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.
ASJC Scopus subject areas
- Physics and Astronomy(all)
- Physical and Theoretical Chemistry