Husimi-Wigner representation of chaotic eigenstates

TL;DR

This paper introduces the Husimi-Wigner representation, a novel phase space method that visualizes chaotic eigenstates by combining features of Husimi and Wigner functions, revealing detailed quantum structures.

Contribution

The paper develops the Husimi-Wigner representation as a new tool to analyze chaotic eigenstates, bridging classical and quantum phase space descriptions.

Findings

Husimi-Wigner functions resemble semiclassical states with dislocations.

The representation captures nonclassical features of chaotic eigenstates.

It provides a detailed phase space visualization of quantum chaos.

Abstract

Just as a coherent state may be considered as a quantum point, its restriction to a factor space of the full Hilbert space can be interpreted as a quantum plane. The overlap of such a factor coherent state with a full pure state is akin to a quantum section. It defines a reduced pure state in the cofactor Hilbert space. The collection of all the Wigner functions corresponding to a full set of parallel quantum sections defines the Husimi-Wigner reresentation. It occupies an intermediate ground between drastic suppression of nonclassical features, characteristic of Husimi functions, and the daunting complexity of higher dimensional Wigner functions. After analysing these features for simpler states, we exploit this new representation as a probe of numerically computed eigenstates of chaotic Hamiltonians. The individual two-dimensional Wigner functions resemble those of semiclassically quantized states, but the regular ring pattern is broken by dislocations.