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Renormalization group approach to chaotic strings

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  • Groote, Stefan
  • Veermäe, Hardi
  • Beck, Christian

Abstract

Coupled map lattices of weakly coupled Chebychev maps, so-called chaotic strings, may have a profound physical meaning in terms of dynamical models of vacuum fluctuations in stochastically quantized field theories. Here we present analytic results for the invariant density of chaotic strings, as well as for the coupling parameter dependence of given observables of the chaotic string such as the vacuum expectation value. A highly nontrivial and selfsimilar parameter dependence is found, produced by perturbative and nonperturbative effects, for which we develop a mathematical description in terms of suitable scaling functions. Our analytic results are in good agreement with numerical simulations of the chaotic dynamics.

Suggested Citation

  • Groote, Stefan & Veermäe, Hardi & Beck, Christian, 2013. "Renormalization group approach to chaotic strings," Chaos, Solitons & Fractals, Elsevier, vol. 53(C), pages 18-33.
    • Handle: RePEc:eee:chsofr:v:53:y:2013:i:c:p:18-33
    DOI: 10.1016/j.chaos.2013.04.004
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    References listed on IDEAS

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    1. Maher, Muhammad & Beck, Christian, 2008. "Chaotic quantization and the mass spectrum of fermions," Chaos, Solitons & Fractals, Elsevier, vol. 37(1), pages 9-15.
    2. Groote, Stefan & Veermäe, Hardi, 2009. "Short chaotic strings and their behaviour in the scaling region," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2354-2359.
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