Publications

My research is mainly centered around the study of functional equations and partial differential equations of quantum physics. Motivated from the need of theoretical foundations and practical efficiency, a major theme in my research work is the derivation of effective macroscopic equations from microscopic theories. Two current projects that I am working on are the derivation of Ginzburg-Landau equations from the Bogolubov-de Gennes equation and the derivation of Maxwell's equations from the density function theory.

Note: I publish under the pen name Ilias Chenn while my legal name is Li Chen. Though my earliest preprints are under the name Li Chen.

In preparation

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• I. Chenn, R. L, Frank, C. Hainzl, I. M. Sigal, (2018) Microscopic Derivation of the Ginzburg-Landau equations.
• I. Chenn, I. M. Sigal, (2018) Macroscopic Electrostatics at Positive Temperature from the Density Functional Theory.
• I. Chenn, I. M. Sigal, (2017) On the Bogoliubov-de Gennes Equations. (In preparation and pending update.)

Preprints

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• I. Chenn, I. M. Sigal, (2018) On Effective PDEs of Quantum Physics. To appear in the Proceedings of the 11th ISAAC 2017, Birkhäuser series "Trends in Mathematics, Research Perspectives".

Journal Publications

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• I. Chenn, G. Fournodavlos, I. M. Sigal, (2018) The Effective Dynamics of the Volume Preserving Mean Curvature Flow. Journal of Statistical Physics. July 2018, Volume 172, Issue 2, pp 458 - 476 [PDF]
• I. Chenn, P. Smyrnelis, I. M. Sigal, (2018) On Abrikosov Lattice Solutions of the Ginzburg-Landau Equations. Mathematical Physics, Analysis and Geometry. March 2018, 21:7 [arXiv:1701.06076] [PDF]