Regensburg 2019 – wissenschaftliches Programm

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KFM: Fachverband Kristalline Festkörper und deren Mikrostruktur

KFM 3: Dielectric, Elastic and Electromechanical Properties

KFM 3.3: Vortrag

Montag, 1. April 2019, 10:30–10:50, PHY 5.0.21

Nonlocal Electrostatics: Lorentzian Kernels or Gradient Theories? — •Jakob Leck — Institut für Festkörperphysik, Technische Universität Darmstadt, Hochschulstraße 6, 64289 Darmstadt

Nonlocal electrostatics is a continuum theory to be used on small length scales when effects of spatial dispersion become relevant. A common ansatz for the kernel in the nonlocal material law is the so-called Fourier-Lorentzian-model, a sum of a local term and the Green function of a Helmholtz-type operator. This leads to a fourth order differential equation for the potential. A different approach consists in a moment expansion of the material law, which leads to a gradient theory, implying similar equations for the potential. In this talk both approaches are compared and it is argued that the gradient theory is to be preferred because it does not require ad hoc assumptions about the kernel. The gradient theory is discussed up to second order and leads to a modified and non-singular near field behaviour in potentials and fields of point charges.