Absence of exponential sensitivity to small perturbations in nonintegrable systems of spins 1/2

Boris V. Fine, Tarek A. Elsayed, C. M. Kropf, A. S. De Wijn

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We show that macroscopic nonintegrable lattices of spins 1/2, which are often considered to be chaotic, do not exhibit the basic property of classical chaotic systems, namely, exponential sensitivity to small perturbations. We compare chaotic lattices of classical spins and nonintegrable lattices of spins 1/2 in terms of their magnetization responses to an imperfect reversal of spin dynamics known as Loschmidt echo. In the classical case, magnetization is exponentially sensitive to small perturbations with a characteristic exponent equal to twice the value of the largest Lyapunov exponent of the system. In the case of spins 1/2, magnetization is only power-law sensitive to small perturbations.

Original languageEnglish
Article number012923
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Issue number1
Publication statusPublished - Jan 31 2014
Externally publishedYes


ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Condensed Matter Physics

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