Using quantum geometry to derive the effective classical equation of motion in a hybrid quantum-classical system

TYPECondensed Matter Seminar
Speaker:Ryan Requist
Organizer:Anna Keselman
Time:14:30 - 15:30
Location:Lidow Nathan Rosen (300)

Consider a classical particle and a generic quantum system that are mutually coupled.  A common scenario is that the Hamiltonian operator depends parametrically on the particle coordinate and at the same time the particle experiences an Ehrenfest-type force.  If the classical particle moves slowly, it drives the quantum system adiabatically.  I derive an effective equation of motion for the classical particle to third order in its velocity.  This is achieved through a formulation of adiabatic perturbation theory that makes essential use of the quantum covariant derivative - a geometric structure induced by the position-dependence of the adiabatic eigenstate.  The third-order equation contains corrections to the effective mass tensor and the curvature of the gauge field, as well as additional terms not seen before.  I will report numerical simulations exploring the qualitative effect of the third-order terms.