Frequency Moment Sum Rules, Recurrence Relations and Continued Fractions in Nonequilibrium Statistical Mechanics

摘要

Dynamical properties of quantum many-body systems, e.g., the electron gas, lattice spins are usually studied via frequency moment sum rules. For example, the dynamic structure factor of the density-density response function in an interacting electron gas can be given a continued fraction expansion in terms of frequency moments. Since only a few moments are known, one is faced with the problem of extracting best information form a continued fraction representation. It is desirable to obtain an approximate form which is sufficiently accurate for comparison with experimental data. The method of recurrence relations provides a convergent procedure for obtaining such physical quantities using approximate higher order frequency moments. This idea seems to work very well for a strongly interacting electron gas at metallic densities. The basic ideas behind this procedure are explained. Reprints. (JHD)