas. We show that the Hankel determinant factorizes as $Δ_n(μ)=μ^{n(n-1)/2}T_n(μ)$ and admits a sector decomposition $T_n(μ)=1+\sum_{q=1}^{n}S_q(μ)$ with sector contributions independent of $n$. We establish $S_q(μ)\sim e^μμ^q/(q!)^2$, providing an independent derivation of the factorial corrections. Together, the Bessel comparison and sector decomposition reveal a rich integrable structure linking discrete Painlevé dynamics, Toda deformations, and Hankel--partition representations.

math-ph↗
arXiv2026

Generalized Charlier Recurrence Coefficients: Hankel Formulas, Laguerre--Freud Dynamics, and Painlevé V Connections

We study the monic recurrence coefficients of the generalized Charlier polynomials associated with the discrete weight \[ ρ_μ(k) = \frac{μ^k}{(k!)^2}, \qquad k\in\mathbb N_0, \qquad μ>0. \] The coefficients $β_n$ and $γ_n$ in the recurrence relation \[ P_{n+1}(x) = (x-β_n)P_n(x)-γ_nP_{n-1}(x) \] are described through complementary moment, determinant, discrete dynamical, and continuous integrable formulations. We give a consistent normalization of the Markov function and its Jacobi continued fraction, and express the recurrence coefficients in terms of Hankel determinants, using a bordered determinant for the diagonal coefficient $β_n$. Starting from the original Laguerre--Freud equations, we derive the local recursive system used for computation and relate it to the Toda deformation. We also recall the known Painlevé~V representations associated with the two-parameter generalized Charlier family, in a normalization consistent with the present specialization. Moment/Hankelconstructions provide complementary moment-theoretic realizations of the recurrence coefficients, while the local Laguerre--Freud recursion provides an independent dynamical construction. Their comparison is used for numerical cross-validation. The numerical results are consistent with the leading large-degree behavior \[ β_n\sim n, \qquad γ_n\simμ. \]

nlin.SI↗
arXiv2026

Generation of renormalized quadratic coefficient in Landau theory: Implications for specific-heat jump calculations in high-temperature superconductors

In this work, Landau's theory is revisited by renormalizing quadratic coefficients derived from nonlinear polynomial equations to account for system dimensionality. In this respect, the generated coefficients, which include an intrinsic energy parameter specific to each material, enable precise specific-heat calculations for a range of high-temperature superconductors near the superconducting transition. To that end, the change in the specific heat jump is explained phenomenologically, which applies to any spatial arrangement and electron interactions that influence system symmetries. Moreover, effects leading to rapid, non-monotonic variation in the specific heat jump, $Δ{C_p}/T_{c}$, across the transition are examined, with particular emphasis on changes attributed to the Sommerfeld coefficient in the normal state. The considerable reduction, disappearance, or significant enhancement of the specific heat anomaly at the superconducting transition is quantitatively explained by incorporating strong fluctuation corrections to the Landau theory for low-dimensional systems. Furthermore, the evolution of specific-heat jumps with system dimensionality is analyzed, and the results are discussed in relation to experimental observations of specific-heat jumps in yttrium- and bismuth-based superconductors, as well as in zero-dimensional superconductors.

cond-mat.supr-con↗
arXiv2026

Constructing Barut-Girardello coherent states for the isotonic oscillator in the DOOT approach

In this work, we study the quantum system of the isotonic oscillator from the perspective of the diagonal operator ordering technique (DOOT). Within this framework, we construct the associated Barut-Girardello and Gazeau-Klauder coherent states. We examine their mathematical properties using reproducing kernels and compute the expectation values of observables that characterize the system and its relevant physical features. Further, we perform the quantization of main classical variables in the complex plane. Then, by exploring the thermal behavior of the physical system in the constructed coherent states, we analyze the properties of mixed states described by a canonical density operator. We also obtain the corresponding Glauber-Sudarshan P-representation.

math-ph↗
arXiv2025

Induced phase transitions and spontaneous symmetry breaking based on the renormalized Ginzburg-Landau theory

