Comment on "Ehrenfest times for classically chaotic systems".

Abstract

In a recent Rapid Communication [P. G. Silvestrov and C. W. J. Beenakker, Phys. Rev. E 65, 035208(R) (2002)], the authors, Silvestrov and Beenakker, introduce a way to lengthen the Ehrenfest time tau for fully chaotic systems. We disagree with several statements made in their paper, and address the following points essential to their conclusions: (1) it is not true that all semiclassical approximations for chaotic systems fail at a so-called "log time" tau proportional, variant -ln( variant Planck's over 2pi ), differing only by a numerical coefficient; and (2) the limitation of the semiclassical approximation as expressed in the authors' Eq. (8) is not limited by their argument leading to Eq. (12).