Mapping Wigner distribution functions into semiclassical distribution functions

Semiclassical propagation of Wigner functions.

We present a comprehensive study of semiclassical phase-space propagation in the Wigner representation, emphasizing numerical applications, in particular as an initial-value representation. Two semiclassical approximation schemes are discussed. The propagator of the Wigner function based on van Vleck's approximation replaces the Liouville propagator by a quantum spot with an oscillatory pattern...

Semiclassical analysis of Wigner functions

Abstract. In this work we study the Wigner functions, which are the quantum analogues of the classical phase space density, and show how a full rigorous semiclassical scheme for all orders of h̄ can be constructed for them without referring to the actual coordinate space wavefunctions from which the Wigner functions are typically calculated. We find such a picture by a careful analysis around th...

Seismic imaging with Wigner distribution functions

The fidelity of depth seismic imaging depends on the accuracy of the velocity models used for wavefield reconstruction. Models can be decomposed in two components corresponding to large scale and small scale variations. In practice, the large scale velocity model component can be estimated with high accuracy using repeated migration/tomography cycles, but the small scale component cannot. When ...

Distribution Functions

Wigner distribution functions for complex dynamical systems: the emergence of the Wigner-Boltzmann equation.

The equation of motion for the reduced Wigner function of a system coupled to an external quantum system is presented for the specific case when the external quantum system can be modeled as a set of harmonic oscillators. The result is derived from the Wigner function formulation of the Feynman-Vernon influence functional theory. It is shown how the true self-energy for the equation of motion i...