Transport of modulated phases by pumping

¹ Department of Theory and Simulation of Complex Systems, ICMA CSIC-Universidad de Zaragoza - E-50009 Zaragoza, Spain
² Mathematics Institute, University of Warwick - Coventry CV4 7AL, UK
³ Departamento de Física de la Materia Condensada, Universidad de Zaragoza E-50009 Zaragoza, Spain
⁴ Departamento de Física Aplicada, Universidad de Zaragoza E-50009 Zaragoza, Spain

Received: 16 May 2002
Accepted: 30 July 2002

Abstract

We give here some definite answers to the question on the possibility of transport of modulated phases by homogeneous pumping of (pinning) energy. They are presented for the convex class of the Frenkel-Kontorova model (discrete sine-Gordon equation). Our approach leads to a rigorous characterization of the transport under dissipative evolution and large pumping time scales. We also show an explicit example of computed phase diagram of the flow. When combined with Discommensuration Theory, our formal approach (essentially rooted in Aubry-Mather theory) gives an exact account of the features and singularities of this complex phase diagram in generic physical terms.