Casimir companion: An invariant of motion for Hamiltonian systems
Frank Boldt, James D. Nulton, Bjarne Andresen, Peter Salamon, and Karl Heinz Hoffmann
Accepted
In this paper a new invariant of motion for Hamiltonian systems is introduced: the Casimir companion. For systems with simple dynamical algebras (e.g., coupled spins, harmonic oscillators) our new invariant is useful in problems that consider adiabatically varying the parameters in the Hamiltonian. In particular, it has proved useful in optimal control of changes in these parameters. The Casimir companion also allows simple calculation of the entropy of non-equilibrium ensembles.