AI summary · arXiv: 2210.03760v1 · cond-mat.stat-mech
Classical limit of measurement-induced transition in many-body chaos in integrable and non-integrable oscillator chains
The essentials
- The study investigates the dynamics of integrable and non-integrable chains of coupled oscillators under continuous weak position measurements in the semiclassical limit.
- In this limit, the dynamics can be described by a standard stochastic Langevin equation.
- A measurement-induced transition is observed, manifesting as a noise- and dissipation-induced chaotic-to-non-chaotic transition similar to stochastic synchronization.
- In the non-integrable chain of anharmonically coupled oscillators, a certain noise level or interaction strength halts the temporal growth and ballistic light cone spread of a classical out-of-time correlator characterized by the Lyapunov exponent and butterfly velocity.
- Both Lyapunov exponent and butterfly velocity act as order parameters vanishing in the non-chaotic phase.
- The butterfly velocity exhibits critical finite size scaling.
- For the integrable model (classical Toda chain), the Lyapunov exponent changes nonmonotonically with increasing noise strength, vanishing at zero noise limit and above a critical noise level but reaching its maximum at an intermediate noise strength.
- The butterfly velocity in the Toda chain exhibits singular behavior approaching zero noise strength - i.e., integrability limit.
- References to previous work are included for further context, discussing equilibrium dynamical correlations in integrable models such as Toda chain and exploring quantum state diffusion localization and quantum dispersion entropy.
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