Related papers: On the Calogero model with negative harmonic term
Quantum dynamical semigroups are applied to the study of the time evolution of harmonic oscillators, both bosonic and fermionic. Explicit expressions for the density matrices describing the states of these systems are derived using the…
The dissipative harmonic oscillator has two representations. In the first representation the central oscillator couples with its position to an oscillator bath. In the second one it couples with its momentum to the bath. Both…
We study the known coherent states of a quantum harmonic oscillator from the standpoint of the original developed noncommutative integration method for linear partial differential equations. The application of the method is based on the…
We present basics of the gauged superfield approach to constructing N-superconformal multi-particle Calogero-type systems developed in arXiv:0812.4276, arXiv:0905.4951 and arXiv:0912.3508. This approach is illustrated by the multi-particle…
The second-order differential equation describes harmonic oscillators, as well as currents in LCR circuits. This allows us to study oscillator systems by constructing electronic circuits. Likewise, one set of closed commutation relations…
The q-deformation of harmonic oscillators is shown to lead to q-nonlinear vibrations. The examples of q-nonlinearized wave equation and Schr\"odinger equation are considered. The procedure is generalized to broader class of nonlinearities…
We construct the Runge-Lenz vector and symmetry algebra of rational Calogero-Coulomb problem, formulated in terms of Dunkl operators. We find that they are proper deformations of their Coulomb counterpart. Together with similar…
Classical oscillator differential equation is replaced by the corresponding (finite time) difference equation. The equation is, then, symmetrized so that it remains invariant under the change d going to -d, where d is the smallest span of…
A mathematical model is formulated for the evolution of plane perturbations in a cosmological two-component statistical system of completely degenerate scalarly charged fermions with an asymmetric scalar Higgs interaction. A complete closed…
We consider the quantum Calogero model, which describes N non-distinguishable quantum particles on the real line confined by a harmonic oscillator potential and interacting via two-body interactions proportional to the inverse square of the…
We preset a variant of the Caldeira-Leggett (CL) model of a harmonic oscillator coupled to an environment. The CL model is a standard tool for studying the physics of decoherence. Our "adapted Caldeira-Leggett" (ACL) model is built in a…
Recent developments on emergence of logarithmic terms in correlators or response functions of models which exhibit dynamical symmetries analogous to conformal invariance in not necessarily relativistic systems are reviewed. The main…
A new one-dimensional model, the multicomponent Calogero model of $B_N$-type confined in the harmonic potential, is introduced. The Lax pair of this model is determined, and then a set of functionally independent conserved operators are…
In this paper, I present a mapping between representation of some quantum phenomena in one dimension and behavior of a classical time-dependent harmonic oscillator. For the first time, it is demonstrated that quantum tunneling can be…
We introduce O-systems (Definition \ref{DO}) of orthogonal transformations of ${\Bbb R}^{m}$, and establish $1-1$ correspondences both between equivalence classes of Clifford systems and that of O-systems, and between O-systems and…
It is proved that a classical (respec. quantum) system consisting of a particle in a constant magnetic field is canonically (respec. unitarily) equivalent to a 2-dimensional harmonic oscillator plus a free particle. It is also shown that…
We discuss a many-particle quantum system, which is obtained by adding some nonhermitian but PT (i.e. combined parity and time reversal) invariant interaction to the $A_{N-1}$ rational Calogero model without confining potential. This model…
We consider the relativistic generalization of the harmonic oscillator problem by addressing different questions regarding its classical aspects. We treat the problem using the formalism of Hamiltonian mechanics. A Lie algebraic technique…
A {\em complex} canonical transformation is found that takes the fourth order derivative Pais-Uhlenbeck oscillator into two independent harmonic oscillators thus showing that this model has energy bounded from below, unitary time-evolution…
The classical and quantum oscillator model on Lie-algebraically deformed nonrelativistic space-time is introduced and analyzed. The corresponding equations of motions are studied using mostly numerical methods. The time-dependent energy…