On Macroscopic Energy Gap for $q$-Quantum Mechanical Systems

TL;DR

This paper investigates the energy gap behavior in q-deformed harmonic oscillators within the Schwenk-Wess algebra, revealing that for values of q close to 1, the energy gap decreases with energy, contrasting with other deformations.

Contribution

It introduces analysis of the macroscopic energy gap in Schwenk-Wess q-quantum systems and compares it with other q-deformations, highlighting conditions where the gap can be avoided.

Findings

Energy gap decreases with energy for q~1

Contrasts with other q-deformations where gap increases

Potential to avoid macroscopic energy gap formation

Abstract

The q-deformed harmonic oscillator within the framework of the recently introduced Schwenk-Wess $q$-Heisenberg algebra is considered. It is shown, that for "physical" values $q\sim1$, the gap between the energy levels decreases with growing energy. Comparing with the other (real) $q$-deformations of the harmonic oscillator, where the gap instead increases, indicates that the formation of the macroscopic energy gap in the Schwenk-Wess $q$-Quantum Mechanics may be avoided.