Frequency moment sum rules, recurrence relations and continued fractions in nonequilibrium statistical mechanics
✍ Scribed by M. Howard Lee
- Publisher
- Elsevier Science
- Year
- 1989
- Tongue
- English
- Weight
- 783 KB
- Volume
- 53
- Category
- Article
- ISSN
- 0010-4655
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✦ Synopsis
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 from 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.