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Dimension-invariance, multifractality and complexity in some classical and quantum systems

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  • Bershadskii, A.

Abstract

Dimension-invariance approach, a dimension-stretching analogue of scale-stretching invariance, is developed for classical and quantum multifractal systems. It is shown, by comparison with laboratory and numerical experiments of different authors, that dimensions-invariance takes place in quantum pseudo-diffusion on lattice in systems with Hamiltonian having multifractal energy spectrum, in turbulence (near-critical generationog of the multiscaling states), for multifractal strange attractors, for mass multifractality in fragmentation, for the diffusion-limited corrosion, for energy dissipation in the fully developed turbulence, and for intermittent multiparticle production in hadron-nucleus interactions. Analogous results are also obtained for a large-scale structure of the universe (CfA catalog of Huchra's compilation of redshifts). Finally, an information complexity of a quantum system is briefly discussed and good correspondence with a recent numerical simulation is established.

Suggested Citation

  • Bershadskii, A., 1997. "Dimension-invariance, multifractality and complexity in some classical and quantum systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 245(3), pages 238-252.
    • Handle: RePEc:eee:phsmap:v:245:y:1997:i:3:p:238-252
    DOI: 10.1016/S0378-4371(97)00313-0
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    References listed on IDEAS

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    1. Meakin, Paul, 1990. "Diffusion-limited droplet coalescence," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 165(1), pages 1-18.
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