A study of the reflection of classical chaos and ergodicity in quantum mechanical systems

This work examines the implications of chaos and ergodicity for quantum mechanical systems. The topics discussed here are relevant to any discussion of the conditions under which a molecular system may be expected to obey statistical theories of reaction dynamics.;The first chapter is a review of the work in this area. We also point out here, the necessity and the relevance of the present work.;In Chapter 2, we explore the applicability of the classical concept of ergodicity to quantum mechanical systems that are away from the classical limit, and do not necessarily become ergodic as h ;Classical chaos is often accompanied by "local" ergodicity--ergodic behavior in regions of phase space that are generally smaller than, but of the same dimensionality as, the energy surface. If there are strong dynamical barriers in phase space impeding the relaxation to statistical equilibrium in the full region of ergodicity, it is often possible to define an approximate form of ergodicity in a smaller region where relaxation occurs temporarily, but quickly. Such "pseudoergodicity" is also a reliable symptom of chaos. In Chapter 3, we use the presence of quantum behavior analogous to pseudoergodicity to study the influence of chaos on quantum systems.;The relationship between trajectories and eigenstates in the chaotic regime has intrigued theorists for some time. In Chapter 4, we examine semiclassical and quantum expectation values for states in the chaotic regime of the Henon-Heiles system, in an attempt to understand the connections between the two.;In Chapter 5, we summarize our work and highlight the important conclusions to emerge from it.