In this study, we present theoretical investigations of phase transitions and critical phenomena in materials through the lens of second-order Ginzburg-Landau theory, in conjunction with considerations of symmetry groups and thermal fluctuations. By addressing the residual effects after a renormalization process, a small number of macroscopic degrees of freedom can effectively replace the infinite number of microscopic degrees of freedom, emphasizing the significant role of dimensionality and the intrinsic characteristics of the system in understanding and analyzing transitions. We highlight several non-universal characteristics of continuous phase transitions near the transition temperature, including the non-monotonic relationship between the critical temperature and dimensionality, as well as the enhancement or disappearance of the specific heat jump in complex superconductors. While the resulting expressions for thermodynamic quantities are complex for one-dimensional systems, obeying Mermin-Wagner's theorem, they are considerably simplified for two-dimensional and three-dimensional systems.

cond-mat.supr-con↗
arXiv2024

Narayana's cows numbers which are concatenations of three repdigits in base $ρ$

Narayana's sequence is a ternary recurrent sequence defined by the recurrence relation $\mathcal{N}_n=\mathcal{N}_{n-1}+\mathcal{N}_{n-3}$ with initial terms $\mathcal{N}_0=0$ and $\mathcal{N}_1=\mathcal{N}_2=\mathcal{N}_3=1$. Let $ρ\geqslant2$ be a positive integer. In this study, it is proved that the $n$th Narayana's number $ \mathcal{N}_n$ which is concatenations of three repdigits in base $ρ$ satisfies $n<5.6\cdot 10^{48}\cdot \log^7ρ$. Moreover, it is shown that the largest Narayana's number which is concatenations of three repdigits in base $ρ$ with $1 \leqslant ρ\leqslant 10$ is $58425=\mathcal{N}_{31}=\overline{3332200}_5=\overline{332223}_7.$

math.NT↗
arXiv2023

Particles and $p-$adic integrals of Spin$\left(\frac{1}{2}\right)$: spin Lie group, $\mathcal{R}(ρ,q)-$gamma and $\mathcal{R}(ρ,q)-$ beta functions, ghost and applications

In this work, we address the $p$-adic analogues of the fermion spin Lie algebras and Lie groups. We consider the extension of the fermion spin Lie groups and Lie algebras to the $p-$adic Lie groups and investigate the way to extend their integral to the zeta function as well. We show that their groups are ghost friendly. In addition, we develop the $\mathcal{R}(p,q)-$deformed calculus for the Bernoulli, Volkenborn, Euler and Genocchi polynomials, and establish related definitions. Finally, we perform a $p-$adic generalization of beta and gamma functions and exhibit some physical applications.

math.NT↗
arXiv2023

Kepler dynamics on a conformable Poisson manifold

The problem of Kepler dynamics on a conformable Poisson manifold is addressed. The Hamiltonian function is defined and the related Hamiltonian vector field governing the dynamics is derived, which leads to a modified Newton second law. Conformable momentum and Laplace-Runge-Lenz vectors are considered, generating $SO(3), SO(4),$ and $SO(1, 3)$ dynamical symmetry groups. The corresponding first Casimir operators of $SO(4)$ and $SO(1, 3)$ are, respectively, obtained. The recursion operators are constructed and used to compute the integrals of motion in action-angle coordinates. Main relevant properties are deducted and discussed.

math-ph↗
arXiv2023

Multi-parameter Fermi-Dirac and Bose-Einstein Stochastic Distributions

In this paper, we characterize the multivariate uniform probability distribution of the first and second kinds in the framework of the $\mathcal{R}(p,q)$-deformed quantum algebras. Their bivariate distributions and related properties, namely ($\mathcal{R}(p,q)$-mean, $\mathcal{R}(p,q)$-variance and $\mathcal{R}(p,q)$-covariance) are computed and discussed. Particular cases corresponding to quantum algebras existing in literature are deduced.

math-ph↗
arXiv2023

Constructive semigroups with apartness -- a state of the art

This chapter aims to provide a clear and understandable picture of constructive semigroups with apartness in Bishop's style of constructive mathematics, BISH. Our theory is partly inspired by the classical case, but it is distinguished from it in two significant aspects: we use intuitionistic logic rather than classical throughout; our work is based on the notion of apartness (between elements of the set, and, later, between elements and its subsets). Following Heyting, at least initially, classical semigroup theory is seen as a guide that helps us to develop the constructive theory of semigroups with apartness. To have a structure, we need a set, a relation, and rules establishing how we will put them together. Working within classical or intuitionistic logic, in order to analyze algebraic structures, it is necessary to start with study on sets and ordered sets, relational systems, etc. A comparative analysis between presented classical and constructive results is also a part of this chapter. All proofs can be found in the Appendix.

