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Ezinvi Baloïtcha

Publications and source records attributed to Ezinvi Baloïtcha.

4 recordsLinked to original sources
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↗
arXiv2013

On nonlinear coherent states properties for electron-phonon dynamics

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.

math-ph↗
arXiv2013

$(q;l,λ)-$deformed Heisenberg algebra: representations, special functions and quantization

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.

math-ph↗