Koopman wavefunctions and Clebsch variables in VlasovMaxwell kinetic theory
Abstract
Motivated by recent discussions on the possible role of quantum computation in plasma simulations, here, we present different approaches to Koopman's Hilbertspace formulation of classical mechanics in the context of VlasovMaxwell kinetic theory. The celebrated Koopmanvon Neumann construction is provided with two different Hamiltonian structures: one is canonical and recovers the usual Clebsch representation of the Vlasov density, the other is noncanonical and appears to overcome certain issues emerging in the canonical formalism. Furthermore, the canonical structure is restored for a variant of the Koopmanvon Neumann construction that carries a different phase dynamics. Going back to van Hove's prequantum theory, the corresponding Koopmanvan Hove equation provides an alternative Clebsch representation which is then coupled to the electromagnetic fields. Finally, the role of gauge transformations in the new context is discussed in detail.
 Publication:

Journal of Plasma Physics
 Pub Date:
 August 2021
 DOI:
 10.1017/S0022377821000805
 arXiv:
 arXiv:2105.00294
 Bibcode:
 2021JPlPh..87d8302T
 Keywords:

 plasma nonlinear phenomena;
 plasma simulation;
 Physics  Plasma Physics;
 Mathematical Physics;
 Quantum Physics
 EPrint:
 20 pages