1997/11/20 by Sanjay Hortikar, Mark Srednicki
Physics and Astronomy · #chao-dyn #cond-mat.mes-hall #nlin.CD
paper · pdf · doi:10.1103/physreve.57.7313
published as Phys. Rev. E 57, 7313 (1998) · 7 pages, no figures, RevTeX
arxiv created 1997/11/20 · arxiv updated 2009/11/30
The expected root-mean-square value of a matrix element Aαβ in a classically chaotic system, where A is a smooth, ℏ-independent function of the coordinates and momenta, and α and β label different energy eigenstates, has been evaluated in the literature in two different ways: by treating the energy eigenfunctions as gaussian random variables and averaging |Aαβ|2 over them; and by relating |Aαβ|2 to the classical time-correlation function of A. We show that these two methods give the same answer only if Berry's formula for the spatial correlations in the energy eigenfunctions (which is based on a microcanonical density in phase space) is modified at large separations in a manner which we previously proposed.