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- Geometry of quantum phases and emergent Newtonian dynamics

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Scientific Areas:

Collection/Series:

PIRSA Number:

13100083

In the first part

of this talk I will discuss how one can characterize geometry of quantum phases

and phase transitions based on the Fubini-Study metric, which characterizes the

distance between ground state wave-functions in the external parameter space.

This metric is closely related to the Berry curvature. I will show that there

are new geometric invariants based on the Euler characteristic.

I will also show how one can directly measure this metric

tensor in simple dynamical experiments. In the second part of the talk I will

discuss emergent nature of macroscopic equations of motion (like Newton's

equations) showing that they appear in the leading order of non-adiabatic

expansion. I will show that the Berry curvature gives the Coriolis force and

the Fubini-Study metric tensor is closely related to the inertia mass. Thus I

will argue that any motion (not necessarily motion in space) is geometrical in

nature.

©2012 Perimeter Institute for Theoretical Physics