Emergent non-adiabatic dynamics and geometric response in interacting systems

Seminar

Speaker: Anatoli Polkovnikov
When: Oct. 15 2014 14:00
Where: Erwin Schrödinger Saal

First I will give a brief introduction to the geometric tensor. Its imaginary part is the Berry curvature and its real part defines the natural metric tensor. Both the Berry curvature and the metric tensor can be used to define various geometric (topological) invariants like the Chern number or the Euler characteristic. Then I will show that the Berry curvature can be measured as the leading non-adiabatic response of observables to slowly changing parameters. Thus measuring the non-adiabatic response of an arbitrary system one can directly probe the Berry curvature and hence the Berry phase and the Chern number. I will discuss how using these ideas topological phase transitions were recently measured in superconducting qubits. I will also discuss how the metric tensor can be measured through the noise or dissipation. Next I will consider the setup where the external parameters themselves are slow dynamical degrees of freedom. I will discuss how one can derive emergent Newtonian dynamics and leading non-Newtonian corrections. I will show that the concept of mass is closely related to the metric tensor. I will illustrate these ideas by computing the inertia mass and the snap modulus of a photon confined to a cavity in two setups when both walls of the cavity move together and when only one wall of the cavity moves.

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