Calculation of canonical properties of a quantum system by path integral numerical methods

Research output

Abstract

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-in
Original languageEnglish
Pages (from-to)270-275
JournalContributions to Plasma Physics
Volume53
Issue number4-5
DOIs
Publication statusPublished - 2013

Fingerprint

partitions
Monte Carlo method
thermodynamic properties
fermions
trajectories
temperature
simulation

Cite this

@article{32b4102cb0ed42298a6fcda3f2e156ff,
title = "Calculation of canonical properties of a quantum system by path integral numerical methods",
abstract = "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-in",
keywords = "Expanded ensembles, Monte Carlo, Path-integral, Quantum statistics",
author = "M.A. Voznesenskiy and P.N. Vorontsov-Velyaminov",
year = "2013",
doi = "10.1002/ctpp.201200092",
language = "English",
volume = "53",
pages = "270--275",
journal = "Contributions to Plasma Physics",
issn = "0863-1042",
publisher = "Wiley-Blackwell",
number = "4-5",

}

TY - JOUR

T1 - Calculation of canonical properties of a quantum system by path integral numerical methods

AU - Voznesenskiy, M.A.

AU - Vorontsov-Velyaminov, P.N.

PY - 2013

Y1 - 2013

N2 - 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-in

AB - 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-in

KW - Expanded ensembles

KW - Monte Carlo

KW - Path-integral

KW - Quantum statistics

U2 - 10.1002/ctpp.201200092

DO - 10.1002/ctpp.201200092

M3 - Article

VL - 53

SP - 270

EP - 275

JO - Contributions to Plasma Physics

JF - Contributions to Plasma Physics

SN - 0863-1042

IS - 4-5

ER -