Semiclassical Husimi Function of Simple and Chaotic Systems

Abstract

We review the semiclassical method proposed in [1], a generalization of this method for n-dimensional system is presented. Using the cited method, we present an analytical method of obtain the semiclassical Husimi Function. The validity of the method is tested using Harmonic Oscillator, Morse Potential and Dikie’s Model as example, we found a good accuracy in the classical limit

Relation Between The Roughness, Linear Entropy and Visibility of A Quantum State, The Jaynes-Cummings Model.

“…The Roughness is a measure that captures the main aspects of the quantum behavior, considering a distance between Wigner and Husimi function. The success of Roughness is due to the fact that although Husimi is a quantum distribution, it is mainly dominated by the classical dynamics since it can be approximately reproduced by classical trajectories for integrable and no-integrable dynamic [31,32]. It is important to highlight that the information about which pure states are "traversed" by the dynamics is not usually easily accessible, but in the diagram R × δ or R × C it is clear which are the states, once they are known for their roughness.…”

“…As Wigner function has all information about the state and Husimi function can approximately be obtained from classical trajectories [31,32], then Roughness can be interpreted as a distance of the quantum state from the most classical positive quantum distribution. In fact, Roughness is close related to Nearest Hilbert-Schmidt distance [33], which is defined as the minimum distance from a coherent state, the difference is that a Gaussian state is not usually the classical distribution [34][35][36][37][38].…”