Geometrical approach to the distribution of the zeroes for the Husimi function

Abstract

We construct a semiclassical expression for the Husimi function of autonomous systems in one degree of freedom, by smoothing with a Gaussian function an expression that captures the essential features of the Wigner function in the semiclassical limit. Our approximation reveals the "center and chord" estructure that the Husimi function inherits from the Wigner function, down to very shallow "valleys", where lie the Husimi zeroes. This explanation for the distribution of zeroes along curves relies on the geometry of the classical torus, rather than the complex analytical properties of the WKB method in the Bargmann representation. We evaluate the zeroes for several examples.