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Localization of information driven by stochastic resetting.

Camille Aron1,2, Manas Kulkarni3

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Stochastic resetting causes a phase transition in chaotic many-body systems, collapsing Lyapunov exponents to zero. This transition arrests information scrambling, localizing it exponentially.

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Area of Science:

  • Physics
  • Complex Systems
  • Statistical Mechanics

Background:

  • Many-body systems exhibit chaotic dynamics, characterized by exponential sensitivity to initial conditions (Lyapunov exponents).
  • Stochastic resetting introduces a non-equilibrium process that can alter system dynamics.

Purpose of the Study:

  • To investigate the impact of stochastic resetting on the dynamics of chaotic many-body systems.
  • To identify and characterize any phase transitions induced by stochastic resetting.

Main Methods:

  • Analytical derivation of the Lyapunov spectrum under stochastic resetting.
  • Analysis of the velocity-dependent Lyapunov exponent at criticality.
  • Numerical simulations using coupled map lattices to validate analytical findings.

Main Results:

  • A sharp dynamical phase transition occurs above a critical resetting rate, causing the Lyapunov spectrum to collapse to zero.
  • At criticality, the velocity-dependent Lyapunov exponent loses analyticity.
  • Information scrambling transitions from ballistic to an arrested regime with exponential localization.

Conclusions:

  • Stochastic resetting fundamentally alters chaotic dynamics, inducing a phase transition.
  • The transition is characterized by the loss of chaos (zero Lyapunov exponents) and arrested information propagation.
  • Critical exponents ν=1/2 and z=2 describe the diverging localization length at criticality.