Applications of deformed oscillators

P. P. Raychev, R. P. Roussev, Nicola Lo Iudice +1 more

A procedure for the construction of a q -deformed version of the Hamiltonian of the three-dimensional harmonic oscillator (HO), based on the application of q -deformed algebras, is presented. The spectrum of this Hamiltonian is not degenerated in the quantum number of the q -deformed angular momentum. The results together with their applicability to the shell model are compared with the predictions of the modified HO.

Chong Li, He‐Shan Song

Won Sang Chung, Abdullah Algin

Abstract In this paper, we consider a system of the q-deformed bosonic Tamm-Dancoff oscillators, whose spectrum has some exponential cutoff factors at high energies. We first investigate the q-calculus in the Tamm-Dancoff (TD) boson algebra, and within this framework, the q-derivative, q-integral and q-exponential function are introduced. Using these properties, we construct a new formalism for the q-deformed quantum mechanics, which accordingly involve the q-adjoint operator and the q-Hermitian operator properties. We then derive the q-deformed Heisenberg relation, and develop the q-Hermitian momentum operator. The q-deformed Schrödinger equation is introduced, and as applications, we study the momentum eigenfunction and one-dimensional box problem. Another application of the TD type deformation onto lattice oscillations is also discussed through a model of the q-deformed Debye solid. Finally, other potential applications of the TD-oscillators gas model are concisely pointed out.

JoséLuis Gruver

Huangcheng Yin

Abstract In this paper, we will use fluctuation dissipation theorem on the harmonic oscillator with time correlation creation annihilation operator as the perturbated term and through calculation, we find that the exact value of the dissipation associated Imχ of this special perturbation harmonic oscillator is exactly equal to π. Next, we give its potential application in the q-deformed harmonic oscillator, which means connect the q-deformed harmonic oscillator with fluctuation dissipation.

Antony Streklas