Jonathan K. Busse

Jonathan K. Busse

he / him

I am a PhD Candidate at the German Aerospace Center (DLR), specializing in long-range interacting classical and quantum systems

Talks and presentations

Zeta Expansion for Long-Range Interacting Classical and Quantum Lattices

November 27, 2025

Seminar presentation, Oberseminar Mathematik, Universität des Saarlandes, Saarbrücken, Germany

Large singular sums play a central role in many areas of pure and applied mathematics and arise prominently in the simulation of classical and quantum systems with long-range interactions. In this talk, I present a collection of numerical methods, based on generalized zeta functions and their derivatives, that enable the efficient and precise simulation of long-range interacting lattice models in previously inaccessible parameter regimes. The Epstein zeta function, a higher-dimensional analogue of the Riemann zeta function that describes oscillatory lattice sums, has recently become an indispensable tool in the numerical treatment of long-range interacting many-body systems.

Zeta Expansion for Long-Range Interactions under Periodic Boundary Conditions with Applications to Micromagnetics

October 02, 2025

Seminar presentation, Seminar für Angewandte Mathematik, ETH Zürich, Zürich, Switzerland

Seminar presentation on the efficient computation of power-law-based interaction potentials in micromagnetics under periodic boundary conditions. The talk addresses the challenge of computing infinite lattice sums for dipolar interactions and generalized Riesz power-law potentials in arbitrary cuboidal domains. We present a method that achieves machine precision by complementing direct summation with correction terms, with exponential convergence and negligible additional computational cost compared to the truncated summation scheme. The approach includes a superexponentially convergent algorithm in terms of generalized zeta functions which requires special functions such as incomplete Bessel functions.

Computation and properties of the Epstein zeta function: Application and numerical challenges

August 23, 2024

Conference talk, SiQuMa24 Conference on Simulation of Quantum Matter, Schloss Dagstuhl

The Epstein zeta function generalizes the Riemann zeta function to oscillatory lattice sums in higher dimensions. Beyond its numerous applications in pure mathematics, it has recently been identified as a key component in simulating exotic quantum materials. In this work, we derive a compact and efficiently computable representation of the Epstein zeta function and examine its analytical properties across all arguments. We introduce a superexponentially convergent algorithm, including error bounds, for computing the Epstein zeta function in arbitrary dimensions. To facilitate the computation of integrals involving the Epstein zeta function, we decompose it into a power-law singularity and a regularized Epstein zeta function, which is analytic in the first Brillouin zone. We present the first implementation of the Epstein zeta function and its regularization for arbitrary real arguments in EpsteinLib, a high-performance C library with Python bindings, and rigorously benchmark its precision and performance against known formulas, achieving full precision across the entire parameter range. Finally, we apply our library to the computation of Casimir energies in multidimensional geometries.