2 research outputs found

    Unpredictability of wave function's evolution in nonintegrable quantum systems

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    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 O(T)∼Tα\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 O(T)∼(log2T)β\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 O(T)\mathcal O(T) needed to predict a state of system for time interval T can be used as universal sign of chaos.Comment: 6 pages, 1 figure Submitted to Journal of Physics

    Complex Dynamics of Real Quantum, Classical and Hybrid Micro-Machines

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    Any real interaction process produces many incompatible system versions, or realisations, giving rise to omnipresent dynamic randomness and universally defined complexity (arXiv:physics/9806002). Since quantum behaviour dynamically emerges as the lowest complexity level (arXiv:quant-ph/9902016), quantum interaction randomness can only be relatively strong, which reveals the causal origin of quantum indeterminacy (arXiv:quant-ph/9511037) and true quantum chaos (arXiv:quant-ph/9511035), but rigorously excludes the possibility of unitary quantum computation, even in an "ideal", noiseless system. Any real computation is an internally chaotic (multivalued) process of system complexity development occurring in different regimes. Unitary quantum machines, including their postulated "magic", cannot be realised as such because their dynamically single-valued scheme is incompatible with the irreducibly high dynamic randomness at quantum complexity levels and should be replaced by explicitly chaotic, intrinsically creative machines already realised in living organisms and providing their quite different, realistic kind of magic. The related concepts of reality-based, complex-dynamical nanotechnology, biotechnology and intelligence are outlined, together with the ensuing change in research strategy. The unreduced, dynamically multivalued solution to the many-body problem reveals the true, complex-dynamical basis of solid-state dynamics, including the origin and internal dynamics of macroscopic quantum states. The critical, "end-of-science" state of unitary knowledge and the way to positive change are causally specified within the same, universal concept of complexity.Comment: 383 pages, 75 eqs, 451 refs; modified format and title, updated references and minor linguistic changes in v5 (published version
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