Reply to the Comment by Casati et al. on "Field theory of the quantum kicked rotor" [Phys. Rev. Lett. 77, 4536 (1996)]

TL;DR

This paper responds to a comment on their previous work, clarifying how the quantum kicked rotor's behavior depends on the number-theoretic properties of the parameter T, especially its rationality or irrationality.

Contribution

The authors demonstrate the sensitivity of their analysis to the rationality of T and connect this to topological aspects, clarifying a debated point in the quantum kicked rotor theory.

Findings

Dependence of the quantum kicked rotor on the rationality of T

Connection between number theory and topological features

Phenomenological implications of rational versus irrational T

Abstract

In a recent comment [cond-mat/9703106] Casati, Izrailev and Sokolov claim that our analysis of the quantum kicked rotor [Phys. Rev. Lett. 77, 4536 (1996), chao-dyn/9609014] seems to miss an important aspect, viz. the difference in behavior between rational and irrational values of the parameter T = tau/4pi (tau being the time between kicks). The fact of the matter is that our approach does depend very sensitively on the number theoretical properties of T. In our reply we show how the 'degree of rationality' is related to the topological aspects of our theory and point out the phenomenological consequences of this connection.