Fluctuation-dissipation-dispersion relation for slowly varying processes

摘要

The famous Callen-Welton formula is generalized to systems with slowly varying parameters. It is shown that not only the dissipation but also the time derivatives of the dispersion determine the amplitude and the width of the spectral lines of the fluctuations. In the general case the contribution of the second effect may be comparable with the first. This contribution is characterized by a new non-local dispersive term which is not related to Joule dissipation and which results from an additional phase shift between the force and the response of the system. The general formalism is illustrated by its applications to an LC-circuit. The influence of the dispersion contributions on the quality factor of the system is discussed.