Linear and logarithmic entanglement production in an interacting chaotic system

TL;DR

This paper studies entanglement growth in coupled chaotic rotors, revealing linear and logarithmic regimes, and links these to energy dynamics and coherence decay, with analytical and numerical agreement.

Contribution

It provides an analytical expression for the transition time between entanglement growth regimes and connects entanglement dynamics to energy and coherence behavior.

Findings

Entanglement entropy exhibits linear then logarithmic growth for weak coupling.

Energy growth transitions from dynamical localization to diffusion over time.

Coherence decay is exponential initially, then follows a power-law.

Abstract

We investigate entanglement growth for a pair of coupled kicked rotors. For weak coupling, the growth of the entanglement entropy is found to be initially linear followed by a logarithmic growth. We calculate analytically the time after which the entanglement entropy changes its profile, and a good agreement with the numerical result is found. We further show that the different regimes of entanglement growth are associated with different rates of energy growth displayed by a rotor. At a large time, energy grows diffusively, which is preceded by an intermediate dynamical localization. The time-span of intermediate dynamical localization decreases with increasing coupling strength. We argue that the observed diffusive energy growth is the result of one rotor acting as an environment to the other which destroys the coherence. We show that the decay of the coherence is initially exponential followed by a power-law.