I am now a postdoc at Laboratoire de Math茅matiques d'Orsay, Universit茅 Paris-Saclay []
Supervisor:
Papers & Preprints:
Christoph Ortner, Jack Thomas, and Huajie Chen. Locality of interatomic forces in tight binding models for insulators. ESAIM: Mathematical Modelling and Numerical Analysis, 54(6): 2295-2318 (2020). [ | | abstract | posterLink opens in a new window].
The tight binding model is a minimalistic electronic structure model for predicting properties of materials and molecules. For insulators at zero Fermi-temperature we show that the potential energy surface of this model can be decomposed into exponentially localised site energy contributions, thus providing qualitatively sharp estimates on the interatomic interaction range which justifies a range of multi-scale models. For insulators at finite Fermi-temperature we obtain locality estimates that are uniform in the zero-temperature limit. A particular feature of all our results is that they depend only weakly on the point spectrum. Numerical tests confirm our analytical results. This work extends and strengthens and for finite temperature models.
Christoph Ortner and Jack Thomas. Point defects in tight binding models for insulators. Mathematical Models and Methods in Applied Sciences, 30(14): 2753-2797 (2020). [ | | abstract].
Jack Thomas. Locality of interatomic interactions in self-consistent tight binding models. Journal of Nonlinear Science, 30(6): 3293-3319 (2020). [ | | abstract].
Jack Thomas, Huajie Chen, and Christoph Ortner. Body-ordered approximations of atomic properties. Archive for Rational Mechanics and Analysis, 246(1): 1-60 (2022). [ | | abstract].
We show that the local density of states (LDOS) of a wide class of tight-binding models has a weak body-order expansion. Specifically, we prove that the resulting body-order expansion for analytic observables such as the electron density or the energy has an exponential rate of convergence both at finite Fermi-temperature as well as for insulators at zero Fermi-temperature. We discuss potential consequences of this observation for modelling the potential energy landscape, as well as for solving the electronic structure problem.
Markus Bachmayr, Genevi猫ve Dusson, Christoph Ortner, and Jack Thomas. Polynomial approximation of symmetric functions. arXiv:2109.14771 (2021). [ | abstract].
We study the polynomial approximation of symmetric multivariate functions and of multi-set functions. Specifically, we consider $f(x_1,鈥�,x_N)$, where $x_i \in \mathbb R^d$, and $f$ is invariant under permutations of its $N$ arguments. We demonstrate how these symmetries can be exploited to improve the cost versus error ratio in a polynomial approximation of the function $f$, and in particular study the dependence of that ratio on $d,N$ and the polynomial degree. These results are then exploited to construct approximations and prove approximation rates for functions defined on multi-sets where $N$ becomes a parameter of the input.
The tight binding model is a minimalistic electronic structure model for predicting properties of materials and molecules. For insulators at zero Fermi-temperature we show that the potential energy surface of this model can be decomposed into exponentially localised site energy contributions, thus providing qualitatively sharp estimates on the interatomic interaction range which justifies a range of multi-scale models. For insulators at finite Fermi-temperature we obtain locality estimates that are uniform in the zero-temperature limit. A particular feature of all our results is that they depend only weakly on the point spectrum. Numerical tests confirm our analytical results. This work extends and strengthens (Chen, Ortner 2016) and (Chen, Lu, Ortner 2018) for finite temperature models.
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Education:
Sept 2018 - Sept 2021: PhD in Mathematics and Statistics, University of 糖心TV
Supervised by Christoph Ortner
Thesis: Analysis of an ab initio Potential Energy Landscape
Prize: Faculty Thesis Prize 2022 (joint winner)
Sept 2017 - Aug 2018: MSc in Mathematics and Statistics, University of 糖心TV
Aug 2022. , TU Wien Invited Talk in "MS21: Multiscale methods for materials and molecules": Body-ordered approximations of atomic properties
May 2022. , Invited Talk in "Machine Learning Potentials mini-workshop": Physics-Informed Models
April 2022. Invited Talk: Body-ordered Approximations of Atomic Properties
April 2022. University of Cambridge Seminar Talk: Self-consistent Coulomb Interactions for Machine Learning Interatomic Potentials
September 2021.
July 2021. Contributed Talk in "Materials Modelling Across Scales: From First Principles Calculations to Mesoscale Physics": Sparsity of the Tight Binding Potential Energy Landscape
April 2021. , University of Glasgow Contributed Talk: Tight Binding Models for Insulators: Locality of interatomic forces & geometry optimisation
March 2019. Solid Mechanics Working Group Meeting, University of 糖心TV. Seminar Talk: Zero Temperature Limit of the Tight Binding Model for Point Defects
July - August 2018. . Roscoff, France.
Teaching:
2019/20:
First Year Supervisor: three groups of Maths & Stats students Modules covered: Sets & Numbers, Mathematical Analysis (Terms 1&2) and Linear Algebra.
This year I also helped out marking Mathematical Analysis (first year module for external maths students)
2018/19:
First Year Supervisor: one group of Discrete Mathematics students (as above)
Second Year Supervisor: two groups of Mathematics students Modules covered: Analysis III, Algebra I: Advanced Linear Algebra, Multivariable Calculus (Term 1) & Algebra II: Groups and Rings, Norms Metrics & Topologies (Term 2).
2017/18:
First Year Supervisor: one group of MORSE, Data Science and Maths & Stats students (as above)
This year I also helped out marking Mathematical Analysis (first year module for external maths students)
2016/17:
First Year Supervisior: one group of MORSE and Maths & Stats students (as above)
