Topological structures in the Husimi flow

TL;DR

This paper investigates the topological features of quantum phase space currents in the Husimi representation, revealing how zeros of the Husimi function influence quantum-classical dynamical differences and particle transmission.

Contribution

It introduces the topological analysis of the Husimi current, highlighting the role of zeros as stagnation points with nonzero charge and their impact on quantum dynamics.

Findings

Zeros of the Husimi function are stagnation points with topological charge.

Pair creation of stagnation points with opposite charge occurs due to charge conservation.

Topological effects influence particle transmission through potential barriers.

Abstract

We study the topological properties of the quantum phase space current in the Husimi representation, focusing on the dynamical differences, induced by these properties, between the quantum and the classical flows. We show that the zeros of the Husimi function are stagnation points of the current and have a nonzero topological charge. Due to overall charge conservation, new stagnation points with opposite charge appear in pairs in the Husimi current and they have important roles in dynamical processes. As an example we show the topological effect of the zeros in the transmission rate of particle through a potential barrier.