PIRSA:13100083

Geometry of quantum phases and emergent Newtonian dynamics

Polkovnikov, A. (2013). Geometry of quantum phases and emergent Newtonian dynamics. Perimeter Institute. https://pirsa.org/13100083

Polkovnikov, Anatoli. Geometry of quantum phases and emergent Newtonian dynamics. Perimeter Institute, Oct. 15, 2013, https://pirsa.org/13100083 

          @misc{ pirsa_PIRSA:13100083,
            doi = {10.48660/13100083},
            url = {https://pirsa.org/13100083},
            author = {Polkovnikov, Anatoli},
            keywords = {Condensed Matter},
            language = {en},
            title = {Geometry of quantum phases and emergent Newtonian dynamics},
            publisher = {Perimeter Institute},
            year = {2013},
            month = {oct},
            note = {PIRSA:13100083 see, \url{https://pirsa.org}}
          }

Anatoli Polkovnikov

Boston College

Talk number
PIRSA:13100083
Collection
Talk Type
Subject
Abstract
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.