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Hopping Kinetics, Quantum Dynamics and Transport

  • Werner EbelingEmail author
  • Vladimir E. Fortov
  • Vladimir Filinov
Chapter
Part of the Springer Series in Plasma Science and Technology book series (SSPST)

Abstract

In this chapter we begin by examining simple models of electron hopping between bound states located on sites or atoms. In particular, we investigate electron hopping on classical dynamic lattices. Then we discuss models of molecular dynamics of electrons based on effective potential interactions, including models of Wigner dynamics with coordinate- and momentum-dependent interactions in phase space. Finally, we study several molecular dynamics models based on wave packet dynamics. The powerful methods of quantum Monte Carlo simulations will be treated in Chaps.  9 and  10.

References

  1. N. Ashcroft. N.D. Mermin, Solid State Physics (Holt, Rinehardt, and Winston, Philadelphia, 1976, Mir Moscow 1979)Google Scholar
  2. H.B. Böttger, V.V. Bryksin, Hopping Conduction in Solids (Akademie-Verlag, Berlin, 1985)Google Scholar
  3. L. Brizhik, A.P. Chetverikov, W. Ebeling, G. Röpke, M.G. Velarde, Phys. Rev. B 85, 245105 (2012)ADSCrossRefGoogle Scholar
  4. R. Car, M. Parrinello, Unified approach for molecular dynamics and density-functional theory. Phys. Rev. Lett. 55, 241–247 (1985)Google Scholar
  5. D.M. Ceperley, B. Alder, Phys. Rev. Lett 45, 566 (1980)ADSCrossRefGoogle Scholar
  6. A.P. Chetverikov, W. Ebeling, M. Jenssen, Yu. Romanovsky, Excitations on rings of molecules, in Stochastic dynamics of reacting biomolecules, ed. by W. Ebeling, et al. (World Scientific, Singapore, 2002)Google Scholar
  7. P. Chetverikov, W. Ebeling, G. Röpke, M.G. Velarde, Anharmonic excitations, time correlations and electric conductivity. Contrib. Plasma Phys. 47, 465–478 (2007)ADSCrossRefGoogle Scholar
  8. A.P. Chetverikov, W. Ebeling, M.G. Velarde, Local electron distributions and diffusion in anharmonic lattices mediated by thermally excited solitons. Eur. Phys. J. B 70, 217–227 (2011)ADSCrossRefGoogle Scholar
  9. A.P. Chetverikov, W. Ebeling, G. Röpke, Hopping transport and stochastic dynamics in plasma layers. Contrib. Plasma Phys. 51, 814–829 (2011)ADSCrossRefGoogle Scholar
  10. A.P. Chetverikov, W. Ebeling, M.G. Velarde, Soliton-like excitations and solectrons in two-dimensional lattices. Eur. Phys. J. B 80, 137–145 (2012)ADSCrossRefGoogle Scholar
  11. A.P. Chetverikov, W. Ebeling, G. Röpke, M.G. Velarde, High electrical conductivity in nonlinear model lattice crystals mediated by thermal excitation of solectrons. Eur. Phys. J. B 87, 153 (2014)ADSMathSciNetCrossRefGoogle Scholar
  12. A.P. Chetverikov, W. Ebeling, M.G. Velarde, On the temperature dependence of fast electron transport in crystal lattices. Eur. Phys. J. B 88, 202 (2015)ADSCrossRefGoogle Scholar
  13. C. Dorso, S. Duarte, J. Randrup, Phys. Lett B 188, 287 (1987)Google Scholar
  14. T. Dornheim, S. Groth, A. Filinov, M. Bonitz, Permutation blocking path integral Monte Carlo: a highly efficient approach to the simulation of strongly degenerate non-ideal fermions. New J. Phys. 17, 073017 (2015)ADSCrossRefGoogle Scholar
  15. T. Dornheim, T. Schoof, S. Groth, A. Filinov, M. Bonitz, Permutation blocking path integral monte carlo approach to the uniform electron gas at finite temperature. J. Chem. Phys. 143, 204101 (2015)ADSCrossRefGoogle Scholar
