Casimir companion: An invariant of motion for Hamiltonian systems

Farnk Boldt; James D. Nulton; Bjarne Bøgeskov Andresen; Peter Salamon; Karl Heinz Hoffmann

doi:10.1103/physreva.87.022116

Casimir companion: An invariant of motion for Hamiltonian systems

Farnk Boldt, James D. Nulton, Bjarne Bøgeskov Andresen, Peter Salamon, Karl Heinz Hoffmann

Condensed Matter Physics

16 Citations (Scopus)

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.

Original language	English
Journal	Physical Review A (Atomic, Molecular and Optical Physics)
Volume	87
Issue number	2
Pages (from-to)	022116
Number of pages	4
ISSN	2469-9926
DOIs	https://doi.org/10.1103/physreva.87.022116
Publication status	Published - 20 Feb 2013

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10.1103/physreva.87.022116

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AU - Boldt, Farnk

AU - Nulton, James D.

AU - Andresen, Bjarne Bøgeskov

AU - Salamon, Peter

AU - Hoffmann, Karl Heinz

PY - 2013/2/20

Y1 - 2013/2/20

N2 - 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.

AB - 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.

U2 - 10.1103/physreva.87.022116

DO - 10.1103/physreva.87.022116

M3 - Journal article

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SP - 022116

JO - Physical Review A (Atomic, Molecular and Optical Physics)

JF - Physical Review A (Atomic, Molecular and Optical Physics)

IS - 2

ER -

Casimir companion: An invariant of motion for Hamiltonian systems

Abstract

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