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Semiclassical Vlasov and fluid models for an electron gas with spin effects

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Abstract

We derive a four-component Vlasov equation for a system composed of spin-1/2 fermions (typically electrons). The orbital part of the motion is classical, whereas the spin degrees of freedom are treated in a completely quantum-mechanical way. The corresponding hydrodynamic equations are derived by taking velocity moments of the phase-space distribution function. This hydrodynamic model is closed using a maximum entropy principle in the case of three or four constraints on the fluid moments, both for Maxwell-Boltzmann and Fermi-Dirac statistics.

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References

  1. C. Suárez, W.E. Bron, T. Juhasz, Phys. Rev. Lett. 75, 4536 (1995)

    Article  ADS  Google Scholar 

  2. J.-Y. Bigot, V. Halté, J.-C. Merle, A. Daunois, Chem. Phys. 251, 181 (2000)

    Article  ADS  Google Scholar 

  3. J.-S. Lauret, C. Voisin, G. Cassabois, C. Delalande, Ph. Roussignol, O. Jost, L. Capes, Phys. Rev. Lett. 90, 057404 (2003)

    Article  ADS  Google Scholar 

  4. R. Schlipper, R. Kusche, B.V. Issendorff, H. Haberland, Appl. Phys. A 72, 255259 (2001)

    Article  Google Scholar 

  5. E.E.B. Campbell, K. Hansen, K. Hoffmann, G. Korn, M. Tchaplyguine, M. Wittmann, I.V. Hertel, Phys. Rev. Lett. 84, 2128 (2000)

    Article  ADS  Google Scholar 

  6. C. Voisin, D. Christofilos, N. Del Fatti, F. Vallée, B. Prével, E. Cottancin, J. Lermé, M. Pellarin, M. Broyer, Phys. Rev. Lett. 85, 2200 (2000)

