Related papers: Polynomially deformed oscillators as k-bonacci osc…
We give a general approach for the construction of deformed oscillators. These ones could be seen as describing deformed bosons. Basing on new definitions of certain quantum series, we demonstrate that they are nothing but the ordinary…
The quantum deformed (1+1) Poincare' algebra is shown to be the kinematical symmetry of the harmonic chain, whose spacing is given by the deformation parameter. Phonons with their symmetries as well as multiphonon processes are derived from…
We study quantum deformations of Poisson orbivarieties. Given a Poisson manifold $(\mathbb{R}^{m},\alpha)$ we consider the Poisson orbivariety $(\mathbb{R}^{m})^{n}/S_{n}$. The Kontsevich star product on functions on $(\mathbb{R}^{m})^{n}$…
Considering a multi-dimensional $q$-oscillator invariant under the (non quantum) group $U(n)$, we construct a $q$-deformed Levi-Civita epsilon tensor from the inner product states. The invariance of this $q$-epsilon tensor is shown to yield…
We present a framework for the study of $q$-difference equations satisfied by $q$-semi-classical orthogonal systems. As an example, we identify the $q$-difference equation satisfied by a deformed version of the little $q$-Jacobi polynomials…
The ``position'' and ``momentum'' operators for the q-deformed oscillator with q being a root of unity are proved to have discrete eigenvalues which are roots of deformed Hermite polynomials. The Fourier transform connecting the…
Assume that $\{a_{n};\,n\geq0\}$ is a sequence of positive numbers and $\sum a_{n}^{\,-1}<\infty$. Let $\alpha_{n}=ka_{n}$, $\beta_{n}=a_{n}+k^{2}a_{n-1}$ where $k\in(0,1)$ is a parameter, and let $\{P_{n}(x)\}$ be an orthonormal polynomial…
It is proved that quasi-exactly soluble potentials corresponding to an oscillator with harmonic, quartic and sextic terms, for which the $n+1$ lowest levels of a given parity can be determined exactly, may be approximated by WKB equivalent…
The generalized deformed oscillator schemes introduced as unified frameworks of various deformed oscillators are proved to be equivalent, their unified representation leading to a correspondence between the deformed oscillator and the N=2…
Several physical systems (two identical particles in two dimensions, isotropic oscillator and Kepler system in a 2-dim curved space) and mathematical structures (quadratic algebra QH(3), finite W algebra $\bar {\rm W}_0$) are shown to…
The quantum deformation of the oscillator algebra and its implications on the phase operator are studied from a view point of an index theorem by using an explicit matrix representation. For a positive deformation parameter $q$ or…
Consider in $L^2 (\R^l)$ the operator family $H(\epsilon):=P_0(\hbar,\omega)+\epsilon Q_0$. $P_0$ is the quantum harmonic oscillator with diophantine frequency vector $\om$, $Q_0$ a bounded pseudodifferential operator with symbol…
One possible data encryption scheme is related to stream ciphers, which use a sufficiently long pseudo-random sequence. To increase the cryptographic strength of the cipher, linear shift algorithms (generated by linear recurrent sequences…
We consider a partially hinged rectangular plate and its normal modes. There are two families of modes, longitudinal and torsional. We study the variation of the corresponding eigenvalues under domain deformations. We investigate the…
We show that the single-mode parafermionic type systems possess supersymmetry, which is based on the symmetry of characteristic functions of the parafermions related to the generalized deformed oscillator of Daskaloyannis et al. The…
The Heisenberg algebra is first deformed with the set of parameters ${q, l, \lambda}$ to generate a new family of generalized coherent states. In this framework, the matrix elements of relevant operators are exactly computed. A proof on…
We extend the theory of Coulomb blockade oscillations to quantum dots which are deformed by the confining potential. We show that shape deformations can generate sequences of conductance resonances which carry the same internal…
The $d$-Fibonacci digraphs $F(d,k)$, introduced here, have the number of vertices following generalized Fibonacci-like sequences. They can be defined both as digraphs on alphabets and as iterated line digraphs. Here we study some of their…
We construct a category of quantum polynomial functors which deforms Friedlander and Suslin's category of strict polynomial functors. The main aim of this paper is to develop from first principles the basic structural properties of this…
We investigate a U(1) gauge invariant quantum mechanical system on a 2D noncommutative space with coordinates generating a generalized deformed oscillator algebra. The Hamiltonian is taken as a quadratic form in gauge covariant derivatives…