Casimir companion: An invariant of motion for Hamiltonian systems

Frank Boldt, James D. Nulton, Bjarne Andresen, Peter Salamon, and Karl Heinz Hoffmann

Phys. Rev. A 87, 022116 – Published 20 February 2013

Abstract

In this paper an invariant of motion for Hamiltonian systems is introduced: the Casimir companion. For systems with simple dynamical algebras (e.g., coupled spins, harmonic oscillators) our 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 nonequilibrium ensembles.

Received 13 July 2012

DOI:https://doi.org/10.1103/PhysRevA.87.022116

Authors & Affiliations

Frank Boldt^1,*, James D. Nulton^2,†, Bjarne Andresen^3,‡, Peter Salamon^2,§, and Karl Heinz Hoffmann^1,∥

¹Institute of Physics, Chemnitz University of Technology – D-09107 Chemnitz, Germany
²Department of Mathematical Science, San Diego State University, San Diego, California 92182, USA
³Niels Bohr Institute, University of Copenhagen, Universitetsparken 5, DK-2100 Copenhagen Ø, Denmark

^*frank.boldt@physik.tu-chemnitz.de
^†jnulton@mail.sdsu.edu
^‡andresen@nbi.ku.dk
^§salamon@math.sdsu.edu
^∥hoffmann@physik.tu-chemnitz.de

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Vol. 87, Iss. 2 — February 2013

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