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SUMMARY:Oliver Matte (Aalborg University)
DTSTART:20200618T100000Z
DTEND:20200618T105000Z
DTSTAMP:20260416T065556Z
UID:IML-SMR/16
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/IML-SMR/16/"
 >Differentiability properties of stochastic flows and semigroup kernels in
  nonrelativistic QED</a>\nby Oliver Matte (Aalborg University) as part of 
 Scattering\, microlocal analysis and renormalisation\n\n\nAbstract\nIn thi
 s talk we consider the Pauli-Fierz model for a finite number of nonrelativ
 istic electrons in an external electrostatic potential interacting with th
 e quantized\, ultraviolet cutoff electromagnetic field. The semigroup gene
 rated by the corresponding Hamiltonian has a Fock space operator-valued in
 tegral 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 o
 f spectral subspaces. The proofs of our results are based on Feynman-Kac f
 ormulas and an analysis of the differentiability properties of solutions t
 o certain stochastic differential equations associated with the Pauli-Fier
 z model. These equations have been introduced by Batu Güneysu\, Jacob Sch
 ach Møller and the present author in an earlier work.\n
LOCATION:https://researchseminars.org/talk/IML-SMR/16/
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