We are organizing a little workshop together with the groups of Benjamin Hinrichs (Paderborn) and Lea Boßmann (FAU Mathematik), centered on the mathematics of quantum systems and applications. This is the second edition of the Erlangen–Paderborn mini-workshop first held in Paderborn last year. The workshop will take place on 22 May 2026 in Villa Jordan, close to the venue of the famous Erlanger Bergkirchweih. Everyone is invited to join—please let us know by filling the form below by 18 May 2026 at latest.

Book of abstracts

Irregular regularizations of Jacobi operators
Felix Fischer (FAU, Physik)

We study a family of Jacobi operators in which the diagonal entries are multiplied by a coupling parameter λ>0. Under suitable conditions, the operator is self-adjoint for every λ, while the formal limit at λ=0 is a symmetric Jacobi operator admitting a one-parameter family of self-adjoint extensions. A central ingredient of our analysis is a detailed study of square-summable generalized eigenvectors in the small-λ regime, which combines discrete WKB methods with Airy-function asymptotics. Using these estimates, we analyze the limiting behavior λ→0 in the strong resolvent sense, proving that for every sequence converging to zero one can extract a subsequence along which the corresponding Jacobi operators converge in the strong resolvent sense to some self-adjoint extension of the limiting operator; conversely, every such extension can be obtained in this way. We call this behavior an essentially singular limit, by analogy with essential singularities in complex analysis.

As an application, we study higher-order squeezing operators arising in quantum optics. Using the connection with Jacobi operators, we show that when the relative strength of the free-field term tends to zero, different self-adjoint extensions of the squeezing operator are selected along different sequences. In particular, this limit does not single out a physically distinguished self-adjoint extension.

Based on arXiv:2605.21355, joint work with D. Burgarth and D. Lonigro.

On the optimal rate of convergence for translation-invariant 1d quantum walks
Pascal Mittenbühler (Paderborn, Mathematik)

We study the convergence rate of translation-invariant discrete-time quantum dynamics on a onedimensional lattice. We prove that the cumulative distributions function of the ballistically scaled position X(t)/t after t steps converges at a rate of t^(−1/3) in the Lévy metric as t→∞. In the special case of step-coin quantum walks with two-dimensional coin space, we recover the same convergence rate for the supremum distance and prove optimality.

The excitation spectrum of Bose gases in the Gross–Pitaevskii regime
Lukas Reichmann (FAU, Mathematik)

I will talk about how to apply a strategy developed by Nam and Triay to prove the low-energy excitation spectrum for Bose gases in the Gross-Pitaevskii regime in the 3-dimensional box with side length 1. This extends previous results by Boccato-Brennecke-Cenatiempo-Schlein and Hainzl-Schlein-Triay to interaction potentials that are not necessarily compactly supported or spherically symmetric. This is based on joint work with A. Triay.

The Floquet–Magnus expansion of unbounded Hamiltonians
Leonhard Richter (FAU, Physik)

The Floquet–Magnus expansion is a widely used tool to derive effective descriptions of time-periodic quantum systems by approximating their dynamics with a time-independent Hamiltonian. However, its standard formulation is, strictly speaking, restricted to bounded Hamiltonians. We extend its definition and analysis to a broad class of time-periodic unbounded Hamiltonians. Our approach is based on an a priori distinct nonperturbative framework for the construction of effective Hamiltonians, which we show to reproduce the Floquet–Magnus expansion. A particular strength of our framework is that it allows us to prove that the resulting effective dynamics approximates the original time evolution propagators to arbitrary order in the high-frequency limit without requiring convergence of the Floquet–Magnus expansion, a condition that is already highly restrictive even in the bounded setting. 

In this talk, I will explain our approach and summarize our main results. In particular, I will illustrate the scope of the method on the quantum Rabi Hamiltonian in the interaction picture, where we recover the rotating-wave approximation and Bloch–Siegert shift at the first two orders. 

Based on joint work with D. Burgarth, R. Hillier, and D. Lonigro.