کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4604373 1337438 2012 39 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
A mathematical formulation of the random phase approximation for crystals
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات آنالیز ریاضی
پیش نمایش صفحه اول مقاله
A mathematical formulation of the random phase approximation for crystals
چکیده انگلیسی

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.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Annales de l'Institut Henri Poincare (C) Non Linear Analysis - Volume 29, Issue 6, November–December 2012, Pages 887-925