Dynamics of quantum trajectories in chaotic systems

¹ Departamento de Química C-IX, Universidad Autónoma de Madrid Cantoblanco, 28049 Madrid, Spain
² Departamento de Física “J.J. Giambiagi”, FCEN, UBA, Pabellón 1 Ciudad Universitaria - 1428 Buenos Aires, Argentina
³ Departamento de Física, ETSI Agrónomos, Universidad Politécnica de Madrid 28040 Madrid, Spain

Received: 7 July 2003
Accepted: 5 September 2003

Abstract

Quantum trajectories defined in the de Broglie-Bohm theory provide a causal way to interpret physical phenomena. In this letter, we use this formalism to analyze the short-time dynamics induced by unstable periodic orbits in a classically chaotic system, a situation in which scars are known to play a very important role. We find that the topologies of the quantum orbits are much more complicated than that of the scarring and associated periodic orbits, since the former have quantum interference built in. Thus scar wave functions are necessary to analyze the corresponding dynamics. Moreover, these topologies imply different return routes to the vicinity of the initial positions, and this reflects in the existence of different contributions in each peak of the survival probability function.