One day meeting in mathematical quantum mechanics
09.02.2018 kl. 13.00 - 17.00
13:00-13:50 Kenichi Ito, University of Kobe
Title: Resolvent expansions for the Schrödinger operator on a graph with rays
Abstract: In this talk we present a complete study of resonance states and resolvent expansions at a threshold for the Schrödinger operator on a graph with a finite number of infinite rays. A precise description of the expansion coefficients reveals their exact correspondence to the generalized eigenspaces, or the threshold types. For the proof we implement the expansion scheme of Jensen-Nenciu (2001) in its full generality. This talk is base on a recent joint work with Arne Jensen, Aalborg University.
14:00-14:50 Grigori Rozenblium, Chalmers Tekniska Högskola
Title: Eigenvalue estimates for the Schrödinger operator on infinite combinatorial and quantum graphs
Abstract: PDF file
14:50-15:10 Coffee break
15:10-16:00 Jean Bellissard, Westfälische Wilhelms-Universität Münster and Georgia Institute of Technology
Title: Periodic Approximations for Energy Spectra of Aperiodic Media
Abstract: This talk will give a summary of the results obtained during the last eight years with collaborators Giuseppe De Nittis, Siegfried Beckus and Horia Cornean, about the mathematical techniques offered to compute or to estimate the spectrum of a Hamiltonian describing the quantum motion of a single particle in an aperiodic medium. Examples treated numerically in the past will start the talk. A short introduction to the mathematical background will be presented, including the groupoid aspects. The concept of continuous field of Hamiltonians will be described. Various rigorous results will be provided, liable to be critical for applications. At least, if time allows, more precise results in the 1D case will be presented.
16:10-17:00 Volker Bach, Technische Universitaet Braunschweig
Title: Beyond the van Hove time scale
Abstract: Given an arbitrarily large, but fixed, time $t >0$, we derive approximations for the time evolution of the spin-boson model in terms of the propagator generated by a free effective Hamiltonian. Our construction rests on the renormalization group induced by the isospectral Feshbach-Schur map. This is joint work with Jacob Schach Möller and Matthias Westrich.
Institut for Matematiske Fag
Skjernvej 4A, rum 5.034