    Article  ADS  Google Scholar 

  7. J.A. Scholl, Ai Leen Koh, J.A. Dionne, Nature 483, 421 (2012)

    Article  ADS  Google Scholar 

  8. Yu. Luo, A.I. Fernandez-Dominguez, A. Wiener, S.A. Maier, J.B. Pendry, Phys. Rev. Lett. 111, 093901 (2013)

    Article  ADS  Google Scholar 

  9. B. Rethfeld, A. Kaiser, M. Vicanek, G. Simon, Phys. Rev. B 65, 214303 (2002)

    Article  ADS  Google Scholar 

  10. M. Aeschlimann, M. Bauer, S. Pawlik, R. Knorren, G. Bouzerar, K.H. Bennemann, Appl. Phys. A 71, 485 (2000)

    Article  ADS  Google Scholar 

  11. C. Guillon, P. Langot, N. Del Fatti, F. Vallée, New J. Phys. 5, 13 (2003)

    Article  ADS  Google Scholar 

  12. D. Pines, P. Nozières, The theory of quantum liquids (W.A. Benjamin, New York, 1966)

  13. F. Calvayrac, P.-G. Reinhard, E. Suraud, C. Ullrich, Phys. Rep. 337, 493 (2000)

    Article  ADS  Google Scholar 

  14. T.V. Teperik, P. Nordlander, J. Aizpurua, A.G. Borisov, Phys. Rev. Lett. 110, 263901 (2013)

    Article  ADS  Google Scholar 

  15. U. Schwengelbeck, L. Plaja, L. Roso, E.C. Jarque, J. Phys. B 33, 1653 (2000)

    Article  ADS  Google Scholar 

  16. J. Daligault, C. Guet, J. Phys. A 36, 5847 (2003)

    Article  MATH  ADS  Google Scholar 

  17. S.V. Fomichev, D.F. Zaretsky, J. Phys. B 32, 5083 (1999)

    Article  ADS  Google Scholar 

  18. D.F. Zaretsky, Ph.A. Korneev, S.V. Popruzhenko, W. Becker, J. Phys. B 37, 4817 (2004)

    Article  ADS  Google Scholar 

  19. G. Manfredi, P.-A. Hervieux, Phys. Rev. B 72, 155421 (2005)

    Article  ADS  Google Scholar 

  20. R. Jasiak, G. Manfredi, P.-A. Hervieux, M. Haefele, New J. Phys. 11, 063042 (2009)

    Article  ADS  Google Scholar 

  21. A. Puente, M. Casas, L. Serra, Physica E 8, 387 (2000)

    Article  ADS  Google Scholar 

  22. L. Serra, A. Puente, Eur. Phys. J. D 14, 77 (2001)

    Article  ADS  Google Scholar 

  23. O. Morandi, P.-A. Hervieux, G. Manfredi, New J. Phys. 11, 073010 (2009)

    Article  ADS  Google Scholar 

  24. O. Morandi, P.-A. Hervieux, G. Manfredi, Phys. Rev. B 81, 155309 (2010)

    Article  ADS  Google Scholar 

  25. E. Beaurepaire, J.-C. Merle, A. Daunois, J.-Y. Bigot, Phys. Rev. Lett. 76, 4250 (1996)

    Article  ADS  Google Scholar 

  26. G.P. Zhang, W. Hübner, Phys. Rev. Lett. 85, 3025 (2000)

    Article  ADS  Google Scholar 

  27. B. Koopmans, J.J.M. Ruigrok, F. Dalla Longa, W.J.M. de Jonge, Phys. Rev. Lett. 95, 267207 (2005)

    Article  ADS  Google Scholar 

  28. J.-Y. Bigot, M. Vomir, E. Beaurepaire, Nat. Phys. 5, 515 (2009)

    Article  Google Scholar 

  29. J.-Y. Bigot, M. Vomir, Ann. Phys. (Berlin) 525, 2 (2013)

    Article  ADS  Google Scholar 

  30. E.P. Wigner, Phys. Rev. 40, 749 (1932)

    Article  ADS  Google Scholar 

  31. A. Dixit, Y. Hinschberger, J. Zamanian, G. Manfredi, P.-A. Hervieux, Phys. Rev. A 88, 032117 (2013)

    Article  ADS  Google Scholar 

  32. Y. Hinschberger, P.-A. Hervieux, Phys. Lett. A 376, 813 (2012)

    Article  MATH  ADS  Google Scholar 

  33. M. Brewczyk, K. Rzążewski, C.W. Clark, Phys. Rev. Lett. 78, 191 (1997)

    Article  ADS  Google Scholar 

  34. A. Banerjee, M.K. Harbola, J. Chem. Phys. 113, 5614 (2000)

    Article  ADS  Google Scholar 

  35. A. Domps, P.-G. Reinhard, E. Suraud, Phys. Rev. Lett. 81, 5524 (1998)

    Article  ADS  Google Scholar 

  36. G. Manfredi, P.-A. Hervieux, F. Haas, New J. Phys. 64, 075316 (2012)

    Google Scholar 

  37. N. Crouseilles, P.-A. Hervieux, G. Manfredi, Phys. Rev. B 78, 155412 (2008)

    Article  ADS  Google Scholar 

  38. B. Eliasson, P.K. Shulka, Phys. Rev. Lett. 96, 245001 (2006)

    Article  ADS  Google Scholar 

  39. B. Eliasson, P.K. Shulka, Phys.-Usp. 53, 51 (2010)

    Article  ADS  Google Scholar 

  40. F. Haas, G. Manfredi, P.K. Shukla, P.-A. Hervieux, Phys. Rev. B 80, 073301 (2009)

    Article  ADS  Google Scholar 

  41. G. Brodin, M. Marklund, New J. Phys. 9, 277 (2007)

    Article  Google Scholar 

  42. E. Madelung, Z. Phys. 40, 322 (1927)

    Article  ADS  Google Scholar 

  43. F.A. Asenjo, V. Muñoz, J.A. Valdivia, S.M. Mahajan, Phys. Plasmas 18, 012107 (2011)

    Article  ADS  Google Scholar 

  44. G. Manfredi, Eur. J. Phys. 34, 859 (2013)

    Article  MATH  Google Scholar 

  45. G. Manfredi, P.-A. Hervieux, Y. Yin, N. Crouseilles, Lect. Notes Phys. 795, 1 (2009)

    Article  ADS  Google Scholar 

  46. L. Barletti, Transport Theor. Stat. Phys. 32, 253 (2003)

    Article  MATH  MathSciNet  ADS  Google Scholar 

  47. O. Morandi, F. Schuerrer, J. Phys. A 44, 265301 (2011)

    Article  ADS  Google Scholar 

  48. D. Querlioz, P. Dollfus, M. Mouis, M. Front Matter, The Wigner Monte Carlo Method for Nanoelectronic Devices (Wiley, Hoboken, 2013)

  49. O. Morandi, Phys. Rev. B 80, 024301 (2009)

    Article  ADS  Google Scholar 

  50. O. Morandi, J. Phys. A 43, 365302 (2010)

    Article  MathSciNet  Google Scholar 

  51. O. Morandi, Comm. Appl. Indust. Math. 1, 474 (2010)

    MathSciNet  Google Scholar 

  52. A. Arnold, H. Steinrück, Z. Angew. Math. Phys. 40, 793 (1989)

    Article  MATH  MathSciNet  Google Scholar 

  53. J. Zamanian, M. Marklund, G. Brodin, New J. Phys. 12, 043019 (2010)

    Article  MathSciNet  ADS  Google Scholar 

  54. J. Zamanian, M. Stefan, M. Marklund, G. Brodin, Phys. Plasmas 17, 102109 (2010)

    Article  ADS  Google Scholar 

  55. G. Ali, G. Mascali, V. Romano, R.C. Torcasio, Acta Appl. Math. 122, 335 (2012)

    MATH  Google Scholar 

  56. M. Trovato, L. Reggiani, J. Phys. A 43, 102001 (2010)

    Article  MathSciNet  ADS  Google Scholar 

  57. V. Romano, Math. Meth. Appl. Sci. 24, 439471 (2001)

    Article  MathSciNet  Google Scholar 

  58. A.M. Anile, O. Muscato, Phys. Rev. B 51, 16740 (1995)

    Article  ADS  Google Scholar 

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Authors and Affiliations

  1. Institut de Physique et Chimie des Matériaux de Strasbourg and Labex NIE, Université de Strasbourg, CNRS UMR 7504, BP 43, 67034, Strasbourg Cedex 2, France

    Jérôme Hurst, Omar Morandi, Giovanni Manfredi & Paul-Antoine Hervieux

Authors
  1. Jérôme Hurst
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  2. Omar Morandi
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  3. Giovanni Manfredi
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  4. Paul-Antoine Hervieux
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Correspondence to Giovanni Manfredi.

Additional information

Contribution to the Topical Issue “Theory and Applications of the Vlasov Equation”, edited by Francesco Pegoraro, Francesco Califano, Giovanni Manfredi and Philip J. Morrison.

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Hurst, J., Morandi, O., Manfredi, G. et al. Semiclassical Vlasov and fluid models for an electron gas with spin effects. Eur. Phys. J. D 68, 176 (2014). https://doi.org/10.1140/epjd/e2014-50205-5

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