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Original Articles

Quantum Corrections to Classical BGK Modes in Phase Space

Pages 137-158 | Received 20 Sep 2005, Accepted 25 Apr 2006, Published online: 04 Dec 2010

References

  • Arnold , A. and Markowich , P. 1990 . The periodic quantum Liouville‐Poisson problem . Bollettino UMI , 7 : 449 – 484 .
  • Bernstein , I. B. , Greene , J. M. and Kruskal , M. D. 1957 . Exact nonlinear plasma oscillations . Phys. Rev. , 108 : 546 – 550 .
  • Buchanan , M. and Dorning , J. J. 1995 . Nonlinear electrostatic waves in collisionless plasmas . Phys. Rev. E , 52 : 3015 – 3033 .
  • Demeio , L. 2001 . A numerical study of linear and nonlinear superpositions of BGK modes . Transp. Theory Stat. Phys. , 30 : 457 – 470 .
  • Demeio , L. Perturbative approach to quantum BGK modes . Proc. VI Congresso SIMAI . May 27–31 , Chia Laguna, Italy.
  • Demeio , L. and Holloway , J. P. 1991 . Numerical simulations of BGK modes . J. Plasma Phys. , 46 : 63 – 84 .
  • Fedele , R. and Man'ko , V. I. 1998 . Quantum‐like corrections and semiclassical description of charged‐particle beam transport . Phys. Rev. E , 58 : 992 – 1001 .
  • Fedele , R. and Miele , G. 1992 . Spherical aberrations in the thermal‐wave model for luminosity estimates in particle accelerators . Phys. Rev. A , 46 : 6634 – 6639 .
  • Fedele , R. and Shukla , P. K. 1992 . Self‐consistent interaction between the plasma wake field and the driving relativistic electron beam . Phys. Rev. A , 45 : 4045 – 4049 .
  • Lange , H. , Toomire , B. and Zweifel , P. F. 1996 . Quantum BGK modes for the Wigner‐Poisson system . Transp. Theory and Stat. Phys. , 25 : 713 – 722 .
  • Maitra , N. T. and Heller , E. J. 1996 . Semiclassical perturbation approach to quantum reflection . Phys. Rev. A , 54 : 4763 – 4769 .
  • Manfredi , G. 2005 . How to Model quantum plasmas . ArXiv e‐print quant‐ph/0505004
  • Marinov , M. S. and Segev , B. 1996 . Quantum tunneling in the Wigner representation . Phys. Rev. A , 54 : 4752 – 4762 .
  • Neunzert , H. 1985 . The “nuclear” Vlasov equation. Methods and results that can(not) be taken over from the “classical” case . Il Nuovo Cimento , 87A : 151 – 161 .
  • Vlasov , A. 1945 . On the kinetic theory of an assembly of particles with collective interaction . J. Phys. , 9 : 25 – 40 .
  • Zweifel , P. F. 1993 . The Wigner transform and the Wigner‐Poisson system . Transp. Theory Stat. Phys. , 22 : 459

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