Chaotic quantum motion in a space-time periodic potential: an exactly solvable model

Abstract

We study the quantum mechanical motion of a particle in a space-time periodic potential of the Chirikov-Taylor type, V(x,t) = ( K 4π 2 ) cos(2πx) ∑ n= − ∞ ∞δ(t−n) .It is well known that the classical mechanical motion can be chaotic, where the chaotic character of the motion manifests itself by a macroscopic momentum diffusion (Brownian motion): 〈( p( t) − p( O)) 2〉 ∼ t. We here show that the quantum mechanical version of this system, under certain conditions, is exactly solvable. It turns out that the momentum diffusion occurs also in the quantum system. This is remarkable, as it seems to contradict the widespread belief that “quantum chaos is impossible”.