math.LO↗
arXiv2023

Generalized hypergeometric coherent states for special functions: mathematical and physical properties

In continuation of our previous works J. Phys. A: Math. Gen. 35, 9355-9365 (2002), J. Phys. A: Math. Gen. 38, 7851 (2005) and Eur. Phys. J. D 72, 172 (2018), we investigate a class of generalized coherent states for associated Jacobi polynomials and hypergeometric functions, satisfying the resolution of the identity with respect to a weight function expressed in terms of Meijer's G-function. We extend the state Hilbert space of the constructed states and discuss the property of the reproducing kernel and its analytical expansion. Further, we provide the expectation values of observables relevant to this quantum model. We also perform the quantization of the complex plane, compute and analyze the probability density and the temporal stability in these states. Using the completeness relation provided by the coherent states, we achieve the thermodynamic analysis in the diagonal $P$-representation of the density operator.

math-ph↗
arXiv2022

Einstein field equation, recursion operators, Noether and master symmetries in conformable Poisson manifolds

We show that a Minkowski phase space endowed with a bracket relatively to a conformable differential realizes a Poisson algebra, confering a bi-Hamiltonian structure to the resulting manifold. We infer that the related Hamiltonian vector field is an infinitesimal Noether symmetry, and compute the corresponding deformed recursion operator. Besides, using the Hamiltonian-Jacobi separability, we construct recursion operators for Hamiltonian vector fields in conformable Poisson-Schwarzschild and Friedmann-Lemaître-Robertson-Walker (FLRW) manifolds, and derive related constants of motion, Christoffel symbols, components of Riemann and Ricci tensors, Ricci constant and components of Einstein tensor. We highlight the existence of a hierarchy of bi-Hamiltonian structures in both the manifolds, and compute a family of recursion operators and master symmetries generating the constants of motion.

math-ph↗
arXiv2022

Theory of constructive semigroups with apartness -- foundations, development and practice

This paper has several purposes. We present through a critical review the results from already published papers on the constructive semigroup theory, and contribute to its further development by giving solutions to open problems. We also draw attention to its possible applications in other (constructive) mathematics disciplines, in computer science, social sciences, economics, etc. Another important goal of this paper is to provide a clear, understandable picture of constructive semigroups with apartness in Bishop's style both to (classical) algebraists and the ones who apply algebraic knowledge.

math.GM↗
arXiv2021

Generalized q-difference equations for general q-polynomials with double q-binomial coefficients

In this paper, we use the generalized q-polynomials with double q-binomial coefficients and homogeneous q-operators [J. Difference Equ. Appl. 20 (2014), 837--851.] to construct q-difference equations with seven variables, which generalize recent works of Jia et al [Symmetry 2021, 13, 1222.]. In addition, we derive Rogers formulas, extended Rogers formulas and Srivastava--Agarwal type bilinear generating functions for generalized q-polynomials, which generalize generating functions for Cigler's polynomials [J. Difference Equ. Appl. 24 (2018), 479--502.]. Finally, we also derive mixed generating functions using q-difference equations.

math.CO↗
arXiv2021

Recursion operator in a noncommutative Minkowski phase space

A recursion operator for a geodesic flow, in a noncommutative (NC) phase space endowed with a Minkowski metric, is constructed and discussed in this work. A NC Hamiltonian function $\mathcal{H}_{nc}$ describing the dynamics of a free particle system in such a phase space, equipped with a noncommutative symplectic form $ω_{nc}$ is defined. A related NC Poisson bracket is obtained. This permits to construct the NC Hamiltonian vector field, also called NC geodesic flow. Further, using a canonical transformation induced by a generating function from the Hamilton-Jacobi equation, we obtain a relationship between old and new coordinates, and their conjugate momenta. These new coordinates are used to re-write the NC recursion operator in a simpler form, and to deduce the corresponding constants of motion. Finally, all obtained physical quantities are re-expressed and analyzed in the initial NC canonical coordinates.

math-ph↗
arXiv2021

Hamiltonian Dynamics for the Kepler Problem in a Deformed Phase Space

This work addresses the Hamiltonian dynamics of the Kepler problem in a deformed phase space, by considering the equatorial orbit. The recursion operators are constructed and used to compute the integrals of motion. The same investigation is performed with the introduction of the Laplace-Runge-Lenz vector. The existence of quasi-bi-Hamiltonian structures is also elucidated. Related properties are studied.

math-ph↗