5 research outputs found
Local Variational Principle
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 groundstate energies
better than the ones given by the Rayleigh-Ritz principle as applied to the
groundstate 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.Comment: 15 pages, 5 figures, one more section adde