Punchets: nonlinear transport in Hamiltonian pump-ratchet hybrids

TL;DR

Punchets are hybrid systems combining ratchet and pump features, exhibiting nonlinear directed transport driven by irregular scattering, with diverse models showing complex current behaviors, including currents against wave propagation direction.

Contribution

This paper introduces and analyzes the nonlinear transport mechanisms in punchets, a novel class of Hamiltonian models combining ratchet and pump features with various driving schemes.

Findings

Directed currents arise from broken spatio-temporal symmetries.

Current direction can oppose wave propagation, highlighting nonlinear effects.

Transport mechanisms depend on the specific model and parameters.

Abstract

"Punchets" are hybrids between ratchets and pumps, combining a spatially periodic static potential, typically asymmetric under space inversion, with a local driving that breaks time-reversal invariance, and are intended to model metal or semiconductor surfaces irradiated by a collimated laser beam. Their crucial feature is irregular driven scattering between asymptotic regions supporting periodic (as opposed to free) motion. With all binary spatio-temporal symmetries broken, scattering in punchets typically generates directed currents. We here study the underlying nonlinear transport mechanisms, from chaotic scattering to the parameter dependence of the currents, in three types of Hamiltonian models, (i) with spatially periodic potentials where only in the driven scattering region, spatial and temporal symmetries are broken, and (ii), spatially asymmetric (ratchet) potentials with a driving that only breaks time-reversal invariance. As more realistic models of laser-irradiated surfaces, we consider (iii), a driving in the form of a running wave confined to a compact region by a static envelope. In this case, the induced current can even run against the direction of wave propagation, drastically evidencing of its nonlinear nature. Quantizing punchets is indicated as a viable research perspective.