Related papers: Special Deformed Exponential Functions Leading to …
Starting on the basis of $q$-symmetric oscillator algebra and on the associate $q$-calculus properties, we study a deformed quantum mechanics defined in the framework of the basic square-integrable wave functions space. In this context, we…
Starting from deformed quantum Heisenberg Lie algebras some realizations are given in terms of the usual creation and annihilation operators of the standard harmonic oscillator. Then the associated algebra eigenstates are computed and give…
For a q-deformed harmonic oscillator, we find explicit coordinate representations of the creation and annihilation operators, eigenfunctions, and coherent states (the last being defined as eigenstates of the annihilation operator). We…
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…
This work addresses the study of the oscillator algebra, defined by four parameters $p$, $q$, $\alpha$, and $\nu$. The time-independent Schr\"{o}dinger equation for the induced deformed harmonic oscillator is solved; explicit analytic…
We construct a new family of q-deformed coherent states $|z>_q$, where $0 < q < 1$. These states are normalizable on the whole complex plane and continuous in their label $z$. They allow the resolution of unity in the form of an ordinary…
We present a theory of quantized radiation fields described in terms of q-deformed harmonic oscillators. The creation and annihilation operators satisfy deformed commutation relations and the Fock space of states is constructed in this…
A new kind of deformed calculus (the D-deformed calculus) that takes place in fractional-dimensional spaces is presented. The D-deformed calculus is shown to be an appropriate tool for treating fractional-dimensional systems in a simple way…
The coherent states for twist-deformed oscillator model provided in article [1] are constructed. Besides, it is demonstrated that the energy spectrum of considered model is labeled by two quantum numbers - by so-called main and azimutal…
Quantum correlations in compound systems are of great importance, and they are fundamental resource for the development of quantum computation protocols and quantum information. In this work we construct bipartite pure coherent states using…
A unified method of calculating structure functions from commutation relations of deformed single-mode oscillator algebras is presented. A natural approach to building coherent states associated to deformed algebras is then deduced.
The Tsallis $q$-exponential function $e_q(x) = (1+(1-q)x)^{\frac{1}{1-q}}$ is found to be associated with the deformed oscillator defined by the relations $\left[N,a^\dagger\right] = a^\dagger$, $[N,a] = -a$, and $\left[a,a^\dagger\right] =…
The Heisenberg algebra is deformed with the set of parameters ${q, l,\lambda}$ to generate a new family of generalized coherent states respecting the Klauder criteria. In this framework, the matrix elements of relevant operators are exactly…
Maths-type q-deformed coherent states with $q > 1$ allow a resolution of unity in the form of an ordinary integral. They are sub-Poissonian and squeezed. They may be associated with a harmonic oscillator with minimal uncertainties in both…
It is shown that q-deformed quantum mechanics (systems with q-deformed Heisenberg commutation relations) can be interpreted as an ordinary quantum mechanics on Kaehler manifolds, or as a quantum theory with second (or first)- class…
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…
Coherent states possess a regularized path integral and gives a natural relation between classical variables and quantum operators. Recent work by Klauder and Whiting has included extended variables, that can be thought of as gauge fields,…
We address quantum systems isospectral to the harmonic oscillator, as those found within the framework of supersymmetric quantum mechanics, as potential resources for continuous variable quantum information. These deformed oscillator…
A deformed boson algebra is naturally introduced from studying quantum mechanics on noncommutative phase space in which both positions and momenta are noncommuting each other. Based on this algebra, corresponding intrinsic noncommutative…
Deformation quantization is a powerful tool to quantize some classical systems especially in noncommutative space. In this work we first show that for a class of special Hamiltonian one can easily find relevant time evolution functions and…