Analytical evaluations of the path integral Monte Carlo thermodynamic and Hamiltonian energies for the harmonic oscillator

被引:3
|
作者
Chin, Siu A. [1 ]
机构
[1] Texas A&M Univ, Dept Phys & Astron, College Stn, TX 77843 USA
来源
JOURNAL OF CHEMICAL PHYSICS | 2023年 / 159卷 / 24期
关键词
Hamiltonians - Harmonic analysis - Oscillators (mechanical) - Thermodynamics;
D O I
10.1063/5.0181447
中图分类号
O64 [物理化学(理论化学)、化学物理学];
学科分类号
070304 ; 081704 ;
摘要
By using 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 thermodynamic energy, converges extremely slowly with an increasing number of beads.
引用
收藏
页数:11
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