Semiclassical Limit of Measurement-Induced Transition in Many-Body Chaos in Integrable and Nonintegrable Oscillator Chains

TL;DR

This paper investigates how measurement-induced transitions affect chaos in classical oscillator chains, revealing a noise-driven transition from chaotic to nonchaotic behavior with distinct dynamics in integrable and nonintegrable models.

Contribution

It demonstrates that measurement-induced chaos transitions in classical oscillator chains can be described by a stochastic Langevin equation, highlighting the roles of noise and interactions in chaos suppression.

Findings

Chaotic-to-nonchaotic transition occurs with increasing noise or decreasing interaction strength.

Lyapunov exponent and butterfly velocity vanish in the nonchaotic phase, acting as order parameters.

Finite-size scaling of butterfly velocity near the transition is observed.

Abstract

We discuss the dynamics of integrable and nonintegrable chains of coupled oscillators under continuous weak position measurements in the semiclassical limit. We show that, in this limit, the dynamics is described by a standard stochastic Langevin equation, and a measurement-induced transition appears as a noise- and dissipation-induced chaotic-to-nonchaotic transition akin to stochastic synchronization. In the nonintegrable chain of anharmonically coupled oscillators, we show that the temporal growth and the ballistic light-cone spread of a classical out-of-time correlator characterized by the Lyapunov exponent and the butterfly velocity, are halted above a noise or below an interaction strength. The Lyapunov exponent and the butterfly velocity both act like order parameter, vanishing in the nonchaotic phase. In addition, the butterfly velocity exhibits a critical finite-size scaling. For the integrable model, we consider the classical Toda chain and show that the Lyapunov exponent changes nonmonotonically with the noise strength, vanishing at the zero noise limit and above a critical noise, with a maximum at an intermediate noise strength. The butterfly velocity in the Toda chain shows a singular behavior approaching the integrable limit of zero noise strength.