title: Absence of exponential sensitivity to small perturbations in nonintegrable systems of spins 1/2.
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.
authors.affiliation: Institute for Theoretical Physics, University of Heidelberg, Philosophenweg 19, 69120 Heidelberg, Germany and Department of Physics, School of Science and Technology, Nazarbayev University, 53 Kabanbai Batyr Ave., Astana 010000, Kazakhstan.
authors.forename: B V
authors.initials: BV
authors.lastname: Fine
authors.affiliation: Institute for Theoretical Physics, University of Heidelberg, Philosophenweg 19, 69120 Heidelberg, Germany.
authors.forename: T A
authors.initials: TA
authors.lastname: Elsayed
authors.affiliation: Institute for Theoretical Physics, University of Heidelberg, Philosophenweg 19, 69120 Heidelberg, Germany and Institute of Physics, University of Freiburg, Hermann-Herder-Str. 3, 79104 Freiburg, Germany.
authors.forename: C M
authors.initials: CM
authors.lastname: Kropf
authors.affiliation: Department of Physics, Stockholm University, 106 91 Stockholm, Sweden.
authors.forename: A S
authors.initials: AS
authors.lastname: de Wijn