SEARCH FOR SUPERLUMINAL PROPAGATION IN HIGH MAGNETIC FIELDS

Abstract

We investigate the possibility of superluminal propagation of massive particles in high magnetic fields. Formal arguments suggest that this could occur in the quantum Hall regime near zero temperature, since here a few conducting states in the center of a broadened Landau band carry a macroscopic Hall current. We investigate the microscopic processes which lead to the high velocities of conducting states in the quantum Hall effest and ask what are the highest possible velocities which can be generated in that way. Our analysis shows that in typical quantum Hall systems at the most a tiny fraction of a carrier wave function can describe superluminal behaviour but that the center of mass velocity is far below the velocity of light. On the other hand, on pure theoretical grounds we can construct special systems (with ≪exotic≫ parameters) where the Schrödinger equation does admit solutions with superluminal center of mass velocities. The described propagation has no analogy in classical physics. Einstein's causality is not violated. The time evolution of the corresponding wave function is similar to that of a recently observed superluminal light pulse.1 We discuss analogies and differences between the two phenomena.