Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Explicit Solution of the Time Evolution of the Wigner Function   Previously, an explicit solution for the time evolution of the Wigner
function was presented in terms of auxiliary phase space coordinates which obey
simple equations that are analogous with, but not identical to, the classical
equations of motion. They can be solved easily and their solutions can be
utilized to construct the time evolution of the Wigner function. In this paper,
the usefulness of this explicit solution is demonstrated by solving a numerical
example in which the Wigner function has strong spatial and temporal variations
as well as regions with negative values. It is found that the explicit solution
gives a correct description of the time evolution of the Wigner function. We
examine next the pseudoparticle approximation which uses classical trajectories
to evolve the Wigner function. We find that the pseudoparticle approximation
reproduces the general features of the time evolution, but there are
deviations. We show how these deviations can be systematically reduced by
including higher-order correction terms in powers of $\hbar^2$.

26
The categories of this paper are: bayes-an
5
The categories of this paper are: gr-qc
10
The categories of this paper are: q-bio
31
The categories of this paper are: ao-sci
34
The categories of this paper are: chem-ph
37
The categories of this paper are: supr-con
36
The categories of this paper are: cmp-lg
15
The categories of this paper are: nucl-ex
22
The categories of this paper are: chao-dyn
6
The categories of this paper are: astro-ph
30
The categories of this paper are: q-alg
29
The categories of this paper are: funct-an
7
The categories of this paper are: hep-th
1
The categories of this paper are: cs
11
The categories of this paper are: hep-lat
27
The categories of this paper are: comp-gas