2002/03/05 by I. B. Ivanov, Ivan Ivanov, Ivanov, I. B.
Computer Science · Physics and Astronomy · #Chaotic Dynamics (nlin.CD) #Computational Complexity (cs.CC) #FOS: Computer and information sciences #FOS: Physical sciences #Quantum Physics (quant-ph) #Quantum optics and atomic interactions #cs.CC #nlin.CD #quant-ph
paper · pdf · doi:10.48550/arxiv.quant-ph/0203019
6 pages, 1 figure Submitted to Journal of Physics A
arxiv created 2002/03/05 · openalex publication_date 2002/03/05 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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)∼ Tα. On the other hand, the evolution of wave functions in integrable systems can be predicted by the fast algorithms \mathcal O(T)∼ (log2 T)β 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.