Dynamical theory of quantum chaos or hidden random matrix ensemble?

TL;DR

This paper critiques a recent claim that a dynamical system's quantum chaos can be fully described by a random matrix ensemble, arguing that essential dynamical features are overlooked in the original theory.

Contribution

It highlights limitations in the previous theory by showing it neglects key dynamical aspects beyond standard random matrix models.

Findings

The original theory does not account for certain dynamical features.

Key dynamical properties are missed by the random matrix analogy.

The critique emphasizes the need for more comprehensive models.

Abstract

In a recent Letter [Phys.Rev.Lett., 77,4536 (1996), chao-dyn/9609014] Altland and Zirnbauer claim that they rigorously proved the complete analogy between a (classically chaotic) dynamical system and disordered (random) solids. The purpose of this Comment is to show that, in fact, their theory fails to take into account dynamical features which go beyond standard random matrix theory description.