Induced effective gauge fields and chaos in large amplitude collective motion

Abstract

Both experiment and theory strongly support the idea that in any treatment of many-body systems, one can safely perform a separation of variables into fast and slow degrees of freedom. Standard wisdom then suggests that at a phenomenological level one can limit the analysis of the low energy properties of a many-body system to an effective description in terms of a Hamiltonian with only kinetic and potential energy terms. In a rigorous treatment of large amplitude motion however, effective gauge fields arise naturally and their introduction is unavoidable. In the simplest picture, one can show that effective gauge fields are manifestations of level or band crossings. Their influence on the dynamics is extremely important: quantum numbers can become fractional and the collective trajectories become chaotic. An important consequence of this is a new picture of dissipation in large amplitude collective motion.