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Mahouton Norbert Hounkonnou

Publications and source records attributed to Mahouton Norbert Hounkonnou.

At least 55 records · Page 3Linked to original sources
arXiv2017

Density operator approach for Landau problem quantum Hamiltonians

In this work, the definition of the density operator on quantum states in Hilbert spaces and some of its aspects relevant in thermodynamics and information-theoretical entropy calculations are given. In this framework, a physical model describing an electron in a magnetic field is investigated. The so-called exotic Landau problem in noncommutative plane is also considered. Then, a model related to the fractional quantum Hall effect is revisited. Thanks to the completeness relations verified by the coherent states (CS) in these models, the thermodynamics is discussed by using the diagonal $P$-representation of thedensity operator. Specifically, the Q-Husimi distribution and the Wehrl entropy are determined.

math-ph↗
arXiv2017

Factorization method and general second order linear difference equation

This paper addresses an investigation on a factorization method for difference equations. It is proved that some classes of second order linear difference operators, acting in Hilbert spaces, can be factorized using a pair of mutually adjoint first order difference operators. These classes encompass equations of hypergeometic type describing classical orthogonal polynomials of a discrete variable.

math-ph↗
arXiv2017

Noncommutative Dirac and Klein-Gordon oscillators in the background of cosmic string: spectrum and dynamics

From a study of an oscillator in a $4D$ NC spacetime, we establish the Hamilton equations of motion. The formers are solved to give the oscillator position and momentum coordinates. These coordinates are used to build a metric similar to that describing a cosmic string. On this basis, Dirac and Klein-Gordon oscillators are investigated. Their spectrum and dynamics are analysed giving rise to novel interesting properties.

hep-th↗
arXiv2017

Photon-added coherent states for shape invariant systems

This paper addresses a full characterization of photon-added coherent states for shape-invariant potentials. Main properties are investigated and discussed. A statistical computation of relevant physical quantities is performed, emphasizing the importance of using generalized hypergeometric functions $_pF_q$ and Meijer's $G$-functions for such a study.

math-ph↗
arXiv2016

Modeling the Influence of Local Environmental Factors on Malaria Transmission in Benin and Its Implications for Cohort Study

Malaria remains endemic in tropical areas, especially in Africa. For the evaluation of new tools and to further ourunderstanding of host-parasite interactions, knowing the environmental risk of transmission-even at a very local scale-isessential. The aim of this study was to assess how malaria transmission is influenced and can be predicted by local climaticand environmental factors. As the entomological part of a cohort study of 650 newborn babies in nine villages in the ToriBossito district of Southern Benin between June 2007 and February 2010, human landing catches were performed to assessthe density of malaria vectors and transmission intensity. Climatic factors as well as household characteristics were recordedthroughout the study. Statistical correlations between Anopheles density and environmental and climatic factors weretested using a three-level Poisson mixed regression model. The results showed both temporal variations in vector density(related to season and rainfall), and spatial variations at the level of both village and house. These spatial variations could belargely explained by factors associated with the house's immediate surroundings, namely soil type, vegetation index andthe proximity of a watercourse. Based on these results, a predictive regression model was developed using a leave-one-outmethod, to predict the spatiotemporal variability of malaria transmission in the nine villages. This study points up theimportance of local environmental factors in malaria transmission and describes a model to predict the transmission risk ofindividual children, based on environmental and behavioral characteristics.

q-bio.PE↗
arXiv2015

Solutions of associative Yang-Baxter equation and $D-$equation in low dimensions and associated Frobenius algebras and Connes cocycles

This work addresses some relevant characteristics of associative algebras in low dimensions. Especially, given 1 and 2 dimensional associative algebras, we explicitly solve associative Yang-Baxter equations and use skew-symmetric solutions to perform double constructions of Frobenius algebras. Besides, we determine related compatible dendriform algebras and solutions of their $ D- $equations. Finally, using symmetric solutions of the latter equations, we proceed to double constructions of corresponding Connes cocycles.

math.RA↗
arXiv2015

Generalized Virasoro algebra: left-symmetry and related algebraic and hydrodynamic properties

Motivated by the work of Kupershmidt (J. Nonlin. Math. Phys. 6 (1998), 222 --245) we discuss the occurrence of left symmetry in a generalized Virasoro algebra. The multiplication rule is defined, which is necessary and sufficient for this algebra to be quasi-associative. Its link to geometry and nonlinear systems of hydrodynamic type is also recalled. Further, the criteria of skew-symmetry, derivation and Jacobi identity making this algebra into a Lie algebra are derived. The coboundary operators are defined and discussed. We deduce the hereditary operator and its generalization to the corresponding $3-$ary bracket. Further, we derive the so-called $ρ-$compatibility equation and perform a phase-space extension. Finally, concrete relevant particular cases are investigated.

math-ph↗
arXiv2015

Solving Navier-Stokes equations coupled with a heat transfer equation using Bagarello's approach and the Hankel transform

In this paper, the dynamics of an incompressible fluid in a bounded connected domain, described by Navier-Stokes equations coupled with a heat transfer equation, is investigated by a method inspired from the non-commutative strategy developed by Bagarello, (see Int. Jour. of Theoretical Physics, 43, issue 12 (2004), p. 2371 - 2394).The solution of involved systems of partial differential equations is derived with the help of the unbounded self-adjoint densely defined Hamiltonian operator of the physical model and the Hankel transform.

