Title: Localization of information driven by stochastic resetting Show Chinese title

Title: 由随机重置驱动的信息定位

Abstract: The dynamics of extended many-body systems are generically chaotic. Classically, a hallmark of chaos is the exponential sensitivity to initial conditions captured by positive Lyapunov exponents. Supplementing chaotic dynamics with stochastic resetting drives a sharp dynamical phase transition: we show that the Lyapunov spectrum, i.e., the complete set of Lyapunov exponents, abruptly collapses to zero above a critical resetting rate. At criticality, we find a sudden loss of analyticity of the velocity-dependent Lyapunov exponent, which we relate to the transition from ballistic scrambling of information to an arrested regime where information becomes exponentially localized over a characteristic length diverging at criticality with an exponent $\nu = 1/2$. We illustrate our analytical results on generic chaotic dynamics by numerical simulations of coupled map lattices. Show Chinese abstract

Abstract: 扩展多体系统的动力学通常是混沌的。 经典上，混沌的一个特征是初始条件的指数敏感性，这由正李雅普诺夫指数捕捉。 在混沌动力学中补充随机重置会引发剧烈的动力学相变：我们证明，李雅普诺夫谱，即完整的李雅普诺夫指数集合，在临界重置率以上会突然坍缩为零。 在临界点，我们发现速度相关的李雅普诺夫指数突然失去解析性，我们将这种现象与信息的弹道扩散到一个被阻止的区域的转变相关联，在该区域中信息随特征长度呈指数局部化，该特征长度在临界点处发散，其指数为$\nu = 1/2$。 我们通过耦合映射格子的数值模拟，对一般的混沌动力学展示了我们的分析结果。