PIRSA:16050049

Wasserstein-geometry as a natural language for Quantum hydrodynamics

Lessel, B. (2016). Wasserstein-geometry as a natural language for Quantum hydrodynamics. Perimeter Institute. https://pirsa.org/16050049

Lessel, Bernadette. Wasserstein-geometry as a natural language for Quantum hydrodynamics. Perimeter Institute, May. 24, 2016, https://pirsa.org/16050049 

          @misc{ pirsa_PIRSA:16050049,
            doi = {10.48660/16050049},
            url = {https://pirsa.org/16050049},
            author = {Lessel, Bernadette},
            keywords = {Quantum Foundations},
            language = {en},
            title = {Wasserstein-geometry as a natural language for Quantum hydrodynamics},
            publisher = {Perimeter Institute},
            year = {2016},
            month = {may},
            note = {PIRSA:16050049 see, \url{https://pirsa.org}}
          }

Bernadette Lessel

Max Planck Institute for the History of Science (MPIWG)

Talk number
PIRSA:16050049
Collection
Talk Type
Subject
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.