Smoothed Wigner functions: a tool to resolve semiclassical structures

The Wigner and Husimi distributions are the usual phase space representations of a quantum state. The Wigner distribution has structures of order 2. On the other hand, the Husimi distribution is a Gaussian smearing of the Wigner function on an area of size and then, it only displays structures of size . We have developed a phase space representation which results a Gaussian smearing of the Wigner function on an area of size , with 1. Within this representation, the Husimi and Wigner functions are recovered when =1 and 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.