Huajie Chen, Christoph Ortner, and Jack Thomas. Locality of interatomic forces in tight binding models for insulators. ESAIM: Math. Model. Num., to appear. [doi | arXiv | abstract]

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.

Christoph Ortner and Jack Thomas. Point defects in tight binding models for insulators. ArXiv e-prints, 2004.05356, 2020. [arXiv | abstract]

We consider atomistic geometry relaxation in the context of linear tight binding models for point defects. A limiting model as Fermi-temperature is sent to zero is formulated, and an exponential rate of convergence for the nuclei configuration is established. We also formulate the thermodynamic limit model at zero Fermi-temperature, extending the results of [H. Chen, J. Lu, C. Ortner. Arch. Ration. Mech. Anal., 2018]. We discuss the non-trivial relationship between taking zero temperature and thermodynamic limits in the finite Fermi-temperature models.

Jack Thomas. Locality of interatomic interactions in self-consistent tight binding models. ArXiv e-prints, 2004.09323, 2020. [arXiv | abstract]

A key starting assumption in many classical interatomic potential models for materials is a site energy decomposition of the potential energy surface into contributions that only depend on a small neighbourhood. Under a natural stability condition, we construct such a spatial decomposition for self-consistent tight binding models, extending recent results for linear tight binding models to the non-linear setting.

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 - present: PhD in Mathematics and Statistics, University of Warwick

Sept 2017 - Aug 2018: MSc in Mathematics and Statistics, University of Warwick

Sept 2013 - Jun 2017: MMath in Mathematics, University of Warwick

Past Projects:

Aug 2018. MSc thesis: Analysis of the Tight Binding Model (Supervised by Prof. Christoph Ortner)

Postponed TBC. Optimality in Mathematical Modelling at Warwick (OPTIM@warwick), University of Warwick. Organised by the SIAM-IMA Warwick student chapter - if you would like to attend, please get in touch!

"Lockdown Lectures" (online conferences / seminars / lectures due to COVID-19):

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)

Associate Member of the Institute of Matematics and its Applications (IMA)

Graduate student member of the Society for Industrial and Applied Mathematics (SIAM)

Statistics, Probability, Analysis & Applied Mathematics (SPAAM) student seminar series organiser - if you would like to give a talk (or know someone that might) let me know!