کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
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4604373 | 1337438 | 2012 | 39 صفحه PDF | دانلود رایگان |

This works extends the recent study on the dielectric permittivity of crystals within the Hartree model [E. Cancès, M. Lewin, Arch. Ration. Mech. Anal. 197 (1) (2010) 139–177] to the time-dependent setting. In particular, we prove the existence and uniqueness of the nonlinear Hartree dynamics (also called the random phase approximation in the physics literature), in a suitable functional space allowing to describe a local defect embedded in a perfect crystal. We also give a rigorous mathematical definition of the microscopic frequency-dependent polarization matrix, and derive the macroscopic Maxwell–Gauss equation for insulating and semiconducting crystals, from a first order approximation of the nonlinear Hartree model, by means of homogenization arguments.
Journal: Annales de l'Institut Henri Poincare (C) Non Linear Analysis - Volume 29, Issue 6, November–December 2012, Pages 887-925