Path integral molecular dynamics for Bose-Einstein and Fermi-Dirac statistics
نویسندگان
چکیده
We propose a promising extension of the path integral molecular dynamics method to Bose-Einstein and Fermi-Dirac statistics. The partition function for the quantum statistics was re-written in a form amenable to the molecular dynamics method with the aid of an idea of pseudopotential for the permutation of particles. Our pseudopotential is a rigorous one describing the whole effect of Bose-Einstein and Fermi-Dirac statistics. For a model calculation, we chose a system consisting of three independent particles in a one-dimensional harmonic well. The calculated total energy was in excellent agreement with the analytical result even near the ground state.
منابع مشابه
آرام کردن مایع فرمی: جدال با علامتهای فرمیونی غیر مستقیم
The fermion sign problem is studied in the path integral formalism. The standard picture of Fermi liquids is first critically analyzed, pointing out some of its rather peculiar properties. The insightful work of Ceperley in constructing fermionic path integrals in terms of constrained world-lines is then reviewed. In this representation, the minus signs associated with Fermi-Dirac statistics a...
متن کاملPath-integral calculation of the third virial coefficient of quantum gases at low temperatures.
We derive path-integral expressions for the second and third virial coefficients of monatomic quantum gases. Unlike previous work that considered only Boltzmann statistics, we include exchange effects (Bose-Einstein or Fermi-Dirac statistics). We use state-of-the-art pair and three-body potentials to calculate the third virial coefficient of (3)He and (4)He in the temperature range 2.6-24.5561 ...
متن کاملPath integral formulation of centroid dynamics for systems obeying Bose–Einstein statistics
This paper presents a formal foundation for the recent extension @J. Chem. Phys. 110, 3647 ~1999!# of the centroid molecular dynamics ~CMD! method to systems obeying Bose–Einstein statistics. It is shown that the introduction of centroid phase space coordinates corresponding to individual physical particles allows one to obtain ~exact! canonical averages within the framework of the bosonic CMD ...
متن کاملOperator Representation of Fermi-Dirac and Bose-Einstein Integral Functions with Applications
Fermi-Dirac and Bose-Einstein functions arise as quantum statistical distributions. The Riemann zeta function and its extension, the polylogarithm function, arise in the theory of numbers. Though it might not have been expected, these two sets of functions belong to a wider class of functions whose members have operator representations. In particular, we show that the Fermi-Dirac and Bose-Einst...
متن کاملBose-Einstein and Fermi-Dirac distributions in nonextensive quantum statistics: An exact approach
Bose-Einstein (BE) and Fermi-Dirac (FD) distributions in nonextensive quantum statistics have been discussed with the use of exact integral representations for the grand canonical partition function [Rajagopal, Mendes and Lenzi, Phys. Rev. Lett. 80, 3907 (1998)]. Integrals along real axis in the case of q > 1.0 are modified by an appropriate change of variable, which makes numerical calculation...
متن کامل