Transference Plans and Uncertainty
Kurt Pagani
TL;DR
This paper explores the application of Optimal Transportation Theory to quantum mechanics, focusing on how cost functions based on Hamiltonians influence the transportation of measures in phase space.
Contribution
It introduces a novel framework connecting optimal transportation with quantum mechanical Hamiltonians and transformation groups.
Findings
Established links between transportation costs and Hamiltonian dynamics
Proposed methods to analyze measure transformations in quantum phase space
Highlighted potential applications in quantum state analysis
Abstract
We discuss methods of Optimal Transportation Theory and its relations to problems in quantum mechanics. This essentially means that the cost function is some Hamiltonian on a phase space (symplectic manifold), and the marginal measures that have to be transported are linked by a (implicit) transformation group.
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Taxonomy
TopicsStochastic processes and financial applications · Neurosurgical Procedures and Complications