Generalized para-Bose states

TL;DR

This paper develops a framework for generalized para-Bose states using integrals of motion, exploring their properties, completeness, and behavior in a time-dependent quadratic Hamiltonian, with applications to the para-Bose oscillator.

Contribution

It introduces generalized para-Bose states with a Wigner parameter, extending squeezed and coherent states, and analyzes their properties and dynamics in a time-dependent setting.

Findings

Generalized states include a Wigner parameter affecting dispersion.

Displacement parameter enables access to odd states.

Mean values oscillate similarly to harmonic oscillator, with corrections.

Abstract

In this paper, we construct integrals of motion in a para-Bose formulation for a general time-dependent quadratic Hamiltonian, which, in its turn, commutes with the reflection operator. In this context, we obtain generalizations for the squeezed vacuum states (SVS) and coherent states (CS) in terms of the Wigner parameter. Furthermore, we show that there is a completeness relation for the generalized SVS owing to the Wigner parameter. In the study of the probability transition, we found that the displacement parameter acts as a transition parameter by allowing access to odd states, while the Wigner parameter controls the dispersion of the distribution. We show that the Wigner parameter is quantized by imposing that the vacuum state has even parity. We apply the general results to the case of the time-independent para-Bose oscillator and find that the mean values of the coordinate and momentum have an oscillatory behavior similarly to the simple harmonic oscillator, while the standard deviation presents corrections in terms of the squeeze, displacement, and Wigner parameters.