  16. T. Dornheim, S. Groth, T. Schoof, C. Hann, M. Bonitz, Ab initio quantum Monte Carlo simulations of the uniform electron gas without fixed nodes: the unpolarized case. Phys. Rev. B 93, 205134 (2016)ADSCrossRefGoogle Scholar
  17. T. Dornheim, H. Thomsen, P. Ludwig, A. Filinov, M. Bonitz, Analyzing quantum correlations made simple. Contrib. Plasma Phys. 56, 371 (2016)ADSCrossRefGoogle Scholar
  18. T. Dornheim et al., Ab initio Quantum Monte Carlo simulation of the warm dense electron gas in the thermodynamic limit, Phys. Rev. Lett. 117, 156403 (2016), arXiv: 1607.08076v2 [physics.plasm-ph]. 9 Sep 2016
  19. C. Dorso, S. Duarte, J. Randrup, Excited electron dynamics modeling of warm matter, Phys. Lett. B 188, 287 (1987); 215, 611 (1988)Google Scholar
  20. W. Ebeling, A. Filinov, M. Bonitz, V. Filinov, T. Pohl, The method of effective potentials in the quantum-statistical theory of plasmas. J. Phys. A: Math. Gen. 39, 4309–4317 (2006)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  21. W. Ebeling, V. Fortov, et al. (eds.), Transport Properties of Dense Plasmas (Birkhäuser, Boston, 1984)Google Scholar
  22. W. Ebeling, I. Leike, U. Leonhardt, Bound states and ionization kinetics in dense plasmas, AIP Conf. Proc. (Atomic Processes in Plasmas, Portland ME 1991) 257, 97–107 (1992)Google Scholar
  23. W. Ebeling, A. Förster, VYu. Podlipchuk, Quantum wave packets simulations of ionization processes in dense plasmas. Phys. Lett. A 218, 297–303 (1996)ADSCrossRefGoogle Scholar
  24. W. Ebeling, Bound state effects in quantum transport theory. Ann. Physik (Leipzig) 33, 350–358 (1976)ADSCrossRefGoogle Scholar
  25. W. Ebeling, G. Röpke, Conductance theory of nonideal plasmas. Ann. Physik (Leipzig) 36, 429–432 (1979)ADSCrossRefGoogle Scholar
  26. W. Ebeling, B. Militzer, F. Schautz, Quasiclassical theory and simulations of hydrogen quantum plasmas. Contrib. Plasma Phys. 37, 137–148 (1997)ADSCrossRefGoogle Scholar
  27. W. Ebeling, F. Schautz, Simulations of the quantum electron gas using momentum-dependent potentials. Phys. Rev. E 56, 3498 (1997)ADSCrossRefGoogle Scholar
  28. W. Ebeling, J. Ortner, Quasiclassical theory and simulations of strongly coupled plasmas. Phys. Scr. T 75, 93–98 (1998)ADSCrossRefGoogle Scholar
  29. W. Ebeling, G.E. Norman, A.A. Valuev, I. Valuev, Quasiclassical theory and molecular dynamics of two-component nonideal plasmas. Contr. Plasma Phys. 39, 61 (1999)ADSCrossRefGoogle Scholar
  30. W. Ebeling, T. Pohl, J.A. Holyst, Nonlinear effects and energy flow in the semiclassical dynamics of atomic electrons in strong laser fields. Laser Phys. 10, 1069–1077 (2000)Google Scholar
  31. W. Ebeling, T. Pohl, Quantum wave packet dynamics. in Quantum limits on the second law, ed. by D.P. Sheehan (AIP Conf. Proc., New York, 2002)Google Scholar
  32. W. Ebeling, L. Schimansky-Geier, YuM Romanovsky (eds.), Stochastic dynamics of interacting biomolecules (World Scientific, Singapore, 2002)zbMATHGoogle Scholar
  33. W. Ebeling, A. Filinov, M. Bonitz, V. Filinov and T. Pohl, The method of effective potentials in the quantum-statistical theory of plasmas, J. Phys. A: Math. Gen. 39 , 4309–4317 (2006)Google Scholar
