自旋1/2的不可积系统中不存在对小扰动的指数敏感性。
Absence of exponential sensitivity to small perturbations in nonintegrable systems of spins 1/2.
作者信息
Fine B V, Elsayed T A, Kropf C M, de Wijn A S
机构信息
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.
Institute for Theoretical Physics, University of Heidelberg, Philosophenweg 19, 69120 Heidelberg, Germany.
出版信息
Phys Rev E Stat Nonlin Soft Matter Phys. 2014 Jan;89(1):012923. doi: 10.1103/PhysRevE.89.012923. Epub 2014 Jan 31.
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.
我们表明，通常被认为是混沌的宏观半自旋非可积晶格，并不表现出经典混沌系统的基本特性，即对小扰动的指数敏感性。我们根据经典自旋的混沌晶格和半自旋非可积晶格对一种被称为洛施密特回波的自旋动力学不完全反转的磁化响应进行了比较。在经典情况下，磁化强度对小扰动呈指数敏感，其特征指数等于系统最大李雅普诺夫指数值的两倍。在半自旋情况下，磁化强度仅对小扰动呈幂律敏感。
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