Fractional Supersymmetry as a Superposition of Ordinary Supersymmetry
It is shown how to derive fractional supersymmetric quantum mechanics of order k as a superposition of k-1 copies of ordinary supersymmetric quantum mechanics.
quant-ph↗
arXiv subjects
M. Daoud
Publications and source records attributed to M. Daoud.
Covariance of noncommutative Grassmann star product
Using the Coherent states of many fermionic degrees of freedom labeled by Graßmann variables, we introduce the noncommutative (precisely non anticommutative) Graßmann star product. The covariance of star product under unitary transformations, particularly canonical ones, is studied. The super star product, based on supercoherent states of supersymmetric harmonic oscillator, is also considered.
math-ph↗
Robertson-Schrödinger intelligent states for two-body Calogero model
Using the Gazeau-Klauder and Klauder-Perelomov coherent states, we derive the Robertson-Schrödinger intelligent states for two-body Calogero quantum system.
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Statistical properties of Klauder-Perelomov coherent states for the Morse potential
We present in this paper a realistic construction of the coherent states for the Morse potential using the Klauder-Perelomov approach . We discuss the statistical properties of these states, by deducing the Q- and P-distribution functions. The thermal expectations for the quantum canonical ideal gas of the Morse oscillators are also calculated.
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Generalized intelligent states of the su(N) algebra
Schr\" odinger-Robertson uncertainty relation is minimized for the quadrature components of Weyl generators of the algebra $su(N)$. This is done by determining explicit Fock-Bargamann representation of the $su(N)$ coherent states and the differential realizations of the elements of $su(N)$. New classes of coherent and squeezed states are explicitly derived.
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Photon-added coherent states for exactly solvable Hamiltonians
Photon-added Gazeau-Klauder and Klauder-Perelomov coherent states are investigated. Application to Pöschl-Teller potentials is given.
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Extended Voros product in the coherent states framework
Using coherent states of the Weyl-Heisenberg algebra $h_N$, extended Voros products and Moyal brakets are derived. The covariance of Voros product under canonical transformations is discussed. Star product related to Barut-Girardello coherent states of the Lie algebra $su(1,1)$ is also considered. The star eigenvalue problem of singular harmonic osillator is investigated.
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Analytic representations based on su(3) coherent states and Robertson intelligent states
Robertson intelligent states which minimize the Schr\" odinger-Robertson uncertainty relation are constructed as eigenstates of a linear combination of Weyl generators of the $su(3)$ algebra. The construction is based on the analytic representations of $su(3)$ coherent states. New classes of coherent and squeezed states are explicitly derived.
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Extended Weyl-Heisenberg algebra and Rubakov-Spiridonov superalgebra: Anyonic realizations
We give the realizations of the extended Weyl-Heisenberg (WH) algebra and the Rubakov-Spiridonov (RS) superalgebra in terms of anyons, characterized by the statistical parameter $ν\in[0,1]$, on two-dimensional lattice. The construction uses anyons defined from usual fermionic oscillators (Lerda-Sciuto construction). The anyonic realization of the superalgebra $sl(1/1)$ is also presented.
hep-th↗
A Generalized Jaynes-Cummings Model: Nonlinear dynamical superalgebra $u(1/1)$ and Supercoherent states
The generalization of the Jaynes-Cummings (GJC) Model is proposed. In this model, the electromagnetic radiation is described by a Hamiltonian generalizing the harmonic oscillator to take into account some nonlinear effects which can occurs in the experimental situations. The dynamical superalgebra and supercoherent states of the related model are explicitly constructed. A relevant quantities (total number of particles, energy and atomic inversion) are computed.
hep-th↗
Generalized coherent and intelligent states for exact solvable quantum systems
The so-called Gazeau-Klauder and Perelomov coherent states are introduced for an arbitrary quantum system. We give also the general framework to construct the generalized intelligent states which minimize the Robertson-Schrödinger uncertainty relation. As illustration, the Pöschl-Teller potentials of trigonometric type will be chosen. We show the advantage of the analytical representations of Gazeau-Klauder and Perelomov coherent states in obtaining the generalized intelligent states in analytical way.
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Generalized Intelligent States for Nonlinear Oscillators
The construction of Generalized Intelligent States (GIS) for the $x^4$% -anharmonic oscillator is presented. These GIS families are required to minimize the Robertson-Schrödinger uncertainty relation. As a particular case, we will get the so-called Gazeau-Klauder coherent states. The properties of the latters are discussed in detail. Analytical representation is also considered and its advantage is shown in obtaining the GIS in an analytical way. Further extensions are finally proposed.
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Coherent and generalized intelligent states for infinite square well potential and nonlinear oscillators
This article is an illustration of the construction of coherent and generalized intelligent states which has been recently proposed by us for an arbitrary quantum system $[ 1] $. We treat the quantum system submitted to the infinite square well potential and the nonlinear oscillators. By means of the analytical representation of the coherent states à la Gazeau-Klauder and those à la Klauder-Perelomov, we derive the generalized intelligent states in analytical ways.
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Fractional supersymmetric Quantum Mechanics as a set of replicas of ordinary supersymmetric Quantum Mechanics
A connection between fractional supersymmetric quantum mechanics and ordinary supersymmetric quantum mechanics is established in this Letter.
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Coherent states à la Klauder-Perelomov for the Pöschl-Teller potentials
In this paper we present a scheme for constructing the coherent states of Klauder-Perelomov's type for a particle which is trapped in Pöschl-Teller potentials.
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Generalized Intelligent States for an Arbitrary Quantum System
Generalized Intelligent States (coherent and squeezed states) are derived for an arbitrary quantum system by using the minimization of the so-called Robertson-Schrödinger uncertainty relation. The Fock-Bargmann representation is also considered. As a direct illustration of our construction, the Pöschl-Teller potentials of trigonometric type will be shosen. We will show the advantage of the Fock-Bargmann representation in obtaining the generalized intelligent states in an analytical way. Many properties of these states are studied.
quant-ph↗
The Moyal Bracket in the Coherent States framework
The star product and Moyal bracket are introduced using the coherent states corresponding to quantum systems with non-linear spectra. Two kinds of coherent state are considered. The first kind is the set of Gazeau-Klauder coherent states and the second kind are constructed following the Perelomov-Klauder approach. The particular case of the harmonic oscillator is also discussed.
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On Two Approaches to Fractional Supersymmetric Quantum Mechanics
Two complementary approaches of N = 2 fractional supersymmetric quantum mechanics of order k are studied in this article. The first one, based on a generalized Weyl-Heisenberg algebra W(k) (that comprizes the affine quantum algebra Uq(sl(2)) with q to k = 1 as a special case), apparently contains solely one bosonic degree of freedom. The second one uses generalized bosonic and k-fermionic degrees of freedom. As an illustration, a particular emphasis is put on the fractional supersymmetric oscillator of order k.
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