5 papers
Computation of anisotropic singular sums from high-order derivatives of Epstein zeta functions
Andreas A. Buchheit, Jonathan K. Busse
The precise and efficient evaluation of large-scale lattice sums involving power-law kernels is a fundamental computational problem in the simulation of classical and quantum syste…
Zeta expansion for long-range interactions under periodic boundary conditions with applications to micromagnetics
Andreas A. Buchheit, Jonathan K. Busse, Torsten Keßler +1
We address the efficient computation of power-law-based interaction potentials of homogeneous -dimensional bodies with an infinite -dimensional array of copies, including the…
Exact lattice summations for Lennard-Jones potentials coupled to a three-body Axilrod-Teller-Muto term applied to cuboidal phase transitions
Andres Robles-Navarro, Shaun Cooper, Andreas A. Buchheit +4
This work provides a rigorous analysis of Bain-type cuboidal lattice transformations, which connect the face-centered cubic (fcc), mean-centered cubic (mcc), body-centered cubic (b…
Epstein zeta method for many-body lattice sums
Andreas A. Buchheit, Jonathan K. Busse
Many-body interactions arise naturally in the perturbative treatment of classical and quantum many-body systems and play a crucial role in the description of condensed matter syste…
Computation and properties of the Epstein zeta function with applications to quantum systems
Andreas A. Buchheit, Jonathan Busse, Ruben Gutendorf
The Epstein zeta function generalises the classical Riemann zeta function to oscillatory lattice sums in higher dimensions and has recently emerged as a key tool in the simulation…