2 research outputs found
Unpredictability of wave function's evolution in nonintegrable quantum systems
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 . On the other
hand, the evolution of wave functions in integrable systems can be predicted by
the fast algorithms 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 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
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