On the simulation of indistinguishable fermions in the many-body Wigner formalism

Journal Article · Thu Jan 01 04:00:00 EST 2015 · Journal of Computational Physics

DOI:https://doi.org/10.1016/J.JCP.2014.09.026· OSTI ID:22382159

Dimov, I.

The simulation of quantum systems consisting of interacting, indistinguishable fermions is an incredible mathematical problem which poses formidable numerical challenges. Many sophisticated methods addressing this problem are available which are based on the many-body Schrödinger formalism. Recently a Monte Carlo technique for the resolution of the many-body Wigner equation has been introduced and successfully applied to the simulation of distinguishable, spinless particles. This numerical approach presents several advantages over other methods. Indeed, it is based on an intuitive formalism in which quantum systems are described in terms of a quasi-distribution function, and highly scalable due to its Monte Carlo nature. In this work, we extend the many-body Wigner Monte Carlo method to the simulation of indistinguishable fermions. To this end, we first show how fermions are incorporated into the Wigner formalism. Then we demonstrate that the Pauli exclusion principle is intrinsic to the formalism. As a matter of fact, a numerical simulation of two strongly interacting fermions (electrons) is performed which clearly shows the appearance of a Fermi (or exchange–correlation) hole in the phase-space, a clear signature of the presence of the Pauli principle. To conclude, we simulate 4, 8 and 16 non-interacting fermions, isolated in a closed box, and show that, as the number of fermions increases, we gradually recover the Fermi–Dirac statistics, a clear proof of the reliability of our proposed method for the treatment of indistinguishable particles.

• OSTI ID: 22382159
• Journal Information: Journal of Computational Physics, Journal Name: Journal of Computational Physics Vol. 280; ISSN JCTPAH; ISSN 0021-9991
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
COMPUTERIZED SIMULATION
CORRELATIONS
DISTRIBUTION FUNCTIONS
ELECTRONS
MANY-BODY PROBLEM
MONTE CARLO METHOD
PAULI PRINCIPLE
PHASE SPACE
QUANTUM MECHANICS
QUANTUM SYSTEMS
SCHROEDINGER EQUATION
STATISTICS