Quasiprobability currents on the sphere

TL;DR

This paper derives analytic expressions for quasiprobability currents on the sphere, analyzing their behavior under unitary and dissipative dynamics, and applies these to study quantum dissipative systems like Kerr and Lipkin models.

Contribution

It provides new analytic formulas for quasiprobability currents on the sphere and explores their spatial distribution in various quantum regimes.

Findings

Analytic expressions for $s$-parametrized currents on the sphere.

Insights into the flow patterns for quadratic Hamiltonians.

Application to Kerr and Lipkin models revealing semiclassical limits.

Abstract

We present analytic expressions for the $s$-parametrized currents on the sphere for both unitary and dissipative evolutions. We examine the spatial distribution of the flow generated by these currents for quadratic Hamiltonians. The results are applied for the study of the quantum dissipative dynamics of the time-honored Kerr and Lipkin models, exploring the appearance of the semiclassical limit in stable, unstable and tunnelling regimes.