Punchets and inverse ratchets surprising applications of nonlinear directed transport

by Thomas Dittrich

at Condensed Matter Theory Seminar

Wed, 08 Jun 2016, 13:30
Physics building (#54) room 207

Abstract

Directed transport by means of nonlinear dynamics has been studied in two alternative frameworks in periodically driven sawtooth potentials ratchets and in the context of driven chaotic scattering pumps The concept of ratchets originates in the analysis of molecular motors whose function can be explained by an interplay of a coherent external force and a breaking of binary symmetries like parity and time reversal Restricting a ratchet to finite a compact space leads to a pump a periodically forced scattering system that generates directed currents As a hybrid between ratchets and pumps punchets generate transport by a local restricted to a compact region in space driving periodic in time of an otherwise static spatially periodic ratchet potential They are inspired e g by metal or semiconductor surfaces irradiated by a collimated laser beam Classically these systems exhibit asymmetric irregular scattering thus giving rise to directed currents They can be quantized in the framework of Floquet scattering as an exact theory for periodically driven scatterers combined with Bloch theory applied to the spatially periodic asymptotic regions Scattering is therefore restricted both by energy conservation modulo the photon energy of the driving and the condition that transitions are allowed only between Bloch bands of the asymptotic regions Another surprising extension of chaotic transport are pacemakers or inverse rectifiers that is nonlinear systems that generate a periodic force as output from a constant input force or torque with a stable frequency over a wide range of system parameters As an emblematic historical example we model and study analytically and numerically the escapement of traditional mechanical clocks The principal elements of the model are two degrees of freedom that of the pendulum or balance wheel with hairspring and that of the anchor wheel coupled by a potential periodic in the anchor wheel angle As energy input we assume a torque on the anchor wheel that does not depend on the angle but parametrically on time through the tension of the mainspring Numerical simulations of this dissipative two degrees of freedom system reproduce the ticking mode of a mechanical clock and show that the period of the ticking is approximately constant over a wide range of the input force We analyze how the specific construction of traditional escapements serves to achieve and optimize this behaviour and also show as that for extreme values of the parameters the same system is capable of chaotic motion hence is a generic case of a two dimensional nonlinear system

Created on 02-06-2016 by Bar Lev, Yevgeny (ybarlev)
Updaded on 02-06-2016 by Bar Lev, Yevgeny (ybarlev)