6 citations · 7 across the 5 of their papers we have counts for
5 papers
A Simple Proof of Unique Continuation for J-holomorphic Curves
Michael VanValkenburgh
In this expository paper, we prove strong unique continuation for J-holomorphic curves by first giving a simple proof of Aronszajn's theorem in the special case of the two-dimensio…
Manipulation of Semiclassical Laguerre-Gaussian Modes: a Model Case
Michael VanValkenburgh
We continue the study, from a semiclassical viewpoint, of Calvo and Picon's operators, as manipulating photon states in quantum communication. In a previous paper, we defined a one…
Manipulation of Semiclassical Photon States
Michael VanValkenburgh
Gabriel F. Calvo and Antonio Picon defined a class of operators, for use in quantum communication, that allows arbitrary manipulations of the three lowest two-dimensional Hermite-G…
Exponential Lower Bounds for Quasimodes of Semiclassical Schrödinger Operators
Michael VanValkenburgh
We prove quantitative unique continuation results for the semiclassical Schrodinger operator on smooth, compact domains. These take the form of exponentially decreasing (in h) loca…
Laguerre-Gaussian Modes and the Wigner Transform
Michael VanValkenburgh
Recent developments in laser physics have called renewed attention to Laguerre-Gaussian (LG) beams of paraxial light. In this paper we consider the corresponding LG modes for the t…