Generalized deformed oscillator for vortices in superfluid films

TL;DR

This paper introduces a new generalized deformed oscillator model to describe vortex observables in superfluid films, revealing unique mathematical properties and a novel boson realization of the su(1,1) algebra.

Contribution

It presents a novel generalized deformed oscillator with a unique structure function for vortices in superfluids, not reducible to perturbative methods or quons, and offers a new boson realization of su(1,1).

Findings

Describes vortex algebra as a generalized deformed oscillator.

Identifies the oscillator's non-perturbative nature and distinct structure function.

Provides a new boson realization of the su(1,1) algebra.

Abstract

The algebra of observables of a system of two identical vortices in a superfluid thin film is described as a generalized deformed oscillator with a structure function containing a linear (harmonic oscillator) term and a quadratic term. In contrast to the deformed oscillators occuring in other physical systems (correlated fermion pairs in a single-$j$ nuclear shell, Morse oscillator), this oscillator is not amenable to perturbative treatment and cannot be approximated by quons. From the mathematical viewpoint, this oscillator provides a novel boson realization of the algebra su(1,1).