Related papers: q-deformed dynamics of q-deformed oscillators
We study main features of the exotic case of q-deformed oscillators (so-called Tamm-Dancoff cutoff oscillator) and find some special properties: (i) degeneracy of the energy levels E_{n_1} = E_{n_1+1}, n_1\ge 1, at the {\em real value}…
A deformed $q$-calculus is developed on the basis of an algebraic structure involving graded brackets. A number operator and left and right shift operators are constructed for this algebra, and the whole structure is related to the algebra…
The elliptic algebra A_{q,p}(sl(N)_{c}) at the critical level c=-N has an extended center containing trace-like operators t(z). Families of Poisson structures, defining q-deformations of the W_N algebra, are constructed. The operators t(z)…
A set of operators, the so-called k-fermion operators, that interpolate between boson and fermion operators are introduced through the consideration of an algebra arising from two non-commuting quon algebras. The deformation parameters q…
We study the canonical quantization of the damped harmonic oscillator by resorting to the realization of the q-deformation of the Weyl-Heisenberg algebra (q-WH) in terms of finite difference operators. We relate the damped oscillator…
Multifractals arise in various systems across nature whose scaling behavior is characterized by a continuous spectrum of multifractal exponents $\Delta_q$. In the context of Anderson transitions, the multifractality of critical wave…
An approach to study a generalization of the classical-quantum transition for general systems is proposed. In order to develop the idea, a deformation of the ladder operators algebra is proposed that contains a realization of the quantum…
The notion of $q$-grading on the enveloping algebra generated by products of q-deformed Heisenberg algebras is introduced for $q$ complex number in the unit disc. Within this formulation, we consider the extension of the notion of…
We found hermitian realizations of the position vector $\vec{r}$, angular momentum $\vec{\Lambda}$ and linear momentum $\vec{p}$ behaving like vectors with respect to the $SU_q(2)$ algebra, generated by $L_0$ and $L_\pm$. They are used to…
We propose a q-deformation of the su(2)-invariant Schrodinger equation of a spinless particle in a central potential, which allows us not only to determine a deformed spectrum and the corresponding eigenstates, as in other approaches, but…
This work addresses a ${\theta}(\hat{x},\hat{p})-$deformation of the harmonic oscillator in a $2D-$phase space. Specifically, it concerns a quantum mechanics of the harmonic oscillator based on a noncanonical commutation relation depending…
We introduce $q$-versions of the Klein-Gordon equation in the three-dimensional $q$-deformed Euclidean space. We determine plane wave solutions to our $q$-deformed Klein-Gordon equations. We show that these plane wave solutions form a…
All classical Lie algebras can be realized \`a la Schwinger in terms of fermionic oscillators. We show that the same can be done for their $q$-deformed counterparts by simply replacing the fermionic oscillators with anyonic ones defined on…
We construct a new model of the quantum oscillator, whose energy spectrum is equally-spaced and lower-bounded, whereas the spectra of position and momentum are a denumerable non-degenerate set of points in [-1,1] that depends on the…
We describe a $q$-deformed dynamical system corresponding to the quantum free particle moving along the circle. The algebra of observables is constructed and discussed. We construct and classify irreducible representations of the system.
Basic idea presented in Parts (I)-(III) for the deformed boson scheme is applied to the case of the su(2)- and su(1,1)-algebras for describing many-body systems consisting of four kinds of boson operators. A possible form of the coherent…
We study the dynamics of a symmetric two-level system strongly coupled to a broadened harmonic mode. Upon mapping the problem onto a spin-boson model with peaked spectral density, we show how analytic solutions can be obtained, at arbitrary…
Quantum algebras (also called quantum groups) are deformed versions of the usual Lie algebras, to which they reduce when the deformation parameter q is set equal to unity. From the mathematical point of view they are Hopf algebras. Their…
The quantum deformation concept is applied to a study of pairing correlations in nuclei with mass 40<A<100. While the nondeformed limit of the theory provides a reasonable overall description of certain nuclear properties and fine structure…
The notion of index is applied to analyze the phase operator problem associated with the photon. We clarify the absence of the hermitian phase operator on the basis of an index consideration. We point out an interesting analogy between the…