Nonlinear Transport in the Stochastic Standard Map

TL;DR

This paper investigates how stochastic noise affects transport in the standard map, revealing two distinct transport regimes—linear driven by noise and nonlinear involving nonlinear dynamics—leading to enhanced transport speeds.

Contribution

It introduces a framework to distinguish between linear and nonlinear transport in a stochastically-driven standard map, highlighting the impact of noise on phase space dynamics.

Findings

Noise destroys invariant manifolds, enabling widespread transport.

Two classes of transport identified: linear and nonlinear.

Nonlinear transport significantly accelerates overall transport.

Abstract

We study a stochastically-driven standard map. The addition of a noise term destroys the invariant manifolds that organize the phase space which allows for more widespread transport than in the noiseless case. Using appropriately defined hitting times to quantify the dynamics, we identify two qualitatively different classes of transport: linear and nonlinear. Linear transport is primarily driven by the stochasticity in the system, while nonlinear transport results from a combination of the nonlinear dynamics and stochasticity and provides a significant speed-up in transport.