1D Particle, 1D Field, 1D Interaction. Simple Exactly Solvable Models based on Finite Rank Perturbations Methods. III. Linear Friction as Radiation Reaction

Abstract

This paper is an electronic application to my set of lectures, subject:`Formal methods in solving differential equations and constructing models of physical phenomena'. Addressed, mainly: postgraduates and related readers. Content: a discussion of the simple models of linear friction, the models, that have the mechanism that is based on radiation reaction. The interactions we will deal are based on equation arrays of the kind: d^2 q(t)/dt^2 =-\Omega^2 q(t)+f_{compl}(t,q,Q), d^2 u(t,x)/dt^2=c^{2}d^2 u(t,x)/dx^2 -4{\gamma}c\delta(x-x_0) F_{src}(t,q,Q) +f_1(t,x), Q(t) = <l(t)|u> >. Central mathematical points: d'Alembert-Kirchhoff-like formulae. Central physical points: phenomena of Radiation Reaction, Braking Radiation and Friction.