Review Articles

Full Text / References

Nonlinear Aspects of Quantum Plasma Physics: Nanoplasmonics and Nanostructures in Dense Plasmas

Bengt ELIASSON and Padma K. SHUKLA¹⁾

Department of Physics, Umeå University, SE-901 87 Umeå, Sweden

1)

Theoretische Physik IV, Ruhr-Universität Bochum, D-44780 Bochum, Germany

(Received 17 September 2008 / Accepted 16 April 2009 / Published 7 July 2009)

Abstract

We present a short review of recent developments in nonlinear quantum plasma physics, including quantum hydrodynamic and effective nonlinear shrödinger equation formalisms, for describing collective phenomena in quantum plasmas. As examples we discuss simulation studies of the formation and dynamics of dark solitons and vortices, and of nonlinear interactions between intense circularly polarized electromagnetic (CPEM) waves and electron plasma oscillations (EPOs) in dense in quantum electron plasmas. The electron dynamics of dark solitons and vortices is governed by a pair of equations comprising the nonlinear Schrödinger and Poisson equations. Both dark solitons and singly charged electron vortices are robust, and the latter tend to form pairs of oppositely charged vortices. The two-dimensional quantum electron vortex pairs survive during collisions under the change of partners. The dynamics of the CPEM waves is governed by a nonlinear Schrödinger equation, which is nonlinearly coupled with the Schrödinger equation of the EPOs via the relativistic ponderomotive force, the relativistic electron mass increase in the CPEM field, and the electron density fluctuations. The present governing equations in one spatial dimension admit stationary solutions in the form dark envelope solitons. The nonlinear equations admit the modulational instability of an intense CPEM pump wave against EPOs, leading to the formation and trapping of localized CPEM wave envelopes in the electron density holes that are associated with positive potential profiles.

Copyright (c) 2009 The Japan Society of Plasma Science and Nuclear Fusion Research

Keywords

quantum plasma, dark soliton, vortex, nonlinear Schrödinger equation, electromagnetic wave, electron plasma oscillation

DOI: 10.1585/pfr.4.032

Full Text

PDF format (2.2Mbytes)

References

• [1] D. Pines, J. Nucl. Energy: Part C: Plasma Phys. 2, 5 (1961).
• [2] G. Manfredi and F. Haas, Phys. Rev. B 64, 075316 (2001).
• [3] G. Manfredi, Fields Inst. Commun. 46, 263 (2005); arxiv:quant-ph/0505004.
• [4] P.K. Shukla and B. Eliasson, Phys. Rev. Lett. 96, 245001 (2006).
• [5] C.L. Gardner and C. Ringhofer, Phys. Rev. E 53, 157 (1996).
• [6] M. Marklund and G. Brodin, Phys. Rev. Lett. 98, 025001 (2007).
• [7] S.X. Hu and C.H. Keitel, Phys. Rev. Lett. 83, 4709 (1999).
• [8] Y.A. Salamin et al., Phys. Rep. 427, 41 (2006).
• [9] S.H. Glenzer et al., Phys. Rev. Lett. 98, 065002 (2007).
• [10] V.M. Malkin et al., Phys. Rev. E 75, 026404 (2007).
• [11] H. Azechi et al., Plasma Phys. Control. Fusion 48, B267 (2006).
• [12] M. Opher et al., Phys. Plasmas 8, 2454 (2001).
• [13] O.G. Benvenuto and M.A. De Vito, Mon. Not. R. Astron. Soc. 362, 891 (2005).
• [14] G. Chabrier et al., J. Phys.: Condens. Matter 14, 9133 (2002).
• [15] G. Chabrier et al., J. Phys. A: Math. Gen. 39, 4411 (2006).
• [16] Y.Y. Lau et al., Phys. Rev. Lett. 66, 1446 (1991).
• [17] L.K. Ang et al., Phys. Rev. Lett. 91, 208303 (2003).
• [18] L.K. Ang and P. Zhang, Phys. Rev. Lett. 98, 164802 (2007).
• [19] E.P. Wigner, Phys. Rev. 40, 749 (1932).
• [20] M. Hillery et al., Phys. Rep. 106, 121 (1984).
• [21] F. Haas, G. Manfredi and M. Feix, Phys. Rev. E 62, 2763 (2000).
• [22] D. Anderson et al., Phys. Rev. E 65, 046417 (2002).
• [23] F. Haas, L.G. Garcia, J. Goedert and G. Manfredi, Phys. Plasmas 10, 3858 (2003).
• [24] F. Haas, Phys. Plasmas 12, 062117 (2005).
• [25] M. Marklund and G. Brodin, Phys. Rev. Lett. 98, 025001 (2007).
• [26] G. Mourou et al., Rev. Mod. Phys. 78, 309 (2006).
• [27] A.K. Harding and D. Lai, Rep. Prog. Phys. 69, 2631 (2006).
• [28] G.V. Shpatakovskaya, JETP 102, 466 (2006).
• [29] W.L. Barnes et al., Nature (London) 424, 824 (2003).
• [30] D.E. Chang et al., Phys. Rev. Lett. 97, 053002 (2006).
• [31] P.A. Markowich et al., Semiconductor Equations (Springer, Berlin 1990).
• [32] K.H. Becker, K.H. Schoenbach and J.G. Eden, J. Phys. D: Appl. Phys. 39, R55 (2006).
• [33] M. Loffredo and L. Morato, Nuovo Cimento Soc. Ital Fis. B 108B, 205 (1993).
• [34] R. Feynman, Statistical Mechanics, A Set of of Lectures (Benjamin, Reading, 1972).
• [35] A. Domps et al., Phys. Rev. Lett. 80, 5520 (1998).
• [36] P. Hohenberg and W. Kohn, Phys. Rev. 136, B864 (1964).
• [37] W. Kohn and L.J. Sham, Phys. Rev. 140, A1133 (1965).
• [38] L. Brey et al., Phys. Rev. B 42, 1240 (1990).
• [39] A.V. Andreev, JETP Lett. 72, 238 (2000).
• [40] M. Marklund and P.K. Shukla, Rev. Mod. Phys. 78, 591 (2006).
• [41] P.K. Shukla et al., Phys. Rep. 138, 1 (1986).
• [42] B.H. Bransden and C.J. Joachain, Quantum Mechanics (2nd Edition) (Pearson Education Limited, Essex, England, 2000).
• [43] D. Bohm and D. Pines, Phys. Rev. 92, 609 (1953).
• [44] E.B. Kolomeisky et al., Phys. Rev. Lett. 85, 1146 (2000).
• [45] I.A. Ivonin, V.P. Pavlenko and H. Persson, Phys. Rev. E 60, 492 (1999).
• [46] P.K. Shukla and B. Eliasson, Phys. Rev. Lett. 99, 096401 (2007).
• [47] C.J. McKinstrie and R. Bingham, Phys. Fluids B 4, 2626 (1992).
• [48] J.H. Marburger and R.F. Tooper, Phys. Rev. Lett. 35, 1001 (1975).
• [49] M. Borghesi et al., Phys. Rev. Lett. 88, 135002 (2002).

This paper may be cited as follows:

Bengt ELIASSON and Padma K. SHUKLA, Plasma Fusion Res. 4, 032 (2009).