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Title: Single-cone finite difference scheme for the (2+1)D Dirac von Neumann equation

Abstract

An explicit finite difference scheme is presented for the von Neumann equation for (2+1)D Dirac fermions. It is founded upon a staggered space–time grid which ensures a single-cone energy dispersion and performs the time-derivative in one sweep using a three-step leap-frog procedure. It enables a space–time-resolved numerical treatment of the mixed-state dynamics of Dirac fermions within the effective single-particle density matrix formalism. Energy-momentum dispersion, stability and convergence properties are derived. Elementary numerical tests to demonstrate stability properties use parameters which pertain to topological insulator surface states. A method for the simulation of charge injection from an electric contact is presented and tested numerically. Potential extensions of the scheme to a Dirac–Lindblad equation, real-space–time Green's function formulations, and higher-order finite-difference schemes are discussed.

Authors:
;
Publication Date:
OSTI Identifier:
22701624
Resource Type:
Journal Article
Journal Name:
Journal of Computational Physics
Additional Journal Information:
Journal Volume: 348; Other Information: Copyright (c) 2017 Elsevier Science B.V., Amsterdam, The Netherlands, All rights reserved.; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0021-9991
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; DENSITY MATRIX; DIRAC EQUATION; ELECTRIC CONTACTS; FERMIONS; MIXED STATES; SPACE-TIME; THREE-DIMENSIONAL CALCULATIONS

Citation Formats

Pötz, Walter, and Schreilechner, Magdalena. Single-cone finite difference scheme for the (2+1)D Dirac von Neumann equation. United States: N. p., 2017. Web. doi:10.1016/J.JCP.2017.07.037.
Pötz, Walter, & Schreilechner, Magdalena. Single-cone finite difference scheme for the (2+1)D Dirac von Neumann equation. United States. doi:10.1016/J.JCP.2017.07.037.
Pötz, Walter, and Schreilechner, Magdalena. Wed . "Single-cone finite difference scheme for the (2+1)D Dirac von Neumann equation". United States. doi:10.1016/J.JCP.2017.07.037.
@article{osti_22701624,
title = {Single-cone finite difference scheme for the (2+1)D Dirac von Neumann equation},
author = {Pötz, Walter and Schreilechner, Magdalena},
abstractNote = {An explicit finite difference scheme is presented for the von Neumann equation for (2+1)D Dirac fermions. It is founded upon a staggered space–time grid which ensures a single-cone energy dispersion and performs the time-derivative in one sweep using a three-step leap-frog procedure. It enables a space–time-resolved numerical treatment of the mixed-state dynamics of Dirac fermions within the effective single-particle density matrix formalism. Energy-momentum dispersion, stability and convergence properties are derived. Elementary numerical tests to demonstrate stability properties use parameters which pertain to topological insulator surface states. A method for the simulation of charge injection from an electric contact is presented and tested numerically. Potential extensions of the scheme to a Dirac–Lindblad equation, real-space–time Green's function formulations, and higher-order finite-difference schemes are discussed.},
doi = {10.1016/J.JCP.2017.07.037},
journal = {Journal of Computational Physics},
issn = {0021-9991},
number = ,
volume = 348,
place = {United States},
year = {2017},
month = {11}
}