Extended Standard Map with Spatio-Temporal Asymmetry

TL;DR

This paper investigates how spatial and temporal asymmetries in an extended standard map influence transport properties, leading to asymmetric diffusion and unidirectional motion, with detailed numerical analysis of parameter dependence.

Contribution

It introduces symmetry-breaking extensions of the standard map and analyzes their impact on transport and diffusion properties, highlighting the role of asymmetries.

Findings

Asymmetries induce unidirectional motion.

Transport properties depend intricately on control parameters.

The model allows feasible analysis of global dynamical behavior.

Abstract

We analyze the transport properties of a set of symmetry-breaking extensions %, both spatial and temporal, of the Chirikov--Taylor Map. The spatial and temporal asymmetries result in the loss of periodicity in momentum direction in the phase space dynamics, enabling the asymmetric diffusion which is the origin of the unidirectional motion. The simplicity of the model makes the calculation of the global dynamical properties of the system feasible both in phase space and in controlling-parameter space. We present the results of numerical experiments which show the intricate dependence of the asymmetric diffusion to the controlling parameters.