Semi-spectral method for the Wigner equation

JOURNAL OF COMPUTATIONAL PHYSICS

卷:305

Article

Furtmaier, O.¹  Succi, S.²  Mendoza, M.¹ 

[1] Swiss Fed Inst Technol, Inst Bldg Mat, CH-8093 Zurich, Switzerland

[2] CNR, Ist Applicaz Calcolo, I-00185 Rome, Italy

关键词: Wigner equation;    Spectral method;    Reaction-advection;   

DOI  :  10.1016/j.jcp.2015.11.023

来源: Elsevier

【 摘 要 】

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(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 and Morse 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. (C) 2015 Elsevier Inc. All rights reserved.

【 授权许可】

Free