Malinin Sergey V, Chernyak Vladimir Y
Department of Chemistry, Wayne State University, 5101 Cass Avenue, Detroit, Michigan 48202, USA.
Phys Rev E Stat Nonlin Soft Matter Phys. 2008 May;77(5 Pt 2):056201. doi: 10.1103/PhysRevE.77.056201. Epub 2008 May 7.
We develop a general semiquantitative picture of nonlinear classical response in strongly chaotic systems. In contrast to behavior in integrable or almost integrable systems, the nonlinear classical response in chaotic systems vanishes at long times. The exponential decay of the response functions in the case of strong chaos is attributed to both exponentially decaying and growing elements in the stability matrices. We calculate the linear and second-order response in one of the simplest chaotic systems: free classical motion on a compact surface of constant negative curvature. The response reveals certain features of collective resonances which do not correspond to any periodic classical trajectories. We demonstrate the relevance of the model for the interpretation of spectroscopic experiments.
我们建立了强混沌系统中非线性经典响应的一般半定量图景。与可积或几乎可积系统中的行为不同，混沌系统中的非线性经典响应在长时间时消失。在强混沌情况下响应函数的指数衰减归因于稳定性矩阵中指数衰减和增长的元素。我们计算了最简单的混沌系统之一中的线性和二阶响应：在具有恒定负曲率的紧致曲面上的自由经典运动。该响应揭示了集体共振的某些特征，这些特征与任何周期性经典轨迹都不对应。我们证明了该模型对于光谱实验解释的相关性。
