ERGOMETRIC THEORY OF THE ERGODIC HYPOTHESIS: SPECTRAL FUNCTIONS AND CLASSICAL ERGODICITY

摘要

The ergometric theory of the ergodic hypothesis is a physical theory for studying ergodicity in quantum many-body systems. It is based on the recurrence relations method, an exact dynamical formalism, well established and applied to numerous models both classical and quantum mechanical. In this work we show that the frequency spectra, in particular the distributions of the frequency, have properties which appear equivalent to the invariant measure and transitivity of phase space in classical ergodicity. We also show that the ergometric statement of the ergodic hypothesis can be reduced to Boltzmann's statement cast in microcanonical ensembles. This reduction indicates that the ergometric theory is a general theory of the ergodic hypothesis.