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Semi-Classical Dynamics in Quantum Spin Systems

Fröhlich, Jürg ; Knowles, Antti ; Lenzmann, Enno

In: Letters in Mathematical Physics, 2007, vol. 82, no. 2-3, p. 275-296

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    Title
    • Semi-Classical Dynamics in Quantum Spin Systems
    Author
    • Fröhlich, Jürg. Institute of Theoretical Physics, ETH Hönggerberg, 8093, Zürich, Switzerland
    • Knowles, Antti. Institute of Theoretical Physics, ETH Hönggerberg, 8093, Zürich, Switzerland
    • Lenzmann, Enno. Department of Mathematics, Massachusetts Institute of Technology, 02139-4307, Cambridge, MA, USA
    Document Type
    • Postprint
    Language
    • English
    Published in
    • Letters in Mathematical Physics, 2007, vol. 82, no. 2-3, p. 275-296. Springer Netherlands
    Other Version
    OAI-PMH Identifier
    • oai:doc.rero.ch:315135
    Summary
    We consider two limiting regimes, the large-spin and the mean-field limit, for the dynamical evolution of quantum spin systems. We prove that, in these limits, the time evolution of a class of quantum spin systems is determined by a corresponding Hamiltonian dynamics of classical spins. This result can be viewed as a Egorov-type theorem. We extend our results to the thermodynamic limit of lattice spin systems and continuum domains of infinite size, and we study the time evolution of coherent spin states in these limiting regimes