Unpredictability of wave function's evolution in nonintegrable quantum systems

Details Unpredictability of wave function's evolution in nonintegrable quantum systems Unpredictability of wave function's evolution in nonintegrable quantum systems

2002-03-05

arxiv.org/abs/quant-ph/0203019v1

Physics

Quantum Physics

6 pages, 1 figure Submitted to Journal of Physics A

Scientific paper

It is shown that evolution of wave functions in nonintegrable quantum systems is unpredictable for a long time T because of rapid growth of number of elementary computational operations $\mathcal O(T)\sim T^\alpha$. On the other hand, the evolution of wave functions in integrable systems can be predicted by the fast algorithms $\mathcal O(T)\sim (log_2 T)^\beta$ for logarithmically short time and thus there is an algorithmic "compressibility" of their dynamics. The difference between integrable and nonintegrable systems in our approach looks identically for classical and quantum systems. Therefore the minimal number of bit operations $\mathcal O(T)$ needed to predict a state of system for time interval T can be used as universal sign of chaos.

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