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Selfadjointness of the Liouville operator for infinite classical systems

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Abstract

We study some properties of the time evolution of an infinite one dimensional hard cores system with singular two body interaction. We show that the Liouville operator is essentially antiselfadjoint on the algebra of local observables. Some consequences of this result are also discussed.

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Authors and Affiliations

  1. Istituto Matematico Università di Camerino, I-Camerino (MC), Italy

    C. Marchioro & M. Pulvirenti

  2. Instituto Matematico Università di Roma, I-Roma, Italy

    A. Pellegrinotti

  3. Istituto Matematico della Facoltà di Ingegneria di Ancona, I-Ancona, Italy

    A. Pellegrinotti

Authors
  1. C. Marchioro
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  2. A. Pellegrinotti
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  3. M. Pulvirenti
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Additional information

Communicated by J. L. Lebowitz

Research partially supported by the Consiglio Nazionale delle Ricerche, G.N.F.M.

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Marchioro, C., Pellegrinotti, A. & Pulvirenti, M. Selfadjointness of the Liouville operator for infinite classical systems. Commun.Math. Phys. 58, 113–129 (1978). https://doi.org/10.1007/BF01609415

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  • DOI: https://doi.org/10.1007/BF01609415

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