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Interactions of Phonons and Rotons with Interfaces in Superfluid Helium

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Abstract

We solve the problem of beams of phonons and rotons incident on, and interacting with, solid surfaces. Phonons and rotons are the quasiparticles of superfluid helium and have a unique dispersion curve. The dispersion curve controls the transmission, reflection and mode change of these quasiparticles at the interface with another medium. We develop a non-local hydrodynamic theory in a consistent and unified way. The structure of the solutions in the quantum fluid is discussed. The creation probabilities of all quasiparticles are derived when any one of them is incident on the interface. The dependencies on frequency and angle are analyzed and the backward reflection and refraction for R − rotons are discussed.

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References

  1. R.J. Donnelly, J.A. Donnelly, R.N. Hills, J. Low Temp. Phys. 44, 471–489 (1981)

    Article  ADS  Google Scholar 

  2. A.F.G. Wyatt, N.A. Lockberie, R.A. Sherlock, Phys. Rev. Lett. 33, 1425 (1974)

    Article  ADS  Google Scholar 

  3. M.A.H. Tucker, A.F.G. Wyatt, Science 283, 1150 (1999)

    Article  ADS  Google Scholar 

  4. D.H.S. Smith, A.F.G. Wyatt, Phys. Rev. B 76, 224519 (2007)

    Article  ADS  Google Scholar 

  5. D.H.S. Smith, A.F.G. Wyatt, Phys. Rev. B 79, 144520 (2009)

    Article  ADS  Google Scholar 

  6. I.N. Adamenko, K.E. Nemchenko, V.A. Slipko, A.F.G. Wyatt, Phys. Rev. Lett. 96, 065301 (2006)

    Article  ADS  Google Scholar 

  7. I.N. Adamenko, K.E. Nemchenko, A.V. Zhukov, M.A.H. Tucker, A.F.G. Wyatt, Phys. Rev. Lett 82, 1482 (1999)

    Article  ADS  Google Scholar 

  8. I.N. Adamenko, Yu.A. Kitsenko, K.E. Nemchenko, A.F.G. Wyatt, Phys. Rev. B 80, 014509 (2009)

    Article  ADS  Google Scholar 

  9. I.M. Khalatnikov, An Introduction to the Theory of Superfluidity (Addison-Wesley, New York, 1998)

    Google Scholar 

  10. I.N. Adamenko, I.M. Fuks, Sov. Phys. JETP 32, 1123 (1971). Zh. Eksp. Teor. Fiz. 59 , 2071 (1970) (in Russian)

    ADS  Google Scholar 

  11. I.M. Khalatnikov, I.N. Adamenko, Sov. Phys. JETP 36, 391 (1973). Zh. Eksp. Teor. Fiz. 63, 745 (1972) (in Russian)

    ADS  Google Scholar 

  12. I.M. Gelfgat, E.S. Syrkin, Sov. J. Low Temp. Fiz 4, 69 (1978). Fiz. Nizk. Temp. 4, 141 (1978) (in Russian)

    Google Scholar 

  13. R.P. Feynman, Statistical Mechanics. A Set of Lectures (Benjamin, Reading, 1972)

    Google Scholar 

  14. V.I. Kruglov, M.J. Collet, Phys. Rev. Lett. 87, 185302-1 (2001)

    Article  ADS  Google Scholar 

  15. S. Balibar, AIP Conf. Proc. 850, 18 (2006)

    Article  ADS  Google Scholar 

  16. F.W. Sheard, R.M. Bowley, G.A. Toombs, Phys. Rev. A 8, 3135 (1973)

    Article  ADS  Google Scholar 

  17. L.P. Pitaevskii, Sov. Phys. JETP 4, 439 (1956). Zh. Eksp. Teor. Fiz. 31, 536 (1956) (in Russian)

    Google Scholar 

  18. L. Pitaevskii, S. Stringari, Phys. Rev. B 45, 13133 (1992)

    Article  ADS  Google Scholar 

  19. I.N. Adamenko, K.E. Nemchenko, I.V. Tanatarov, Phys. Rev. B 67, 104513 (2003)

    Article  ADS  Google Scholar 

  20. K.R. Atkins, Phys. Rev. 116, 1339–1343 (1959)

