2006 Theses Doctoral

Chaos and the Weak Quantum-Classical Transition

Greenbaum, Benjamin Dylan

Although a closed quantum system lacks clear signatures of classical chaos, it has been shown numerically that correspondence between an open quantum system and open classical system can be established. This phenomenon is explored for the case of an unconditioned evolution, where a system interacts with its environment, but the environment does not extract any information. This has been dubbed the “weak” transition and stands in contrast to the “strong” version where information is extracted by the environment. The transition is numerically mapped for the classically chaotic Duffing oscillator. Closed quantum and classically chaotic systems fail to agree due to the presence of fine scale structure in the classical evolution and the abundance of nonlocal interference in the quantum evolution. We show how noise mitigates both of these effects by suppressing the foliation of the classical unstable manifold while simultaneously acting as a passive filter of nonlocal quantum interference. The predicted transition parameter values are tested numerically for the Duffing oscillator. Finally, we explore whether these mechanisms are responsible for the emergence of classical chaos. While they do modify closed system spectral arguments against chaotic behavior, they do not provide a signature of chaotic dynamics. This stands in contrast to the trajectory level chaos observed in the strong transition.

Keywords: nonlinear dynamics, quantum-classical transition, theoretical physics