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Properties of certain matrices related to the equilibrium configuration of the one-dimensional many-body problems with the pair potentialsV 1(x)=−log ∣sinx∣ andV 2(x)=1/sin2 x

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Abstract

It is shown that at equilibrium certain matrices associated to the one-dimensional many-body problems with the pair potentialsV 1(x)=−log∣sinx∣ andV 2(x)=1/sin2 x have a very simple structure. These matrices are those that characterize the small oscillations of these systems around their equilibrium configurations, and, for the second system, the Lax matrices that demonstrate its integrability.

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Authors and Affiliations

  1. Istituto di Fisica, Università di Roma, I-00185, Roma, Italy

    F. Calogero

  2. Istituto Nazionale di Fisica Nucleare, Sezione di Roma, I-00185, Roma, Italy

    F. Calogero

  3. Institute of Theoretical and Experimental Physics, SU-117259, Moscow, USSR

    A. M. Perelomov

Authors
  1. F. Calogero
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  2. A. M. Perelomov
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Communicated by J. Moser

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Calogero, F., Perelomov, A.M. Properties of certain matrices related to the equilibrium configuration of the one-dimensional many-body problems with the pair potentialsV 1(x)=−log ∣sinx∣ andV 2(x)=1/sin2 x . Commun.Math. Phys. 59, 109–116 (1978). https://doi.org/10.1007/BF01614245

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  • DOI: https://doi.org/10.1007/BF01614245

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