The Husimi Distribution: Development and Applications

Abstract

The Husimi distribution, introduced by Kodi Husimi in 1940 [1], is a quasi-probability distribution commonly used to study the correspondence between quantum and classical dynamics [2]. Also, it is employed to describe systems in different areas of physics such as Quantum Mechanics, Quantum Optics, Information Theory [3–8]. Additionally, in nanotechnology it is possible to obtain a clear description of localization –which corresponds to classicality– and is crucial to determine correctly the size of systems when the particle dynamics takes into account mobility boundaries [9]. Among its properties, it is always positive definite and unique, conversely it cannot be considered as a true probability distribution over the quantum-mechanical phase space, reason why it is often considered as a quasi probability distribution. Although it possesses no correct marginal properties, its usefulness is to allow the assessment of the expectation values in quantum mechanics in a way similar to the classical case [10]. The semiclassical Husimi probability distribution refers to a special type of probability, this is for simultaneous but approximate location of position and momentum in phase space.