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In this paper, I describe the weak limits of the measures associated to the eigenfunctions of the Laplacian on a Quantum graph for a generic metric in terms of the Gauss map of the determinant manifold. I describe also all the limits with minimal support (the scars).
We introduce quantum hypergraphs, in analogy with the theory of quantum graphs developed over the last 15 years by many authors. We emphasize some problems that arise when one tries to define a Laplacian on a hypergraph.
begin{abstract} We show that if the initial profile $qleft( xright) $ for the Korteweg-de Vries (KdV) equation is essentially semibounded from below and $int^{infty }x^{5/2}leftvert qleft( xright) rightvert dx<infty,$ (no decay at $-infty$ is require
We derive a new variational principle, leading to a new momentum map and a new multisymplectic formulation for a family of Euler--Poincare equations defined on the Virasoro-Bott group, by using the inverse map (also called `back-to-labels map). This
The fully compressible semi-geostrophic system is widely used in the modelling of large-scale atmospheric flows. In this paper, we prove rigorously the existence of weak Lagrangian solutions of this system, formulated in the original physical coordin
We consider the semi-classical limit of the quantum evolution of Gaussian coherent states whenever the Hamiltonian $mathsf H$ is given, as sum of quadratic forms, by $mathsf H= -frac{hbar^{2}}{2m},frac{d^{2},}{dx^{2}},dot{+},alphadelta_{0}$, with $al