Work­shop 'Ma­the­ma­ti­cal Phy­sics in the He­art of Ger­ma­ny IV'

To register for the workshop, please send a short message to Benjamin Hinrichs.

For directions to Paderborn University and a campus map, see this page. The workshop will take place on the third floor of building H.

The conference lunch takes place at Gasthaus Haxterpark, which is only a short walk away from the university.

Location: Room H3.203 @ Paderborn University

9.30 - 10.15 Welcome & Coffee

10.15 - 11.05 Dirk-André Deckert (München)

11.15 - 12.05 Christian Lejsek (Jena)

12.30 - 13.45 Lunch @ Haxterpark

14.00 - 14.50 Sören Petrat (Bremen)

15.00 - 15.50 Sorour Karimi Dehbokri (Braunschweig, online)

16.00 - 16.30 Coffee Break

16.30 - 17.20 Sascha Lill (Milan)

Dirk-André Deckert: Vacuum polarisation without infinities

I will present an approach to construct the polarisation current of the quantum vacuum in an external electromagnetic field. Up to one remaining degree of freedom of a real number, I will demonstrate key points how to extract the well-known second order term without ill-defined terms from beginning to end. This is a joint work with Franz Merkl and Markus Nöth.

Sorour Karimi Dehbroki: Convergent Renormalization Group Flow of Spectral Problems
in Quantum Field Theory

The renormalization group (RG) method based on the isospectral Feshbach-Schur map is a powerful tool in the spectral analysis of Hamiltonians in quantum field theory, particularly for nonrelativistic quantum electrodynamics models (Pauli-Fierz Hamiltonians). The renormalization transformation Rρ is defined on a closed subset D of an infinite-dimensional Banach space W of sequences of coupling functions which parametrize the Hamiltonians.

In 2003, a novel operator-theoretic renormalization group method was introduced and applied to analyze a general class of Hamiltonians on Fock space by Bach, Chen, Fröhlich, and Sigal. This served as a demonstration of the potency of the smooth Feshbach map to possess a codimension-1
contractivity property, i.e., the contractivity of Rρ on D up to a single coupling function.

The new result presents in the talk is that, by employing a space of coupling functions with higher regularity, we achieve full contractivity on a closed subset, leading to a unique fixed point. This allows us to characterize the properties of the fixed point precisely.

Christian Lejsek: Analyticity of the Ground State in the Standard Model of  Non-Relativistic QED

In the talk we will give the definition of the standard model of non-relativistic qed. We discuss analyticity in the dilation parameter and the coupling constant of the ground state in this model. For the result we introduce a so called generalized Pauli-Fierz transformation, which allows us to apply operator theoretic renormalization as introduced in "Smooth Feshbach map and operator-theoretic renormalization group methods" by Bach, Chen, Fröhlich and Sigal. This is joint work with D. Hasler.

Sascha Lill: Recent Progress on the Momentum Distribution of a Fermi Gas

We consider a fermionic gas, both in the mean-field and in the dilute regime. The momentum  distribution of this system gives full information about its 2-point correlation function at equal times and thus about the presence of quasiparticles as postulated by Fermi liquid theory.

We present recent progress on the establishment of conjectures for the momentum distribution via bosonization techniques. Our proofs hold for trial states, that are energetically close to the ground state, and reveal a discontinuity of the momentum distribution at the Fermi surface, which is in agreement with Fermi liquid theory.

The talk is based on joint work with N. Benedikter, E. L. Giacomelli, A. B. Lauritsen and D. Naidu.

Sören Petrat: Asymptotic Expansions in Bosonic Mean-field Limits

The mean-field limit for bosonic quantum systems has long served as a simple model in which interesting physical effects such as Bose-Einstein condensation can be studied. Recently, we have studied asymptotic expansions in this framework, which are expansions in a small parameter such as the inverse particle number. In this presentation I would like to give an overview over recent progress in proving such expansions. In earlier works we proved them for zero temperature for low-lying eigenvalues and eigenstates of the Hamiltonian, and for the dynamics. These results imply Edgeworth expansions for expectation values of certain operators, expansions for the binding energy of the ground state, and for the interaction energy of quasi-particles. Furthermore, we have proven a result for the Bose-Hubbard model on a finite graph in a coupled limit of infinite temperature and weak interaction.