2 citations · 3 across the 6 of their papers we have counts for
9 papers
The Lorentzian Calderón problem on vector bundles
Sean Gomes, Lauri Oksanen
In this paper we study a Lorentzian version of the Calderón problem, which is concerned with the determination of a connection and potential on a Hermitian vector bundle over a Lor…
Scattering regularity for small data solutions of the nonlinear Schrödinger equation
Jesse Gell-Redman, Sean Gomes, Andrew Hassell
Using the Fredholm theory of the linear time-dependent Schrödinger equation set up in our previous article arXiv:2201.03140, we solve the final-state problem for the nonlinear Schr…
Propagation of singularities and Fredholm analysis for the time-dependent Schrödinger equation
Jesse Gell-Redman, Sean Gomes, Andrew Hassell
We study the time-dependent Schrödinger operator acting on functions defined on , where, using coordinates and $t \in \ma…
Self-focal points of ellipsoids of dimension
Sean Gomes, Steve Zelditch
A self-focal point of a Riemannian manifold is a point so that every geodesic starting from returns to at some positive time. It is called a pole if all geodesi…
Caustics of weakly Lagrangian distributions
Sean Gomes, Jared Wunsch
We study semiclassical sequences of distributions associated to a Lagrangian submanifold of phase space $\lag \subset T^*X$. If is a semiclassical Lagrangian distributi…
Semiclassical scarring on tori in KAM Hamiltonian systems
Sean Gomes, Andrew Hassell
We show that for almost all perturbations in a one-parameter family of KAM Hamiltonians on a smooth compact surface, for almost all KAM Lagrangian tori , we can find a semicla…
KAM Hamiltonians are not Quantum Ergodic
Sean Gomes
We show that under generic conditions, the quantisation of a -parameter family of KAM perturbations of a completely integrable and Kolmogorov non-degenerate Gevrey sm…
Quantum ergodicity in mixed and KAM Hamiltonian systems
Sean Gomes
In this thesis, we investigate quantum ergodicity for two classes of Hamiltonian systems satisfying intermediate dynamical hypotheses between the well understood extremes of ergodi…
Percival's Conjecture for the Bunimovich Mushroom Billiard
Sean Gomes
The Laplace-Beltrami eigenfunctions on a compact Riemannian manifold whose geodesic billiard flow has mixed character have been conjectured by Percival to split into two comple…