arXiv subjects
Publications and source records attributed to Mahouton Norbert Hounkonnou.
This work mainly addresses a construction of Gazeau-Klauder type coherent states for a Pöschl-Teller model. Relevant characteristics are investigated. Induced geometry and statistics are studied. Then the Berezin - Klauder - Toeplitz quantization of the classical phase space observables is presented.
This paper addresses a construction of an n-ary star product. Relevant identities are given. Besides, the formalism is illustrated by a computation of eigenvalues and eigenfunctions for a physical system of coupled oscillators in an n dimensional phase space.
This work addresses a full characterization of three new q-polynomials derived from the $q-$oscillator algebra. Related matrix elements and generating functions are deduced. Further, a connection between Hahn factorial and q-Gaussian polynomials is established.
This paper addresses a construction of new $q-$Hermite polynomials with a full characterization of their main properties and corresponding raising and lowering operator algebra. The three-term recursive relation as well as the second-order differential equation obeyed by these new polynomials are explicitly derived. Relevant operator actions, including the eigenvalue problem of the deformed oscillator and the self-adjointness of the related position and momentum operators, are investigated and analyzed. The associated coherent states are constructed and discussed with an explicit resolution of the induced moment problem.
This paper addresses a modified ($G'/G$)-expansion method to obtain new classes of solutions to nonlinear partial differential equations (NPDEs). The cases of Burgers, KdV and Kadomtsev-Petviashvili NPDEs are exhaustively studied. Relevant graphical representations are shown in each case.
This work addresses a construction of a dual pair of nonlinear coherent states (NCS) in the context of changes of bases in the underlying Hilbert space for a model pertaining to the condensed matter physics, which obeys a $f$-deformed Heisenberg algebra. The existence and properties of reproducing kernel in the NCS Hilbert space are studied and discussed; the probability density and its dynamics in the basis of constructed coherent states are provided. A Glauber-Sudarshan $P$-representation of the density matrix and relevant issues related to the reproducing kernel properties are presented. Moreover, a NCS quantization of classical phase space observables is performed and illustrated in a concrete example of $q$-deformed coherent states. Finally, an exposition of quantum optical properties is given.
A full characterization of $(p,q)$-deformed Fibonacci and Lucas polynomials is given. These polynomials obey non-conventional three-term recursion relations. Their generating functions and Fourier integral transforms are explicitly computed and discussed. Relevant results known in the literature are examined as particular cases.
This paper addresses a general method of polynomial transformation of hypergeometric equations. Examples of some classical special equations of mathematical physics are generated. Heun's equation and exceptional Jacobi polynomials are also treated.
This paper addresses a new characterization of Sudarshan's diagonal representation of the density matrix elements $ρ(z',z)$, derivedfrom $(q;l,λ)-$deformed boson coherent states.The induced $ρ(z',z)$ self-reproducing property with the associated self-reproducing kernel $K(z',z)$ is computed and analyzed. An explicit construction of novel classes of generalized continuous $(q;l,λ)-$Hermite polynomials is provided with the corresponding recursion relations and exact resolution of the moment problems giving their orthogonality weight functions. Besides, the Berezin-Klauder-Toeplitz quantization of classical phase space observables and relevant normal and anti-normal forms are investigated and discussed.
This work addresses the study of the oscillator algebra, defined by four parameters $p$, $q$, $α$, and $ν$. The time-independent Schrödinger equation for the induced deformed harmonic oscillator is solved; explicit analytic expressions of the energy spectrum are given. Deformed states are built and discussed with respect to the criteria of coherent state construction. Various commutators involving annihilation and creation operators and their combinatorics are computed and analyzed. Finally, the correlation functions of matrix elements of main normal and antinormal forms, pertinent for quantum optics analysis, are computed.
This paper deals with a polymeric matrix composite material. The matrix behaviour is described by the modified Rabotnov's nonlinear viscoelastic model assuming the material is nonlinear viscoelastic. The parameters of creep and stress-relaxation kernels of the model are determined. From the experimental data related to kernels approximated by spline functions and by means of the method of weighted residual, the formulas for the determination of viscoelastic parameters are derived.
This work prolongs recent investigations by Bergeron et al [see 2012 J. Phys. A: Math. Theo. 45 244028] on new SUSYQM coherent states for Pöschl-Teller potentials. It mainly addresses explicit computations of eigenfunctions and spectrum associated to the higher order hierarchic supersymmetric Hamiltonian. Analysis of relevant properties and normal and anti-normal forms is performed and discussed. Coherent states of the hierarchic first order differential operator $A_{m,ν,β}$ of the Pöschl-Teller Hamiltonian $H_{ν,β}^{(m)}$ and their characteristics are studied.
The Heisenberg algebra is deformed with the set of parameters ${q, l,λ}$ to generate a new family of generalized coherent states respecting the Klauder criteria. In this framework, the matrix elements of relevant operators are exactly computed. Then, a proof on the sub-Poissonian character of the statistics of the main deformed states is provided. This property is used to determine the induced generalized metric.
This paper stands for an application of the noncommutative (NC) Noether theorem, given in our previous work [AIP Proc 956 (2007) 55-60], for the NC complex Grosse-Wulkenhaar model. It provides with an extension of a recent work [Physics Letters B 653 (2007) 343-345]. The local conservation of energy-momentum tensors (EMTs) is recovered using improvement procedures based on Moyal algebraic techniques. Broken dilatation symmetry is discussed. NC gauge currents are also explicitly computed.
This work prolongs, using an operator method, the investigations started in our recent paper J. Math. Phys. 51., 102108 on the spectrum and states of the harmonic oscillator on twisted Moyal plane, where rather a Moyal-star-algebraic approach was used. The physical spectrum and states of the harmonic oscillator on twisted Moyal space, obtained here by solving the corresponding differential equation, are similar to those of the ordinary Moyal space, with different parameters. This fortunately contrasts with the previous study which produced unexpected results, i.e. infinitely degenerate states with energies depending on the coordinate functions.
Main properties of noncommutative (NC) gauge theory are investigated in a $2-$dimensional twisted Moyal plane, generated by vector fields $X_{a}=e_{a}^μ(x)\partial_μ;$ the dynamical effects are induced by a non trivial tensor $e_{a}^μ(x)$. Connections in such a NC space are defined. Symmetry analysis is performed and related NC action is proved to be invariant under defined NC gauge transformations. A locally conserved Noether current is explicitly computed. Both commuting and noncommutative vector fields $X_{a}$ are considered.
In this paper, we propose some algorithms for analytical solution construction to nonlinear polynomial partial differential equations with constant function coefficients. These schemes are based on one-(single), two- (double) or three- (triple) function expansion methods. Most of the existing expansion function methods are well recovered from the mentioned schemes. The effectiveness of these methods has been tested on some nonlinear partial differential equations (NLPDEs) describing important phenomena in physics.
The first part of this work deals with a formalism of vector coherent states construction for a system of $M$ Fermi-type modes associated with $N$ bosonic modes. Then follows a generalization to a Hamiltonian describing the translational motion of the center of mass of a nanoparticle. The latter gives rise to a new mechanism for the electronic energy relaxation in nanocrystals, intensively studied today in condensed matter physics. Finite degeneracies of the involved Hamiltonian systems are also investigated. The defined vector coherent states satisfy relevant mathematical properties of continuity, resolution of identity, temporal stability and action identity.