论文标题
随机基质理论的非线性扰动
Nonlinear perturbation of Random Matrix Theory
论文作者
论文摘要
我们考虑通过随机矩阵理论描述的线性振荡器或量子状态的系统，并分析其时间演化如何受到非线性扰动的影响。我们的数值结果表明，在某个混乱上面边界弱或中度的非线性会导致有限数量的自由度的动态热化，而能量等电优于线性本本特征，这是经典统计机制定律所预期的。显示系统温度在广泛的范围内从正值变为负值，并且确定系统特征对初始注入能量的依赖性。在混乱的边界下方，动力学由Kolmogorov-Arnold-Moser的集成性描述。由于随机矩阵理论的普遍特征，我们认为所获得的结果描述了其非线性扰动的通用特性。
We consider a system of linear oscillators, or quantum states, described by Random Matrix Theory and analyze how its time evolution is affected by a nonlinear perturbation. Our numerical results show that above a certain chaos border a weak or moderate nonlinearity leads to a dynamical thermalization of a finite number of degrees of freedom with energy equipartition over linear eigenmodes as expected from the laws of classical statistical mechanics. The system temperature is shown to change in a broad range from positive to negative values and the dependence of system characteristics on the initial injected energy is determined. Below the chaos border the dynamics is described by the Kolmogorov-Arnold-Moser integrability. Due to universal features of Random Matrix Theory we argue that the obtained results describe the generic properties of its nonlinear perturbation.