  34. V. Filinov, M. Bonitz, A. Filinov, V. Golubnychiy, Wigner function quantum molecular dynamics, arXiv:cond-mat/0611560v1 [cond-mat.str-el]. 21 Nov 2006
  35. H. Feldmeier, K. Bieler, J. Schnack, Nucl. Phys. A 596, 493 (1995)Google Scholar
  36. A. Förster, D. Beule, H. Conrads, W. Ebeling, Highly ionized carbon in capillary discharge plasma. Contr. Plasma Phys. 38, 655–660 (1998)ADSCrossRefGoogle Scholar
  37. A. Förster, T. Kahlbaum, W. Ebeling, Equation of state and phase diagram of fluid helium in the region of partial ionization. Laser Part. Beams 10, 253–262 (1992)ADSCrossRefGoogle Scholar
  38. P.E. Grabowski, A. Markmann, M.S. Murillo, C.A. Fichtl, D.F. Richards, V.S. Batista, F.R. Graziani, I.V. Morozov, I.A. Valuev, Wave packet spreading and localization in electron-nuclear scattering. Phys. Rev. E 87, 063104 (2013)ADSCrossRefGoogle Scholar
  39. J.-P. Hansen, I.R. McDonald, E.L. Pollock, Phys. Rev. A 11, 1025 (1975)ADSCrossRefGoogle Scholar
  40. S. Groth, T. Dornheim, M. Bonitz, Free energy of the uniform electron gas: testing analytical models against first principle results, arXiv:1611.05695v1 [physics.plasm-ph]. 17 Nov 2016
  41. J.-P. Hansen, I.K. McDonald, Microscopic simulation of a strongly coupled hydrogen plasma. Phys. Rev. A 23, 2041–2059 (1981)ADSCrossRefGoogle Scholar
  42. A. Heeger, S. Kivelson, J.R. Schrieffer, W.P. Su, Rev. Mod. Phys. 60, 781 (1988)ADSCrossRefGoogle Scholar
  43. D. Hennig, M.G. Velarde, A.P. Chetverikov, W. Ebeling, Phys. Rev. E 76, 046602 (2007)ADSCrossRefGoogle Scholar
  44. E.J. Heller, J. Chem. Phys. 62, 1544 (1975)ADSCrossRefGoogle Scholar
  45. B. Holst, M. French, R. Redmer, Electronic transport coefficients from ab initio simulations and application to dense liquid hydrogen. Phys. Rev. B 83, 235120 (2011)ADSCrossRefGoogle Scholar
  46. B. Jakob, P.-G. Reinhard, C. Toepffer, G. Zwicknagel, Phys. Rev. E 76, 036406 (2007)ADSCrossRefGoogle Scholar
  47. G. Kalman (ed.), Strongly Coupled Coulomb Systems (Pergamon Press 1998)Google Scholar
  48. V.S. Karakhtanov, R. Redmer, H. Reinholz, G. Röpke, Transport coefficients in dense plasmas including ion-ion structure factor. Contrib. Plasma Phys. 51, 355–360 (2011)ADSCrossRefGoogle Scholar
  49. V.V. Karasiev, T. Sjostrom, S.B. Trickey, Comparison of DFT and finite temperature HF approximation. Phys. Rev. E 86, 056704 (2012)ADSCrossRefGoogle Scholar
  50. G. Kelbg, Quantenstatistik der Gase mit Coulombwechselwirkung, Ann. Physik (Leipzig) 12, 219–224, 354–360 (1963), 14, 394–403 (1964)Google Scholar
  51. D. Klakow, C. Toepffer, P.-G. Reinhard, Phys. Lett. A 192(55) (1994), J. Chem. Phys. 101(10766) (1994)Google Scholar
  52. Y.L. Klimontovich, Kinetic Theory Of Nonideal Gases And Nonideal Plasmas (Nauka, Moskva, 1975) (Pergamon, Oxford, 1982)Google Scholar
  53. Y.L. Klimontovich, Statistical Physics (in Russ.) (Nauka Moskva 1982), (Engl. transl., Harwood, 1984)Google Scholar
  54. M. Knaup, P.-G. Reinhard, C. Toepffer, G. Zwicknagel, Wave packet molecular dynamics simulations of hydrogen at mbar pressures. Comput. Phys. Commun. 147, 202–204 (2002)ADSCrossRefzbMATHGoogle Scholar
  55. M. Knaup, P.-G. Reinhard, C. Toepffer, G. Zwicknagel, J. of Physics A: Math. Gen. 36, 6165 (2003)ADSCrossRefGoogle Scholar
  56. Y.L. Klimontovich, Statistical Theory of Open Systems(in Russian). vol. I, II, III, (Janus, Moscow 1995, 1999, 2001)Google Scholar
