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

Research output: Contribution to journalArticle

21 Citations (Scopus)

Abstract

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
Volume89
Issue number1
DOIs
Publication statusPublished - Jan 31 2014
Externally publishedYes

Fingerprint

Small Perturbations
Magnetization
perturbation
sensitivity
magnetization
exponents
Spin Dynamics
Largest Lyapunov Exponent
Characteristic Exponents
spin dynamics
Reversal
Imperfect
Chaotic System
echoes
Power Law

ASJC Scopus subject areas

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

Cite this

Absence of exponential sensitivity to small perturbations in nonintegrable systems of spins 1/2. / Fine, Boris V.; Elsayed, Tarek A.; Kropf, C. M.; De Wijn, A. S.

In: Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, Vol. 89, No. 1, 012923, 31.01.2014.

Research output: Contribution to journalArticle

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