Quantum Mode Coupling Theory and Path Integral Monte Carlo

Abstract

A theory for dynamical correlations in quantum liquids is presented. The approach is based on augmenting an exact quantum generalized Langevin equation (QGLE) for the Kubo transform of the dynamical correlation of interest, combined with an approximation for the memory kernel obtained within the framework of a quantum mode‐coupling theory (QMCT) developed by Rabani and Reichman. The solution to the quantum generalized Langevin equation requires as input static equilibrium information which is generated from a path‐integral Monte Carlo method suitable for observables that combine positions and momenta of all particles. The theory is applied to the case of liquid para‐hydrogen and liquid ortho‐deuterium near their triple points. Good agreement for the intermediate scattering function, for the self‐diffusion constant, and for the real time velocity autocorrelation function is obtained in comparison to experimental measurements and to numerical results obtained from a maximum entropy analytic continuation approach.