Mon, Nov 17, 2014, 1:15 pm to 2:30 pm
PCTS Seminar Room
I will overview relations between the non-adiabatic response and the geometric tensor. In particular, I will show how the Berry curvature (imaginary part of the geometric tensor) and the topological phase transitions can be engineered and measured using non-adiabatic response and discuss recent experiments in superconducting qubits. The real part of the geometric tensor (Fubini-Study metric) can be measured through noise or imaginary part of the linear response susceptibility. In turn this metric can be used to construct new geometric and topological invariants based on the Euler characteristic. In the last part of the talk I will show that the Newtonian or Hamiltonian dynamics is emergent from the non-adiabatic response and that the notion of the mass is closely related to the metric tensor. I will discuss leading corrections beyond the Hamiltonian dynamics. I will demonstrate general results using simple examples of particles or photons confined to a cavity.