Classical and quantum chaotic pumps

22/05/2009, 10:30

Thomas Dittrich, CeiBA - Complejidad and Universidad Nacional de Colombia, Bogota, Colombia

I present a synopsis of directed transport in driven chaotic scattering systems. If all spatio-temporal symmetries are broken that correspond to an inversion of momentum, reflection and transmission probabilities from either side in a scattering system can become different, allowing for a global left-right asymmetry in transport, i.e., for directed currents. The underlying dynamic mechanism is a corresponding asymmetry in the system's chaotic repeller. By contrast with adiabatic (peristaltic) pumping, it does not require two parameters to be varied independently. As it occurs in a strongly nonlinear regime of fast and strong driving, no perturbative or adiabatic approximations apply; in particular, chaotic pumps manifestly violate linear response. Upon quantization, mechanisms of chaotic transport largely carry over to the semiclassical regime.

Beyond charge/mass currents, also directed transport of quantities like angular momentum is possible if they couple to the scattering potential via, e.g., a magnetic field. On the quantum mechanical level, this corresponds to spin-polarized currents. Where they coincice with zeros of charge transport, pure spin separation is achieved. I illustrate these findings with numerical results for a number of simple model systems, such as vertically or laterally driven square or smooth potential wells, that could be realized experimentally as semiconductor superlattices.