Publications

You can also find my articles on my Google Scholar profile.

Journal Articles

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

Published in Journal of Computational Physics, 2026

This paper addresses the efficient computation of power-law-based interaction potentials of homogeneous n-dimensional bodies with an infinite d-dimensional array of copies, including their higher-order derivatives.

Recommended citation: Buchheit, A. A., Busse, J. K., Keßler, T., & Rybakov, F. N. (2026). "Zeta Expansion for Long-Range Interactions under Periodic Boundary Conditions with Applications to Micromagnetics." Journal of Computational Physics, 114885. DOI: 10.1016/j.jcp.2026.114885
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Exact lattice summations for Lennard-Jones potentials coupled to a three-body Axilrod-Teller-Muto term applied to cuboidal phase transitions

Published in Journal of Chemical Physics, 2025

This paper provides a rigorous analysis of Bain-type cuboidal lattice transformations, incorporating a general (n,m) Lennard-Jones two-body potential and a long-range repulsive Axilrod-Teller-Muto (ATM) three-body potential.

Recommended citation: Robles-Navarro, A., Cooper, S., Buchheit, A. A., Busse, J. K., Burrows, A., Smits, O., & Schwerdtfeger, P. (2025). "Exact lattice summations for Lennard-Jones potentials coupled to a three-body Axilrod-Teller-Muto term applied to cuboidal phase transitions." J. Chem. Phys. 163, 094104. DOI: 10.1063/5.0276677
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Preprints

Epstein zeta method for many-body lattice sums

Published in arXiv, 2025

This paper presents an efficiently computable representation of many-body lattice sums in terms of singular integrals over products of Epstein zeta functions.

Recommended citation: Buchheit, A. A., & Busse, J. K. (2025). "Epstein zeta method for many-body lattice sums." arXiv preprint arXiv:2504.11989.
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Computation and properties of the Epstein zeta function with high-performance implementation in EpsteinLib

Published in arXiv, 2024

This paper establishes the Epstein zeta function as a powerful tool in numerical analysis by rigorously investigating its analytical properties and enabling its efficient computation.

Recommended citation: Buchheit, A. A., Busse, J., & Gutendorf, R. (2024). "Computation and properties of the Epstein zeta function with high-performance implementation in EpsteinLib." arXiv preprint arXiv:2412.16317.
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Software

EpsteinLib: Fast and Efficient Computation of the Epstein Zeta Function

Published in GitHub, 2024

EpsteinLib is a C library and Python package for fast and efficient computation of the Epstein zeta function for arbitrary multidimensional lattices.

Recommended citation: Buchheit, A. A., Busse, J., Gutendorf, R., & Schmitz, J. (2024). EpsteinLib: Fast and Efficient Computation of the Epstein Zeta Function. GitHub. https://github.com/epsteinlib/epsteinlib
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Jonathan K. Busse