PATH-INTEGRAL QUANTUM MONTE CARLO STUDIES OF THE STATIC AND TIME-DEPENDENT THERMODYNAMICS OF THE VIBRATIONAL PROPERTIES OF CRYSTALS

A review is given of recent efforts at using the path-integral formulation of the quantum Monte Carlo to study the static and dynamic properties of crystals. The computation of the static properties of energy, specific heat and lattice constant as functions of temperature for systems of atoms interacting by Lennard-Jones (12-6) potentials is first considered. Results for fcc systems appropriate to neon and argon are presented and these are compared with analytical results from the effective potential and improved self-consistent theories and with results from the harmonic approximation. In addition, some earlier investigations on the static properties of a one-dimensional chain of atoms are also considered and compared with the exact solutions for these properties in the corresponding classical system. A discussion of the time-dependent thermodynamic properties of a one-dimensional quantum chain of atoms is made in terms of the response functions which describe the inelastic neutron scattering from the chain. A continued fraction representation, based on the work of Mori [1], is presented for these response functions and the coefficients in the continued fraction are computed using the static path-integral quantum Monte Carlo method. Improvements on Mori’s method applied to the quantum chain are made by using molecular dynamics results for the corresponding classical chain of atoms to guide in terminating the continued fraction representation of the quantum response functions.