Quantum bound to chaos and the semiclassical limit

Abstract

We discuss the quantum bound on chaos in the context of the free propagation of a particle in an arbitrarily curved surface at low temperatures. The semiclassical calculation of the Lyapunov exponent can be performed in much the same way as the corresponding one for the `Loschmidt echo'.The bound appears here as the impossibility to scatter a wave, by effect of the curvature, over characteristic lengths smaller than the deBroglie wavelength.