Sören Sanders // University of Oldenburg

Online databases

orcid.org/0000-0003-3933-4588

Sample publications

[article] bibtex | Go to document
S. Sanders and M. Holthaus, "Hypergeometric continuation of divergent perturbation series: I. Critical exponents of the Bose–Hubbard model" New Journal of Physics, vol. 19, iss. 10, p. 103036.
@article{Sanders_2017a, author = {Sören Sanders and Martin Holthaus}, title = {{Hypergeometric continuation of divergent perturbation series: I. Critical exponents of the Bose–Hubbard model}}, journal = {New Journal of Physics}, volume = {19}, number = {10}, pages = {103036}, url = {http://stacks.iop.org/1367-2630/19/i=10/a=103036}, year={2017}, abstract={We study the connection between the exponent of the order parameter of the Mott insulator-to-superfluid transition occurring in the two-dimensional Bose–Hubbard model, and the divergence exponents of its one- and two-particle correlation functions. We find that at the multicritical points all divergence exponents are related to each other, allowing us to express the critical exponent in terms of one single divergence exponent. This approach correctly reproduces the critical exponent of the three-dimensional XY universality class. Because divergence exponents can be computed in an efficient manner by hypergeometric analytic continuation, our strategy is applicable to a wide class of systems.} }
[article] bibtex | Go to document
S. Sanders and M. Holthaus, "Hypergeometric continuation of divergent perturbation series: II. Comparison with Shanks transformation and Padé approximation" Journal of Physics A: Mathematical and Theoretical, vol. 50, iss. 46, p. 465302.
@article{Sanders_2017b, author = {Sören Sanders and Martin Holthaus}, title = {{Hypergeometric continuation of divergent perturbation series: II. Comparison with Shanks transformation and Padé approximation}}, journal = {Journal of Physics A: Mathematical and Theoretical}, volume = {50}, number = {46}, pages = {465302}, url = {http://stacks.iop.org/1751-8121/50/i=46/a=465302}, year = {2017}, abstract = {We explore in detail how analytic continuation of divergent perturbation series by generalized hypergeometric functions is achieved in practice. Using the example of strong-coupling perturbation series provided by the two-dimensional Bose–Hubbard model, we compare hypergeometric continuation to Shanks and Padé techniques, and demonstrate that the former yields a powerful, efficient and reliable alternative for computing the phase diagram of the Mott insulator-to-superfluid transition. In contrast to Shanks transformations and Padé approximations, hypergeometric continuation also allows us to determine the exponents which characterize the divergence of correlation functions at the transition points. Therefore, hypergeometric continuation constitutes a promising tool for the study of quantum phase transitions.}

Ph.D. Thesis

[phdthesis] bibtex
S. Sanders, "Hypergeometric analytic continuation: A novel approach to the quantum phase transition from a Mott insulator to a superfluid" PhD Thesis , 2018.
@phdthesis{Sanders_2018, title = {Hypergeometric analytic continuation: A novel approach to the quantum phase transition from a Mott insulator to a superfluid}, author = {Sanders, Sören}, month = {May}, year = {2018}, school = {Carl von Ossietzky Universität Oldenburg}, note = {supervisor: Professor Dr. Martin Holthaus} }

Master/Bachelor Thesis

[mastersthesis] bibtex
S. Sanders, "Reflected Brownian Motion and Local Time" Master's Dissertation , 2012.
@mastersthesis{Sanders_2012, title = {{Reflected Brownian Motion and Local Time}}, author = {Sanders, Sören}, month = {June}, year = {2012}, school = {TU Kaiserslautern}, note = {supervisor: Professor Dr. Jörn Saß} }

Talks

Analytical Continuation of Perturbation Series in the Context of Phase Transitions,
DPG Spring meeting,
March 2016, Regensburg, Germany

Hypergeometric Extrapolation of the Strong Coupling Perturbation Series of the Bose-Hubbard model in 2d,
DPG Spring meeting,
March 2015, Berlin, Germany

Posters

Sören Sanders and Christoph Heinisch: Dimensional Crossover of the Phase Diagram within a Layered Bose-Hubbard System, Frontiers of Condensed Matter Summer School in August 2014, San Sebastian, Spain.

Sören Sanders: Critical exponents from a Landau-like approach, DPG Spring Meeting in March 2018, Berlin, Germany.

Teaching

Lectures

Lecture: Preparatory Mathematics Course for Physics Students (German) (Winter 2016/2017)
Lecture: Preparatory Mathematics Course for Physics Students (German) (Winter 2015/2016)

Tutorials

Tutorial to Quantum Structure of Matter (Summer 2018)
Colloquium to the Introduction into Theoretical Physics (Summer 2017)
Tutorial to Mathematical Methods for Physicists (Winter 2016/2017)
Tutorial to the Classical Fields and Particles Lecture (Winter 2014/2015)
Tutorial to the Introduction into Theoretical Physics (Summer 2014)

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Sören Sanders