2024/06/28 by Siu A. Chin, Chin, Siu A.
Materials Science · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #FOS: Physical sciences #Other Condensed Matter (cond-mat.other) #Quantum Physics (quant-ph) #Thermal properties of materials
paper · pdf · doi:10.48550/arxiv.2406.20039
openalex publication_date 2024/06/28 · openalex created_date 2024/07/02 · openalex updated_date 2026/07/28
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.