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Quantum-Classical Modeling of Chemical Phenomena

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Dynamics of interacting electrons

Xu Yang

Princeton

Abstract:   We study the dynamics of interacting electrons in crystals based on the time dependent density functional theory, and aim at possible applications in nano-optics and semi conductor modeling. On one hand, we looked at the Thomas-Fermi model coupled with microscopic Maxwell system which could be used in describing the many body quantum effects in surface plasmon polariton. On the other, we studied the electron dynamics in semiconductor using the Hartree-Fock model, and mainly focused on the case of many electrons interacted through Coulomb potentials. There have been two different time regimes corresponding to two different homogenized systems. For the high frequency regime (short time dynamics), we obtained an effective dynamic dielectric response system; for the low frequency regime (long time dynamics), we obtain effective transport-type equations.

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