Mathematical Physics in the Heart of Germany V

Conference at TU Braunschweig,

If you wish to join us for the conference dinner please send an e-mail to i.stoll@tu-bs.de by April 7, 2025.

Jean-Bernard Bru (U of the Basque Country and BCAM):
Impact of Exchange Interactions
- Abstract: In this talk, we will explain the effect of quantum interactions exchanging different types of particles. We will consider a system made of two fermions and one boson, in order to study the effect of such an off-diagonal interaction term, having in mind the physics of cuprate superconductors. We will in particular show the existence of exponentially localized dressed bound fermion pairs. We will give particular attention to the regime of very large on-site (Hubbard) repulsions, because this situation can be relevant for cuprate superconductors.

Jakob Geisler (TU Braunschweig):
New Aspects of the Smooth Feshbach Map and Operator-Theoretic Renormalization Group Methods
- Abstract: Two similar tools in the spectral analysis of operators defined on Hilbert space are revised. The isospectral Feshbach-Schur map and the smooth Feshbach map are introduced and compared. A new symmetry in the smooth Feshbach map is observed and further analyzed for operators defined on Fock space. This observation allows for the first time an operator-theoretic renormalization transformation, based on the smooth Feshbach map, which satisfies a semigroup structure.

David Hasler (U Jena):
Approximating the density of states for Poisson distributed random Schroedinger operators
- Abstract: We consider a Schroedinger operator with random potential distributed according to a Poisson process. We show that expectations of matrix elements of the resolvent as well as the density of states can be approximated to arbitrary precision in powers of the coupling constant. The expansion coefficients are given in terms of expectations obtained by Neumann expanding the potential around the free Laplacian. One can control these expansion coefficients in the infinite volume limit. We show that for this limit the boundary value as the spectral parameter approaches the real axis exists as well. Our results are valid for arbitrary strength of the disorder parameter, including the small disorder regime.

Jens Hoppe (TU Braunschweig):
Orthogonal Polynomials and Quantum Minimal Surfaces

Javier Valentín Martín (U Paderborn):
Ultraviolet renormalization of Spin Boson Models with normal and 2-nilpotent interactions
- Abstract: Spin-Boson Models describe the interaction of a bosonic quantum field with a spin system. In this talk, we will study a generalized version of these models presenting ultraviolet divergences. For normal interactions, we construct a renormalized Hamiltonian via a dressing transformation, while for 2-nilpotent interactions, renormalization is achieved through the use of Interior Boundary Conditions (IBC). In both cases, the domain of the renormalized Hamiltonian is explicit, and the resulting operator can be obtained as the norm (or strong) resolvent limit of regular Hamiltonians. By combining both approaches, we obtain a more general renormalized model that incorporates both interaction types.