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V. Hussin

Publications and source records attributed to V. Hussin.

10 recordsLinked to original sources
arXiv2020

Nonclassical States for Non-Hermitian Hamiltonians with the Oscillator Spectrum

We show that the standard techniques that are utilized to study the classical like properties of the pure states for Hermitian systems can be adjusted to investigate the classicality of pure states for non-Hermitian systems. The method is applied to the states of complex-valued potentials that are generated by Darboux transformations and can model both non-PT-symmetric and PT-symmetric oscillators exhibiting real spectra.

quant-ph↗
arXiv2019

Constant curvature holomorphic solutions of the supersymmetric grassmannian sigma model: the case of $G(2,4)$

We explore the constant curvature holomorphic solutions of the supersymmetric grassmannian sigma model $G(M,N)$ using in particular the gauge invariance of the model. Supersymmetric invariant solutions are constructed via generalizing a known result for ${C}P^{N-1}$. We show that some other such solutions also exist. Indeed, considering the simplest case of $G(2,N)$ model, we give necessary and sufficient conditions for getting the constant curvature holomorphic solutions. Since, all the constant curvature holomorphic solutions of the bosonic $G(2,4)$ $σ$-model are known, we treat this example in detail.

hep-th↗
arXiv2018

Classical ladder functions for Rosen-Morse and curved Kepler-Coulomb systems

Ladder functions in classical mechanics are defined in a similar way as ladder operators in the context of quantum mechanics. In the present paper, we develop a new method for obtaining ladder functions of one dimensional systems by means of a product of two `factor functions'. We apply this method to the curved Kepler-Coulomb and Rosen-Morse II systems whose ladder functions were not found yet. The ladder functions here obtained are applied to get the motion of the system.

math-ph↗
arXiv2013

Squeezed coherent states and the one-dimensional Morse quantum system

The Morse potential one-dimensional quantum system is a realistic model for studying vibrations of atoms in a diatomic molecule. This system is very close to the harmonic oscillator one. We thus propose a construction of squeezed coherent states similar to the one of harmonic oscillator using ladder operators. Properties of these states are analysed with respect to the localization in position, minimal Heisenberg uncertainty relation, the statistical properties and illustrated with examples using the finite number of states in a well-known diatomic molecule.

math-ph↗
arXiv2010

Squeezed coherent states and the Morse quantum system

The Morse potential quantum system is a realistic model for studying vibrations of atoms in a diatomic molecule. This system is very close to the harmonic oscillator one. We thus propose a construction of squeezed coherent states similar to the one of harmonic oscillator using ladder operators. Properties of these states are analysed with respect to the localization in position, minimal Heisenberg uncertainty relation, the statistical properties and illustrated with examples using the finite number of states in a well-known diatomic molecule.

math-ph↗
arXiv2010

Canonical surfaces associated with projectors in grassmannian sigma models

We discuss the construction of higher-dimensional surfaces based on the harmonic maps of $S^2$ into $CP^{N-1}$ and other grassmannians. We show that there are two ways of implementing this procedure - both based on the use of the relevant projectors. We study various properties of such projectors and show that the Gaussian curvature of these surfaces, in general, is not constant. We look in detail at the surfaces corresponding to the Veronese sequence of such maps and show that for all of them this curvature is constant but its value depends on which mapping is used in the construction of the surface.

math-ph↗
arXiv2009

Gardner's deformations of the N=2 supersymmetric a=4-KdV equation

We prove that P.Mathieu's Open problem on constructing Gardner's deformation for the N=2 supersymmetric a=4-Korteweg-de Vries equation has no supersymmetry invariant solutions, whenever it is assumed that they retract to Gardner's deformation of the scalar KdV equation under the component reduction. At the same time, we propose a two-step scheme for the recursive production of the integrals of motion for the N=2, a=4-SKdV. First, we find a new Gardner's deformation of the Kaup-Boussinesq equation, which is contained in the bosonic limit of the super-hierarchy. This yields the recurrence relation between the Hamiltonians of the limit, whence we determine the bosonic super-Hamiltonians of the full N=2, a=4-SKdV hierarchy. Our method is applicable towards the solution of Gardner's deformation problems for other supersymmetric KdV-type systems.

nlin.SI↗
arXiv2006

Susy CP^(N-1) model and surfaces in R^(N^2-1)

We describe surfaces in R^{N^2-1} generated by the holomorphic solutions of the supersymmetric CP^{N-1} model. We show that these surfaces are described by the fundamental projector constructed out of the solutions of this model and that in the CP^{N-1} case the corresponding surface is a sphere. Although the coordinates of the sphere are superfields the sphere's curvature is constant. We show that for N>2 the corresponding surfaces can also be constructed from the similar projector.

math-ph↗
arXiv1997

Classification of the quantum deformation of the superalgebra $GL(1|1)$

We present a classification of the possible quantum deformations of the supergroup $GL(1|1)$ and its Lie superalgebra $gl(1|1)$. In each case, the (super)commutation relations and the Hopf structures are explicitly computed. For each $R$ matrix, one finds two inequivalent coproducts whether one chooses an unbraided or a braided framework while the corresponding structures are isomorphic as algebras. In the braided case, one recovers the classical algebra $gl(1|1)$ for suitable limits of the deformation parameters but this is no longer true in the unbraided case.

q-alg↗