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Classical non-linear waves in dispersive nonlocal media, and the theory of superfluidity

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  • Putterman, S.J.
  • Roberts, P.H.

Abstract

The solution to nonlocal dispersive classical hydrodynamics is investigated at the fourth order of nonlinearity. At this order an extra degree of freedom appears as a result of the additive conservation of wave number in the interaction of beams of sound waves, and represents a broken symmetry. The resulting equations of motion for the background plus a distribution of sound waves are the Landau two-fluid hydrodynamics of 4He with dispersion at higher frequencies. Reasonable choices for the energy as a functional of density lead to phonon-roton type spectra. The normal fluid flow can thus be viewed either as the Stokes drift of the acoustic field or as the fluctuations of the macroscopic equations of motion of the ground state. In the case of normal dispersion the sound wave interaction is at least sixth order in the nonlinearity, and the appropriate solutions are presented. The general conclusions are unchanged though transport phenomena will be dramatically affected.

Suggested Citation

  • Putterman, S.J. & Roberts, P.H., 1983. "Classical non-linear waves in dispersive nonlocal media, and the theory of superfluidity," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 117(2), pages 369-397.
    • Handle: RePEc:eee:phsmap:v:117:y:1983:i:2:p:369-397
    DOI: 10.1016/0378-4371(83)90122-X
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