A mathematical formulation of the random phase approximation for crystals

Abstract

This works extends the recent study on the dielectric permittivity of crystals within the Hartree model [E. Cances and M. Lewin, Arch. Rational Mech. Anal., 197 (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.

References in corpus (1)

• A new approach to the modelling of local defects in crystals: the reduced Hartree-Fock case

Cited by in corpus (10)

• The Hartree equation for infinitely many particles. I. Well-posedness theory
• A mathematical analysis of the GW0 method for computing electronic excited energies of molecules
• On Derivation of the Poisson-Boltzmann Equation
• On linear stability of crystals in the Schroedinger-Poisson model
• On orbital stability of ground states for finite crystals in fermionic Schrödinger--Poisson model
• On stability of ground states for finite crystals in the Schroedinger-Poisson model
• A mathematical analysis of the adiabatic Dyson equation from time-dependent density functional theory
• Mean--field stability for the junction of quasi 1D systems with Coulomb interactions
• The reduced Hartree-Fock model with self-generated magnetic fields
• On the dispersion decay for crystals in the linearized Schrödinger-Poisson model