# A mean-field model for disordered crystals

Date(s) : 02/06/2015   iCal
10 h 00 min - 11 h 00 min

$In this talk, we consider disordered quantum crystals in the reduced Hartree-$
Fock (rHF) framework. The nuclei are supposed to be classical particles arranged
around a reference periodic configuration. We first study crystals with extended defects, such as dislocations or doping in semi-conductors, with nuclear density
$\mu = \mu_{per} + \nu$
where $\mu_{per}$ is a periodic nuclear distribution corresponding to the background
perfect crystal and $\nu$ represents the defect. We next consider a family of nuclear
distributions $\mu(\omega, \cdot)$, where $\omega$ spans a probability space $\Omega$. Under some assumptions
on the nuclear distribution $\mu$, we prove the existence of an electronic
ground state $\gamma$, solution of the rHF equations with short-range Yukawa interaction for both types of systems. We obtain partial results for Coulomb
interacting systems. We also consider the case of crystals with a low concentration
of random defects.

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