Excess electrons in simple fluids. IV. Real time behavior

The polaron theory for an excess electron in liquids due to Chandler et al. [J. Chem. Phys. 81, 1975 (1984)] is extended to the real time domain by the method of analytic continuation. For the case of an adiabatic solvent, the theory predicts that the electron momentum correlations relax nonexponentially in time, and that this long time tail contributes to a diminuation of the electron mobility. However, for short ranged forces, a mean-field approximation employed in this application of the polaron theory leads to a decay that is one power of t-1 higher than the generally accepted result for the quantum Lorenz gas. Along with this analytical analysis, we present numerical solutions of the analytically continued equations for the case of an adiabatic hard sphere solvent. We find that at low solvent densities, the electronic states are relatively diffuse, and the absorption spectra is maximum at the zero frequency diffusive mode. In this density regime, the electron mobility is a decreasing function of temperature. At higher densities, the electron mobility drops precipitously and the spectra has its maxima at a nonzero frequency. Here, the mobility is an increasing function of temperature. Corresponding behaviors of the electron mean-square displacement correlation function are discussed. The high density behaviors are the dynamical consequences of ground state dominance or self-trapping where diffusion requires excitation to high energy extended states. These results augment our earlier work on the equilibrium or thermodynamic consequences of this theory