One-day meeting in mathematical analysis


27.10.2017 kl. 13.00 - 17.00



Kl. 13:00-13:45  Frokost

Kl. 14:00-14:50 Oliver Matte (Aalborg)
Title: A Bismut-Elworthy-Li type formula in non-relativistic quantum electrodynamics.

Abstract: Together with B. Güneysu and J.S. Møller, we recently studied stochastic differential equations associated with the standard model of non-relativistic quantum electrodynamics. In this talk we discuss the differentiability properties of the corresponding stochastic flow. Furthermore, we derive a Bismut-Elworthy-Li type formula for the derivatives of elements in the range of the semi-group generated by the Pauli-Fierz operator. We finally explain how to prove smoothness of the Fock space operator-valued semi-group kernel.

Kl. 14:50-15:10 Kaffe og kage

Kl. 15:10-kl 16:00 Radu Purice (Bucharest)

Title: Spectral analysis of the bottom of the spectrum of 2-dimensional periodic Hamiltonians in slowly varying magnetic fields.

Abstract: Consider a periodic Schrödinger operator in two dimensions, perturbed by a weak magnetic field whose intensity slowly varies in space. We show in great generality that the bottom of the spectrum of the corresponding magnetic Schrödinger operator develops spectral islands  separated by gaps, reminding of a Landau-level structure. Joint work with Horia Cornean and Bernard Helffer.

Kl. 16:10-17:00 Bernard Helffer (Nantes)

Title: On the semi-classical analysis of the groundstate energy of the Dirichlet Pauli operator.

Abstract:  We consider the Dirichlet Pauli operator in bounded connected domains in the plane, with a semi-classical parameter. We show, in particular, that, as soon the magnetic field does not vanish identically,  the ground state energy of this Pauli operator will be exponentially small as the semi-classical parameter tends to zero and estimate this decay rate. This is joint work with Hynek Kovarik and Mikael Persson Sundqvist.



Institut for Matematiske Fag


Skjernvej 4A, auditorium 5.034

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