Titlebook: Microlocal Methods in Mathematical Physics and Global Analysis; Daniel Grieser,Stefan Teufel,Andras Vasy Conference proceedings 2013 Sprin

Ruptured-Disk

情节剧

外露

单调女

Local Smoothing with a Prescribed Loss for the Schrödinger EquationIn ., the Schrödinger propagator at time . is unitary on .. spaces. However, solutions to the linear Schrödinger equation on . are smoother . in time, and . in space:

FAST

Propagation Through Trapped Sets and Semiclassical Resolvent EstimatesLet .,..We are interested in semiclassical resolvent estimates of the form. for . > 0,. with.,. > 1 ∕ 2. We ask: how is the function .(.) for which (1) holds affected by the relationship between the support of . and the trapped set at energy ., defined by .Here .and ..

施魔法

A Nonlinear Adiabatic Theorem for Coherent StatesWe present a result obtained in collaboration with Rémi Carles on the propagation of coherent states for a 1-d cubic nonlinear Schrödinger equation in a semi-classical regime (.):

watertight,

The Effective Hamiltonian in Curved Quantum Waveguides and When It Does Not WorkWe are concerned with the singular operator limit for the Dirichlet Laplacian in a three-dimensional curved tube (cf. Fig. 1) when its cross-section shrinks to zero.

起皱纹

GREG

态学

On the Closure of Elliptic Wedge OperatorsWe present a semi-Fredholm theorem for the minimal extension of an elliptic differential operator on a manifold with wedge singularities and give, under suitable assumptions, a full asymptotic expansion of the trace of the resolvent.