    Article  ADS  Google Scholar 

  21. F. Dalfovo, A. Lastri, L. Pricaupenko, S. Stringari, J. Treiner, Phys. Rev. B 52, 1193–1209 (1995)

    Article  ADS  Google Scholar 

  22. G.B. Whitham, Linear and Nonlinear Waves (Wiley, New York, 1974)

    MATH  Google Scholar 

  23. I.N. Adamenko, K.E. Nemchenko, I.V. Tanatarov, J. Low Temp. Phys. 1381/2, 397 (2005)

    Article  ADS  Google Scholar 

  24. I.N. Adamenko, K.E. Nemchenko, I.V. Tanatarov, Low Temp. Phys. 32, 187 (2006). Fiz. Nizk. Temp. 32, 255 (2006) (in Russian)

    Article  ADS  Google Scholar 

  25. I.N. Adamenko, K.E. Nemchenko, I.V. Tanatarov, J. Low Temp. Phys. 1441–3, 13 (2006)

    Article  ADS  Google Scholar 

  26. I.N. Adamenko, K.E. Nemchenko, I.V. Tanatarov, Phys. Rev. B 77, 174510 (2008)

    Article  ADS  Google Scholar 

  27. I.N. Adamenko, K.E. Nemchenko, I.V. Tanatarov, J. Phys.: Conf. Ser. 150(3), 032107 (2009)

    Article  ADS  Google Scholar 

  28. L.D. Landau, E.M. Lifshitz, Fluid Mechanics Course of Theoretical Physics, vol. 6 (Pergamon Press, London, 1987). Butterworth-Heinemann (1987)

    MATH  Google Scholar 

  29. F.D. Gahov, Boundary Problems (Gos. Izdat. Fiz.-Mat. Lit., Moskow, 1958) (in Russian)

    Google Scholar 

  30. R. Mittra, S.W. Lee, Analytical Techniques in the Theory of Guided Waves (Macmillan, New York, 1971)

    MATH  Google Scholar 

  31. D.V. Anosov, A.A. Bolibruch, The Riemann-Hilbert Problem. Aspects of Mathematics (Friedrich, Vieweg, 1994)

    MATH  Google Scholar 

  32. L.I. Mandelshtamm, Lectures on Optics, Relativity Theory and Quantum Mechanics (Nauka, Moskow, 1972) (in Russian)

    Google Scholar 

  33. F.A. Andreev, Sov. Phys. JETP 19, 1228 (1964). Zh. Eksp. Teor. Fiz. 46, 1823 (1964) (in Russian)

    Google Scholar 

  34. A.F. Andreev, Sov. Phys. JETP 4, 1084 (1963). Zh. Eksp. Teor. Fiz. 43, 1535, (1962) (in Russian)

    ADS  Google Scholar 

  35. I.N. Adamenko, K.E. Nemchenko, I.V. Tanatarov, A.F.G. Wyatt, J. Phys.: Condens. Matter 20, 245103 (2008)

    Article  ADS  Google Scholar 

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Authors and Affiliations

  1. National Science Center “Kharkov Institute of Physics and Technology”, Academicheskaya St. 1, Kharkov, 61108, Ukraine

    I. V. Tanatarov

  2. Karazin Kharkov National University, Svobody Sq. 4, Kharkov, 61077, Ukraine

    I. N. Adamenko & K. E. Nemchenko

  3. School of Physics, University of Exeter, Exeter, EX4 4QL, UK

    A. F. G. Wyatt

Authors
  1. I. V. Tanatarov
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  2. I. N. Adamenko
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  3. K. E. Nemchenko
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  4. A. F. G. Wyatt
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Corresponding author

Correspondence to A. F. G. Wyatt.

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Tanatarov, I.V., Adamenko, I.N., Nemchenko, K.E. et al. Interactions of Phonons and Rotons with Interfaces in Superfluid Helium. J Low Temp Phys 159, 549–575 (2010). https://doi.org/10.1007/s10909-010-0165-8

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  • DOI: https://doi.org/10.1007/s10909-010-0165-8

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