An Optimal Transport View On Schroedinger's Equation

Details An Optimal Transport View On Schroedinger's Equation An Optimal Transport View On Schroedinger's Equation

2008-04-29

arxiv.org/abs/0804.4621v3

Physics

Mathematical Physics

Scientific paper

We show that the Schroedinger equation is a lift of Newton's law of motion on the space of probability measures, where derivatives are taken w.r.t. the Wasserstein Riemannian metric. Here the potential is the sum of the total classical potential energy of the extended system and its Fisher information. The precise relation is established via a well known ('Madelung') transform which is shown to be a symplectic submersion of the standard symplectic structure of complex valued functions into the canonical symplectic space over the Wasserstein space. All computations are conducted in the framework of Otto's formal Riemannian calculus for optimal transportation of probability measures

Affiliated with

Also associated with

No associations

Rating

An Optimal Transport View On Schroedinger's Equation does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with An Optimal Transport View On Schroedinger's Equation, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and An Optimal Transport View On Schroedinger's Equation will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-210042