Quasiprobability distribution functions for finite-dimensional discrete phase spaces: Spin-tunneling effects in a toy model

TL;DR

This paper introduces a method using quasiprobability distribution functions on discrete phase spaces to analyze spin tunneling effects in finite quantum systems, demonstrated through the Lipkin-Meshkov-Glick model.

Contribution

It develops a novel formalism for finite-dimensional phase spaces and applies it to study spin tunneling and energy gaps in a specific quantum model.

Findings

Discrete Husimi function evolution obtained for the Lipkin-Meshkov-Glick model

Energy gap analyzed via angle-based potential approach

Entropy functionals discussed in the context of spin tunneling

Abstract

We show how quasiprobability distribution functions defined over $N^{2}$-dimensional discrete phase spaces can be used to treat physical systems described by a finite space of states which exhibit spin tunneling effects. This particular approach is then applied to the Lipkin-Meshkov-Glick model in order to obtain the time evolution of the discrete Husimi function, and as a by-product the energy gap for a symmetric combination of ground and first excited states. Moreover, we also show how an angle-based potential approach can be efficiently employed to explain qualitatively certain features of the energy gap in terms of a spin tunneling. Entropy functionals are also discussed in this context. Such results reinforce not only the formalism per se but also the possibility of some future potential applications in other branches of physics.