Density matrix interpretation of solutions of Lie-Nambu equations

Abstract

The spectrum of a density matrix $ρ(t)$ is conserved by a Lie-Nambu dynamics if $ρ(t)$ is a self-adjoint and Hilbert-Schmidt solution of a nonlinear triple-bracket equation. This generalizes to arbitrary separable (positive- and indefinite-metric) Hilbert spaces the previous result which was valid for finite-dimensional Hilbert spaces.