Wasserstein-geometry as a natural language for Quantum hydrodynamics



Playing this video requires the latest flash player from Adobe.

Download link (right click and 'save-as') for playing in VLC or other compatible player.


Recording Details

Speaker(s): 
Scientific Areas: 
Collection/Series: 
PIRSA Number: 
16050049

Abstract

In this talk I would like to put forward Wasserstein-geometry as a natural language for Quantum hydrodynamics. Wasserstein-geometry is a formal, infinite dimensional, Riemannian manifold structure on the space of probability measures on a given Riemannian manifold. The basic equations of Quantum hydrodynamics on the other hand are given by the Madelung equations. In terms of Wasserstein-geometry, Madelung equations appear in the shape of Newton's second law of motion, in which the geodesics are disturbed by the influence of a quantum potential. This was pointed out in 2008 by Max. K. von Renesse. Finally, based on the notion of Wasserstein-distance, I will will briefly introduce a natural notion of Shape Space and some of its properties.