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arXiv · 2510.07394

Localization of information driven by stochastic resetting

Camille Aron·Manas Kulkarni
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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 $\nu = 1/2$ and a dynamical exponent $z=2$. We illustrate our analytical results on generic chaotic dynamics by numerical simulations of coupled map lattices.

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Camille Aron, Manas Kulkarni. 2025-10-08. Localization of information driven by stochastic resetting. https://doi.org/10.1103/pkgb-mp8s

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