Evolution under in-plane topological driving fields following Jordan curves

JESÚS CASADO-PASCUAL; A. A, REYNOSO

Montevideo

Conferencia; Sólidos 2019: VIII Congreso Nacional de Sólidos y Primer Encuentro Bi-Nacional (Argentina-Uruguay); 2019

Using intrinsic properties of Jordan curves, we identify relations among system averaged quantities having the ability to indicate the topology of a driving planar field. Our result is valid beyond TLMs, survives in the presence of dissipation, and applies to both periodic (i.e. Floquet) and non-periodic time-dependence drivings along the Jordan curve. Remarkably, for the case of elliptical drivings we obtain a Jordanian relation independent on the position of the ellipse, which, for symmetrical traveled ellipses, it is connected to the geometrical average of the driving field, namely, the contribution of the driving to the dynamic phase.