Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Semi-Spectral Method for the Wigner equation   We propose a numerical method to solve the Wigner equation in quantum systems
of spinless, non-relativistic particles. The method uses a spectral
decomposition into $L^2(\mathbb{R}^d)$ basis functions in momentum-space to
obtain a system of first-order advection-reaction equations. The resulting
equations are solved by splitting the reaction and advection steps so as to
allow the combination of numerical techniques from quantum mechanics and
computational fluid dynamics by identifying the skew-hermitian reaction matrix
as a generator of unitary rotations. The method is validated for the case of
particles subject to a one-dimensional (an-)harmonic potential using
finite-differences for the advection part. Thereby, we verify the second order
of convergence and observe non-classical behavior in the evolution of the
Wigner function.

30
The categories of this paper are: q-alg
17
The categories of this paper are: q-fin
33
The categories of this paper are: plasm-ph
15
The categories of this paper are: nucl-ex
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The categories of this paper are: comp-gas
8
The categories of this paper are: hep-ex
21
The categories of this paper are: adap-org
9
The categories of this paper are: nlin
14
The categories of this paper are: math-ph
31
The categories of this paper are: ao-sci
34
The categories of this paper are: chem-ph
12
The categories of this paper are: nucl-th
23
The categories of this paper are: solv-int
18
The categories of this paper are: econ
16
The categories of this paper are: stat
24
The categories of this paper are: dg-ga