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Records in the classical and quantum standard map

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  • Srivastava, Shashi C.L.
  • Lakshminarayan, Arul

Abstract

Record statistics is the study of how new highs or lows are created and sustained in any dynamical process. The study of the highest or lowest records constitute the study of extreme values. This paper represents an exploration of record statistics for certain aspects of the classical and quantum standard map. For instance the momentum square or energy records is shown to behave like that of records in random walks when the classical standard map is in a regime of hard chaos. However different power laws is observed for the mixed phase space regimes. The presence of accelerator modes are well-known to create anomalous diffusion and we notice here that the record statistics is very sensitive to their presence. We also discuss records in random vectors and use it to analyze the quantum standard map via records in their eigenfunction intensities, reviewing some recent results along the way.

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  • Srivastava, Shashi C.L. & Lakshminarayan, Arul, 2015. "Records in the classical and quantum standard map," Chaos, Solitons & Fractals, Elsevier, vol. 74(C), pages 67-78.
    • Handle: RePEc:eee:chsofr:v:74:y:2015:i:c:p:67-78
    DOI: 10.1016/j.chaos.2014.12.011
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    References listed on IDEAS

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    1. Gregory Schehr & Satya N. Majumdar, 2013. "Exact record and order statistics of random walks via first-passage ideas," Papers 1305.0639, arXiv.org.
    2. Satya N. Majumdar & Gregory Schehr & Gregor Wergen, 2012. "Record statistics and persistence for a random walk with a drift," Post-Print hal-00744525, HAL.
    3. Daniel Gembris & John G. Taylor & Dieter Suter, 2002. "Trends and random fluctuations in athletics," Nature, Nature, vol. 417(6888), pages 506-506, May.
    4. Satya N. Majumdar & Gregory Schehr & Gregor Wergen, 2012. "Record statistics and persistence for a random walk with a drift," Papers 1206.6972, arXiv.org, revised Aug 2012.
    5. Gregor Wergen & Miro Bogner & Joachim Krug, 2011. "Record statistics for biased random walks, with an application to financial data," Papers 1103.0893, arXiv.org.
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    Cited by:

    1. Claude Godreche & Satya N. Majumdar & Gregory Schehr, 2017. "Record statistics of a strongly correlated time series: random walks and L\'evy flights," Papers 1702.00586, arXiv.org.

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