Asymmetric transport in the bouncer model: Mixed, time dependent, noncompact dynamics

TL;DR

This paper investigates how time-dependent dynamics in a generalized bouncer model with mixed phase space and Fermi acceleration lead to asymmetric transport, revealing stretched exponential decay behaviors through an efficient numerical approach.

Contribution

It introduces a novel numerical scheme for analyzing time-dependent transport in a complex dynamical system with mixed phase space and unbounded velocities.

Findings

Asymmetric transport effects observed in the model.

Stretched exponential decay patterns identified.

Numerical scheme effectively captures complex dynamics.

Abstract

We consider time-dependence of dynamical transport, following a recent study of the stadium billiard in which classical transmission and reflection probabilities were shown to exhibit exponential or algebraic decay depending on the choice of the lead or "hole". The system considered here is much more general, having a generic mixed phase space structure, time-dependence of the dynamics, and Fermi acceleration (trajectories with unbounded velocity). We propose an efficient numerical scheme for this model, observe the asymmetric transport effect, and discuss observed stretched exponential decays.