Hermitian structure for the linearized Vlasov-Poisson and Vlasov-Maxwell equations

Abstract

The linearized Vlasov-Poisson and Vlasov-Maxwell equations are shown to have a structure closely related to the evolution equation of quantum mechanics, in terms of a nonstandard Hilbert space. This Hermitian structure yields information about spectral properties, as well as a theory for dynamical invariants. We find accordingly how certain well-known features of the spectrum generalize to the nonuniform case, and we also rederive a recently found exact dynamical invariant in a very natural and simple way.