Abstract

Complex systems often exhibit phenomena on widely differing timescales, which simplifies their description. An everyday example is a swinging bucket of water. When the bucket moves slowly, the water surface remains nearly horizontal, an approximation known as the Born-Oppenheimer Approximation (BOA). The BOA is widely used in quantum chemistry, where a similar timescale separation arises due to the mass difference between nuclei and electrons. However, as the bucket rotation rate increases, the BOA breaks down, and pseudo forces cause the water to reach a state of new "moving" equilibrium. I will describe a systematic framework, dubbed the Moving-BOA, to compute this state in generic quantum and classical systems. The Moving-BOA reveals rich dynamics; for example, the fast degrees of freedom can get entangled and squeezed, and their motion can synchronize with that of the slow degrees of freedom.