Andreas Alexander Buchheit

Andreas Alexander Buchheit
Universität des Saarlandes | UKS · Department of Applied Mathematics

Dr. rer. nat

About

8
Publications
415
Reads
How we measure 'reads'
A 'read' is counted each time someone views a publication summary (such as the title, abstract, and list of authors), clicks on a figure, or views or downloads the full-text. Learn more
20
Citations
Introduction
As a postdoctoral researcher in applied mathematics, I am working on implementing and developing novel mathematical methods and algorithms for solving hard problems, ranging from integer programming problems, with applications to condensed matter systems and workforce scheduling, to the efficient simulation of macroscopic crystals on an atomic level.
Additional affiliations
January 2019 - present
Universität des Saarlandes
Position
  • PhD Student
Description
  • As a PhD student in Applied Mathematics, I am working on implementing and developing novel mathematical methods and algorithms for simulating macroscopic condensed matter systems.
August 2015 - December 2018
Universität des Saarlandes
Position
  • Research Associate
Education
January 2019 - June 2021
Universität des Saarlandes
Field of study
  • Applied Mathematics
October 2013 - June 2015
Universität des Saarlandes
Field of study
  • Theoretical Physics
October 2011 - June 2013
Universität des Saarlandes
Field of study
  • Theoretical Physics

Publications

Publications (8)
Article
We extend the classical Euler–Maclaurin (EM) expansion to sums over multidimensional lattices that involve functions with algebraic singularities. This offers a tool for a precise and fast evaluation of singular sums that appear in multidimensional long-range interacting systems. We find that the approximation error decays exponentially with the ex...
Preprint
Full-text available
Continuum limits are a powerful tool in the study of many-body systems, yet their validity is often unclear when long-range interactions are present. In this work, we rigorously address this issue and put forth an exact representation of long-range interacting lattices that separates the model into a term describing its continuous analogue, the int...
Article
Full-text available
We develop a new expansion for representing singular sums in terms of integrals and vice versa. This method provides a powerful tool for the efficient computation of large singular sums that appear in long-range interacting systems in condensed matter and quantum physics. It also offers a generalised trapezoidal rule for the precise computation of...
Thesis
This thesis is concerned with the development of the singular Euler–Maclaurin expansion, a novel method that allows for the efficient evaluation of large sums over values of functions with singularities. The method offers an approximation to the sum whose runtime is independent of the number of summands and whose error falls of exponentially with t...
Preprint
Full-text available
We extend the classical Euler-Maclaurin expansion to sums over multidimensional lattices that involve functions with algebraic singularities. This offers a tool for the precise quantification of the effect of microscopic discreteness on macroscopic properties of a system. First, the Euler-Maclaurin summation formula is generalised to lattices in hi...
Preprint
Full-text available
We generalise the Euler-Maclaurin expansion and make it applicable to the product of a differentiable function and an asymptotically smooth singularity. The difference between sum and integral is written as a differential operator acting on the non-singular factor only plus a remainder integral. The singularity can be included in generalised Bernou...
Article
The classical ground state of the Frenkel–Kontorova model is investigated for the case of a globally deformable substrate potential, whose amplitude is a function of the position of all particles. This system serves as an idealised description of a one-dimensional crystal of trapped ions in an optical cavity, where the deformable potential originat...
Article
Full-text available
The progress in high-precision spectroscopy requires one to check the accuracy of theoretical models such as the master equation describing spontaneous emission of atoms. For this purpose, we systematically derive a master equation of an atom interacting with the modes of the electromagnetic field which naturally includes interference in the decay...

Network

Cited By

Projects

Projects (2)
Project
In this project, we generalize the 300-year-old Euler-Maclaurin summation formula to long-range interacting lattices in higher dimensions. Our method provides rigorous analytical insights into the properties of long-range interacting systems and their phase transitions. In addition, it offers an efficient way for computing time evolutions of long-range interacting systems.