2002/09/30 by Cristian Predescu · 1 citation
Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Quantum, superfluid, helium dynamics #Spectroscopy and Quantum Chemical Studies #cond-mat.stat-mech
paper · pdf · doi:10.1103/physreve.66.066133
published as Phys. Rev. E 66, 066133 (2002) · 15 pages, 5 figures, one more section added
openalex publication_date 2002/12/26 · arxiv created 2003/06/05 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A generalization of the Gibbs-Bogoliubov-Feynman inequality for spinless particles is proven and then illustrated for the simple model of a symmetric double-well quartic potential. The method gives a pointwise lower bound for the finite-temperature density matrix and it can be systematically improved by the Trotter composition rule. It is also shown to produce ground state energies better than the ones given by the Rayleigh-Ritz principle as applied to the ground state eigenfunctions of the reference potentials. Based on this observation, it is argued that the local variational principle performs better than the equivalent methods based on the centroid path idea and on the Gibbs-Bogoliubov-Feynman variational principle, especially in the range of low temperatures.