Analytical evaluations of the Path Integral Monte Carlo thermodynamic and Hamiltonian energies for the harmonic oscillator

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Main Author:	Chin, Siu A.
Format:	Preprint
Published:	2024
Subjects:	Quantum Physics Other Condensed Matter
Online Access:	Acceder al recurso
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author	Chin, Siu A.
author_facet	Chin, Siu A.
contents	By use of the recently derived $universal$ discrete imaginary-time propagator of the harmonic oscillator, both thermodynamic and Hamiltonian energies can be given analytically, and evaluated numerically at each imaginary time step, for $any$ short-time propagator. This work shows that, using only currently known short-time propagators, the Hamiltonian energy can be optimized to the twelfth order, converging to the ground state energy of the harmonic oscillator in as few as three beads. This study makes it absolutely clear that the widely used second-order primitive approximation propagator, when used in computing the thermodynamic energy, converges extremely slowly with increasing number of beads.
format	Preprint
id	arxiv_https___arxiv_org_abs_2406_20039
institution	arXiv
publishDate	2024
record_format	arxiv
spellingShingle	Analytical evaluations of the Path Integral Monte Carlo thermodynamic and Hamiltonian energies for the harmonic oscillator Chin, Siu A. Quantum Physics Other Condensed Matter By use of the recently derived $universal$ discrete imaginary-time propagator of the harmonic oscillator, both thermodynamic and Hamiltonian energies can be given analytically, and evaluated numerically at each imaginary time step, for $any$ short-time propagator. This work shows that, using only currently known short-time propagators, the Hamiltonian energy can be optimized to the twelfth order, converging to the ground state energy of the harmonic oscillator in as few as three beads. This study makes it absolutely clear that the widely used second-order primitive approximation propagator, when used in computing the thermodynamic energy, converges extremely slowly with increasing number of beads.
title	Analytical evaluations of the Path Integral Monte Carlo thermodynamic and Hamiltonian energies for the harmonic oscillator
topic	Quantum Physics Other Condensed Matter
url	https://arxiv.org/abs/2406.20039

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