<title>Computational complexity of classical and quantum dynamics</title>

Abstract

A concept of computational complexity is applied for analysis of classical and quantum dynamical systems. It is argued that evolution of wave functions in nonintegrable quatnum systems lies in complexity class EXP because of rapid growth of number of elementary computational operations needed to predict their future. On the other hand, evolution of wave functions in integrable systems can be predicted by the fast algorithms and thus it belongs to P class. This difference between integrable and nonintegrable systems in our approahc looks identically for classical and quantum systems. In this paper an informational approach is applied for analysis of dynamics in classical and quantum systems to find a universal different between integrable and nonintegrable motion. As a basic tool to analyze compleixty of dynamics we use a number of elementary computational operations O(T) (computational complexity) needed to determine a state of a sytem for time interval T.