Published in Numerische Mathematik, 2026
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. (2026). "Epstein zeta method for many-body lattice sums." Numerische Mathematik. DOI: 10.1007/s00211-026-01558-y
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Published in IMA Journal of Numerical Analysis, 2026
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. K., & Gutendorf, R. (2026). "Computation and properties of the Epstein zeta function with applications to quantum systems." IMA Journal of Numerical Analysis, drag057. DOI: 10.1093/imanum/drag057
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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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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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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. github.com/epsteinlib
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