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A Macroscopic System with Undamped Periodic Compressional Oscillations

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Abstract

A class of macroscopic systems is described which have the remarkable feature that they can sustain undamped compressional radial oscillations. They consist of an arbitrary number of particles confined by a harmonic potential and interacting among themselves through conservative forces scaling as the inverse cube of distances. The radial oscillation leads to a variation of the thermodynamic quantities characterizing the system. The system therefore does not approach equilibrium, since the (macroscopic) amplitude of the oscillation does not decrease as time goes to infinity. The oscillation is harmonic and isochronous, that is, its frequency is fixed and independent of the initial condition. These results hold independently of the dimension of the system and are also valid in the quantal context.

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Acknowledgements

We wish to acknowledge with thanks the hospitality, extended many times, to one of us (F.C.) by the Centro Internacional de Ciencias (CIC) in Cuernavaca, and to the other one of us (F.L.) by the Physics Department of the University of Rome “La Sapienza” (including a two-week visit in May 2010, when the main results reported in this paper were obtained). This paper was completed during the Scientific Gathering on “Integrable systems—continuous and discrete—and the transition to chaos” hosted by CIC in November-December 2012. FL also wishes to acknowledge the financial support of the following projects: Proyecto de profesores asistentes of the Departamento de Física of the Universidad de los Andes as well as Projects CONACyT 44020 and UNAM–DGAPA–PAPIIT IN113311.

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Authors and Affiliations

  1. Dipartimento di Fisica, Università di Roma “La Sapienza”, Rome, Italy

    F. Calogero

  2. Istituto Nazionale di Fisica Nucleare, Sezione di Roma, Rome, Italy

    F. Calogero

  3. Instituto de Ciencias Físicas, UNAM, Cuernavaca, Mexico

    F. Leyvraz

  4. Centro Internacional de Ciencias, Cuernavaca, Mexico

    F. Leyvraz

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  1. F. Calogero
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  2. F. Leyvraz
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Correspondence to F. Leyvraz.

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Calogero, F., Leyvraz, F. A Macroscopic System with Undamped Periodic Compressional Oscillations. J Stat Phys 151, 922–937 (2013). https://doi.org/10.1007/s10955-013-0741-9

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  • DOI: https://doi.org/10.1007/s10955-013-0741-9

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