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Title: Extraction of ground state properties by discretized path integral formulations

Abstract

We offer a way of determining the temperature range in which a path integral (PI) formulation of the quantum partition function works well and a way of calculating the ground state properties without employing extremely low temperatures (in order to elude the awkward problem that the quantities calculated by the PI formulation become inaccurate with decreasing temperature owing to unavoidable truncation of an infinite number of path integral variables). The fact that the PI energy, specific heat, etc. behave in a low temperature range against physical laws makes it possible to locate the ''marginal'' temperature at which the PI specific heat begins to grow infinitely and to estimate the lowest temperature at which the PI formulation functions well (the ''threshold temperature''). Whether or not the threshold temperature is low enough to extract only the ground state properties can be answered by either checking if the PI energy and free energy are equal at the threshold temperature or checking if the PI specific heat is relatively small thereat. If the system is in the ground state at the threshold temperature obtained, it is recommended to calculate the ground state properties at this temperature. This scheme can be executed by Monte Carlomore » methods, being open to many-particle systems. Using the discretized PI formulations, we apply the above procedure to a harmonic oscillator and a double-well potential. It is concluded that this scheme is successful at least as long as the potential is a slowly varying function of coordinates.« less

Authors:
; ;
Publication Date:
Research Org.:
Department of Basic Technology, Faculty of Engineering, Yamagata University, Yonezawa 992, Japan
OSTI Identifier:
6966786
Resource Type:
Journal Article
Journal Name:
J. Chem. Phys.; (United States)
Additional Journal Information:
Journal Volume: 89:5
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; QUANTUM MECHANICS; MONTE CARLO METHOD; PARTITION FUNCTIONS; GROUND STATES; HARMONIC OSCILLATORS; INTEGRALS; SAMPLING; ELECTRONIC EQUIPMENT; ENERGY LEVELS; EQUIPMENT; FUNCTIONS; MECHANICS; OSCILLATORS; 657002* - Theoretical & Mathematical Physics- Classical & Quantum Mechanics

Citation Formats

Kono, H, Takasaka, A, and Lin, S H. Extraction of ground state properties by discretized path integral formulations. United States: N. p., 1988. Web. doi:10.1063/1.454980.
Kono, H, Takasaka, A, & Lin, S H. Extraction of ground state properties by discretized path integral formulations. United States. https://doi.org/10.1063/1.454980
Kono, H, Takasaka, A, and Lin, S H. 1988. "Extraction of ground state properties by discretized path integral formulations". United States. https://doi.org/10.1063/1.454980.
@article{osti_6966786,
title = {Extraction of ground state properties by discretized path integral formulations},
author = {Kono, H and Takasaka, A and Lin, S H},
abstractNote = {We offer a way of determining the temperature range in which a path integral (PI) formulation of the quantum partition function works well and a way of calculating the ground state properties without employing extremely low temperatures (in order to elude the awkward problem that the quantities calculated by the PI formulation become inaccurate with decreasing temperature owing to unavoidable truncation of an infinite number of path integral variables). The fact that the PI energy, specific heat, etc. behave in a low temperature range against physical laws makes it possible to locate the ''marginal'' temperature at which the PI specific heat begins to grow infinitely and to estimate the lowest temperature at which the PI formulation functions well (the ''threshold temperature''). Whether or not the threshold temperature is low enough to extract only the ground state properties can be answered by either checking if the PI energy and free energy are equal at the threshold temperature or checking if the PI specific heat is relatively small thereat. If the system is in the ground state at the threshold temperature obtained, it is recommended to calculate the ground state properties at this temperature. This scheme can be executed by Monte Carlo methods, being open to many-particle systems. Using the discretized PI formulations, we apply the above procedure to a harmonic oscillator and a double-well potential. It is concluded that this scheme is successful at least as long as the potential is a slowly varying function of coordinates.},
doi = {10.1063/1.454980},
url = {https://www.osti.gov/biblio/6966786}, journal = {J. Chem. Phys.; (United States)},
number = ,
volume = 89:5,
place = {United States},
year = {Thu Sep 01 00:00:00 EDT 1988},
month = {Thu Sep 01 00:00:00 EDT 1988}
}