Moving beyond Born and Oppenheimer for Dynamics, Thermodynamics and Quantum Geometry

Complex systems often exhibit phenomena on widely differing timescales, which simplifies their description. In the microscopic realm, nuclei are slow and heavy while the electrons are fast and light. This separation of scale is fundamental to quantum chemistry, atomic physics and in condensed matter, forming the basis for chemical bonding, quantum electrodynamics and electronic Bloch bands.

The Born-Oppenheimer approximation (BOA), which slaves the fast degrees of freedom to the slow ones at each instant of time, has been the workhorse of these systems for nearly a 100 years. However, it misses several important effects which are a consequences of the feedback between the fast and the slow degrees of freedom; for instance, the mass renormalization of the slow degree of freedom and entanglement between the fast degrees of freedom. I will introduce a systematic framework to go beyond the BOA, and present its startling consequences for dynamics, thermodynamics and quantum geometry in model systems. In particular, we will find that the fast degrees of freedom can dynamically entangle/squeeze, that quantum geometry is dynamical, and that there are new thermodynamic forces in such systems.