math-ph↗
arXiv2015

Control of ordinary differential equations using Bagarello's operator approach : Case of forced harmonic oscillator systems

This work deals with the study of an optimal control of a system of nonlinear differential equations using the Bagarello's operator approach, recently introduced in a paper (Int. Jour. of Theoretical Physics, 43, issue 12 (2004), p. 2371 - 2394). The control problem is reduced by using the Pontryagin's maximum principle, to a system of ordinary differential equations with unknown state and adjoint variables. Its solution is then described in terms of a series expansion of commutators involving an unbounded self-adjoint, densely defined, system Hamiltonian operator H and initial position operators. Relevant simple applications are discussed.

math-ph↗
arXiv2015

Generalizing Bagarello's operator approach to solve a class of partial differential equations

The non-commutative strategy developed by Bagarello (see Int. Jour. of Theoretical Physics, 43, issue 12 (2004), p. 2371 - 2394) for the analysis of systems of ordinary differential equations (ODEs) is extended to a class of partial differential equations (PDEs), namely evolution equations and Navier-Stokes equations. Systems of PDEs are solved using an unbounded self-adjoint, densely defined, Hamiltonian operator and a recursion relation which provides a multiple commutator and a power series solution. Numerous examples are given in this work.

math-ph↗
arXiv2015

Center-symmetric algebras and bialgebras: relevant properties and consequences

Lie admissible algebra structures, called center-symmetric algebras, are defined. Main properties and algebraic consequences are derived and discussed. Bimodules are given and used to build a center-symmetric algebra on the direct sum of underlying vector space and a finite dimensional vector space. Then, the matched pair of center-symmetric algebras is established and related to the matched pair of sub-adjacent Lie algebras. Besides, Manin triple of center-symmetric algebras is defined and linked with their associated matched pairs. Further, center-symmetric bialgebras of center-symmetric algebras are investigated and discussed. Finally, a theorem yielding the equivalence between Manin triple of center-symmetric algebras, matched pairs of Lie algebras and center-symmetric bialgebras is provided.

math.RA↗
arXiv2015

Coherent states for Landau levels: algebraic and thermodynamical properties

This work describes coherent states for a physical system governed by a Hamiltonian operator, in two dimensional space, of spinless charged particles subject to a perpendicular magnetic field B, coupled with a harmonic potential. The underlying su(1, 1) Lie algebra and Barut-Girardello coherent states are constructed and discussed. Then, the Berezin - Klauder - Toeplitz quantization, also known as coherent state (or anti-Wick) quantization, is discussed. The thermodynamics of such a quantum gas system is elaborated and analyzed.

math-ph↗
arXiv2015

Pair production of Dirac particles in a d+1-dimensional noncommutative space-time

This work addresses the computation of the propability of fermionic particle pair production in $(d+1)-$ dimensional noncommutative Moyal space. Using the Seiberg-Witten maps that establish relations between noncommutative and commutative field variables, to first order in the noncommutative parameter $θ$, we derive the probability density of vacuum-vacuum pair production of Dirac particles. The cases of constant electromagnetic, alternating time-dependent and space-dependent electric fields are considered and discussed.

hep-th↗
arXiv2014

Even and odd generalized hypergeometric coherent states

In this paper, we investigate a large class of generalized hypergeometric states $|p,q,z\rangle$, depending on a complex variable $z$ and two sets of parameters, $(a_1,\cdots,a_p)$ and $(b_1,\cdots,b_q)$. Even and odd generalized hypergeometric states $|p,q,z\rangle_e$ and $|p,q,z\rangle_o$ are also defined and analyzed. The moment problem is solved by the Mellin transform techniques. For particular values of $p$ and $q$, the photon-counting statistics, quantum optical properties and geometry of these states are discussed.

math-ph↗
arXiv2014

Generalized q-deformed Tamm-Dancoff oscillator algebra and associated coherent states

In this paper, we propose a full characterization of a generalized $q-$deformed Tamm-Dancoff oscillator algebra and investigate its main mathematical and physical properties. Specifically, we study its various representations and find the condition satisfied by the deformed $q-$number to define the algebra structure function. Particular Fock spaces involving finite and infinite dimensions are examined. A deformed calculus is performed as well as a coordinate realization for this algebra. A relevant example is exhibited. Associated coherent states are constructed. Finally, some thermodynamics aspects are computed and discussed.

math-ph↗
arXiv2014

New families of q and (q;p)-Hermite polynomials

In this paper, we construct a new family of q-Hermite polynomials denoted by Hn(x,s|q). Main properties and relations are established and proved. In addition, is deduced a sequence of novel polynomials, Ln(. ,.|q), which appear to be connected with well known (q,n)-exponential functions E{q,n}(.), introduced by Ernst in his work entitled: (A New Method for q-calculus, Uppsala Dissertations in Mathematics, Vol. 25, 2002). Relevant results spread in the literature are retrieved as particular cases. Fourier integral transforms are explicitly computed and discussed. A (q;p)-extension of the Hn(x,s|q) is also provided.

math.CA↗