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Calculation of Canonical Properties of a Quantum System by Path Integral Numerical Methods
Author(s) -
Voznesenskiy M. A.,
VorontsovVelyaminov P. N.
Publication year - 2013
Publication title -
contributions to plasma physics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.531
H-Index - 47
eISSN - 1521-3986
pISSN - 0863-1042
DOI - 10.1002/ctpp.201200092
Subject(s) - path integral formulation , partition function (quantum field theory) , monte carlo method , auxiliary field , physics , statistical physics , quantum monte carlo , coulomb , ground state , path integral monte carlo , canonical ensemble , quantum , function (biology) , quantum mechanics , mathematics , statistics , biology , electron , evolutionary biology
We propose a new approach in obtaining the partition function of a system of several interacting particles (fermions) in external field within path integral Monte Carlo method based on direct averaging of the exchange contributions over the positive weight determined by non‐closed trajectories. This procedure is performed at fixed temperatures, ranging to rather low values. The complete partition function for each temperature is then obtained within an expanded ensemble procedure. We found a good agreement of data obtained by the new method with results of previously proposed path‐integral‐expanded‐ensemble Monte Carlo calculations [1, 2]. The new approach allows to reach observably lower temperatures compared to method [1, 2], thus providing a significant reduce of the sign problem. It yields an independent way to treat thermal properties of quantum systems, so the good agreement with previous data [1, 2] allows us to test and state the validity of both approaches. Simulations for systems of 2 up to 5 non‐interacting particles and particles interacting with Coulomb repulsion in 3 D harmonic field were performed. The presented approach allows one to carry out calculations for low temperatures that makes it possible to extract data for the ground‐state energy and low‐temperature thermodynamics. (© 2013 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)