Differentiability properties of stochastic flows and semigroup kernels in nonrelativistic QED

Oliver Matte (Aalborg University)

18-Jun-2020, 10:00-10:50 (4 years ago)

Abstract: In this talk we consider the Pauli-Fierz model for a finite number of nonrelativistic electrons in an external electrostatic potential interacting with the quantized, ultraviolet cutoff electromagnetic field. The semigroup generated by the corresponding Hamiltonian has a Fock space operator-valued integral kernel. We study the differentiability properties of this kernel, with respect to time and electron positions, away from the singularities of the electrostatic potential. We further obtain new decay and regularity results on possible ground state eigenvectors and more general elements of spectral subspaces. The proofs of our results are based on Feynman-Kac formulas and an analysis of the differentiability properties of solutions to certain stochastic differential equations associated with the Pauli-Fierz model. These equations have been introduced by Batu Güneysu, Jacob Schach Møller and the present author in an earlier work.

mathematical physicsanalysis of PDEsspectral theory

Audience: researchers in the topic


Scattering, microlocal analysis and renormalisation

Series comments: Mondays: aarhusuniversity.zoom.us/j/9036772485 Meeting ID: 903 677 2485

Thursdays: us02web.zoom.us/j/6094800950 Meeting ID: 609 480 0950

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Links to the slides can be found here: drive.google.com/file/d/1uu6ZvU6zlGalJpZR7ZDi7igsvBMBylOA/view

Organizers: Claudio Dappiaggi, Jacob Schach Møller, Michał Wrochna*
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