arXiv subjects
Publications and source records attributed to Kurt Pagani.
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 $H(q,p)$ on a phase space (symplectic manifold), and the marginal measures that have to be transported are linked by a (implicit) transformation group.
This note reports on some attempts to examine if and under which conditions the naturally scaled probability measures associated to an orthonormal basis of a classical Paley-Wiener space converge to a uniform distribution (on a compact set in momentum space). The results are still quite unsatisfactory, yet we got some indications that for inf-compact functions (symbols) and domains for which some generalized Weyl law holds, the measures converge weakly to a (generalized) Fermi ball.
We have a look at the probability measures induced by Schrodinger wave functions on phase space.
We show the point-wise definiteness and some other properties of the energy-momentum tensor for a certain class of Euler-Lagrange equations under quite general conditions.
We present some simple relations between the absolute minimizers of the functional $||Du+Xu||$, where $X$ is a vector field on $R^n$, and ground state solutions to the (non-relativistic) Schroedinger equation. This article is a byproduct of the study of the more general functional $||ADu+F'(u)X||$.