Smoothed Wigner functions: a tool to resolve semiclassical structures

Abstract

The Wigner and Husimi distributions are the usual phase space representations of a quantum state. The Wigner distribution has structures of order ħ2. On the other hand, the Husimi distribution is a Gaussian smearing of the Wigner function on an area of size ħ and then, it only displays structures of size ħ. We have developed a phase space representation which results a Gaussian smearing of the Wigner function on an area of size ħσ, with σ≥1. Within this representation, the Husimi and Wigner functions are recovered when σ=1 and $ \sigma \gtrsim 2 $ respectively. We treat the application of this intermediate representation to explore the semiclassical limit of quantum mechanics. In particular we show how this representation uncover semiclassical hyperbolic structures of chaotic eigenstates.