Bitte benutzen Sie diese Referenz, um auf diese Ressource zu verweisen:
Volltext verfügbar? / Dokumentlieferung
doi:10.22028/D291-44524
Titel: | Singular Euler–Maclaurin expansion on multidimensional lattices |
VerfasserIn: | Buchheit, Andreas A. Keßler, Torsten |
Sprache: | Englisch |
Titel: | Nonlinearity |
Bandnummer: | 35 |
Heft: | 7 |
Verlag/Plattform: | IOP Publishing |
Erscheinungsjahr: | 2022 |
DDC-Sachgruppe: | 510 Mathematik |
Dokumenttyp: | Journalartikel / Zeitschriftenartikel |
Abstract: | 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 expansion order for band-limited functions and that the runtime is independent of the number of particles. First, the EM summation formula is generalised to lattices in higher dimensions, assuming a sufficiently regular summand function. We then develop this new expansion further and construct the singular Euler–Maclaurin expansion in higher dimensions, an extension of our previous work in one dimension, which remains applicable and useful even if the summand function includes a singular function factor. We connect our method to analytical number theory and show that all operator coefficients can be efficiently computed from derivatives of the Epstein zeta function. Finally we demonstrate the numerical performance of the expansion and efficiently compute singular lattice sums in infinite two-dimensional lattices, which are of relevance in condensed matter, statistical, and quantum physics. An implementation in mathematica is provided online along with this article. |
DOI der Erstveröffentlichung: | 10.1088/1361-6544/ac73d0 |
URL der Erstveröffentlichung: | https://iopscience.iop.org/article/10.1088/1361-6544/ac73d0 |
Link zu diesem Datensatz: | urn:nbn:de:bsz:291--ds-445248 hdl:20.500.11880/39736 http://dx.doi.org/10.22028/D291-44524 |
ISSN: | 1361-6544 0951-7715 |
Datum des Eintrags: | 27-Feb-2025 |
Fakultät: | MI - Fakultät für Mathematik und Informatik |
Fachrichtung: | MI - Mathematik |
Professur: | MI - Prof. Dr. Sergej Rjasanow |
Sammlung: | SciDok - Der Wissenschaftsserver der Universität des Saarlandes |
Dateien zu diesem Datensatz:
Es gibt keine Dateien zu dieser Ressource.
Alle Ressourcen in diesem Repository sind urheberrechtlich geschützt.