A path integral Einstein model for characterizing the equilibrium states of low temperature solids

Abstract

A variational Einstein model for describing low temperature solids is developed from a Feynman path integral perspective. The theory can be used to predict fully quantum mechanical values for the thermodynamics (e.g., free energy, entropy, internal energy, etc.) and the equilibrium structure (e.g., pair and angular correlation functions) of a solid. The theory has also been generalized to treat low temperature solids which contain impurity species. The independent harmonic oscillator assumption implicit in the Einstein model allows the results to be cast in a straightforward analytic form. Additionally, the path integral formulation of the model yields solutions which explicitly depend on the path integral discretization parameter P. One can thus systematically examine the equilibrium behavior of a solid ranging from the classical to the quantum limits. The Einstein model is applied to examine the behavior of solid hydrogen and solid hydrogen containing lithium impurities.