  57. W.D. Kraeft et al., Quantum Statistics Of Charged Particle Systems (Plenum, New York, 1986)CrossRefGoogle Scholar
  58. R. Kubo, Statistical-mechanical theory of irreversible processes. I. General theory and simple applications to magnetic and conduction problems. J. Phys. Soc. Jpn. 12, 570–586 (1957)ADSMathSciNetCrossRefGoogle Scholar
  59. A.S. Larkin, V.S. Filinov, Wigner’s pseudo-particle relativistic dynamics in external potential field. Phys. Lett. A 378, 1876–1882 (2014)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  60. A.S. Larkin, V.S. Filinov, V.E. Fortov, Path integral representation of the Wigner function. Contr. Plasma Phys. 56(3–4), 197–213 (2016)ADSGoogle Scholar
  61. Y.S. Lavrinenko, I.V. Morozov, A. Valuev, Reflecting boundary conditions for classical and quantum molecular dynamics. Contr. Plasma Phys. 56, 448–458 (2016)ADSCrossRefGoogle Scholar
  62. U. Leonhardt, W. Ebeling, Ionization and recombination coefficients of excited states in nonideal hydrogen plasmas. Physica A 192, 249–261 (1993)ADSCrossRefGoogle Scholar
  63. E.M. Lifshits, P. Pitaevskii, in Physical Kinetics, vol. 10 (Course of Theoretical Physics (Pergamon, New York, 1981)Google Scholar
  64. W.R. Magro, D.M. Ceperley, C. Pierleoni, B. Bernu, Phys. Rev. Lett. 76, 1240 (1996)ADSCrossRefGoogle Scholar
  65. B. Militzer, E.L. Pollock, Phys. Rev. E 61, 3470 (2000)ADSCrossRefGoogle Scholar
  66. I.V. Morozov, I.A. Valuev, J. Phys. A: Math. Theor. 42, (214044) (2009); Contributions Plasma Physics 52, 140 (2012)Google Scholar
  67. J. Ortner, I.M. Tkachenko, Phys. Rev. A 46, 7882 (1992)ADSCrossRefGoogle Scholar
  68. J. Ortner, F. Schautz, W. Ebeling, Quasiclassical molecular-dynamics simulations of the electron gas. Phys. Rev. E 56, 4665–4670 (1997)ADSCrossRefGoogle Scholar
  69. J. Ortner, F. Schautz, W. Ebeling, Investigations of the dynamic properties of the electron gas by quasi-classical simulations, in Strongly coupled plasmas ed. by G. Kalman et al. (Plenum Press, New York, 1998)Google Scholar
  70. J. Ortner, I. Valuev, W. Ebeling, Semiclassical dynamics and time correlations in two-component plasmas. Contr. Plasma Phys. 39, 311–321 (1999)ADSCrossRefGoogle Scholar
  71. J. Ortner, I. Valuev, W. Ebeling, Electric microfield distribution in two-component plasmas. Contr. Plasma Phys. 40, 555–685 (2000)ADSCrossRefGoogle Scholar
  72. R.G. Parr, W. Yang, Density-Functional Theory of Atoms and Molecules (Oxford University Press, New York, 1989)Google Scholar
  73. R. Redmer, B. Holst, F. Hensel (eds.), Metal-to-Nonmetal Transitions (Springer, Berlin, 2010)zbMATHGoogle Scholar
  74. H. Reinholz, G. Röpke, S. Rosmej, R. Redmer, Conductivity of warm dense matter including electron-electron collisions. Phys. Rev. E 91, 043105 (2015)ADSCrossRefGoogle Scholar
  75. G. Röpke, W. Ebeling, W.D. Kraeft, Quantum-statistical conductance theory of nonideal plasmas by use of the force-force correlation function method. Physica A 101, 243–254 (1980)ADSCrossRefGoogle Scholar
  76. T. Pohl, U. Feudel, W. Ebeling, Bifurcations of a semi-classical atom in a periodic field. Phys. Rev. E 65, 046228 (2002)ADSCrossRefGoogle Scholar
  77. S. Sadykova, W. Ebeling, I. Valuev, I. Sokolov, Contrib. Plasma Phys. 49, 76 (2009)ADSCrossRefGoogle Scholar
  78. S.P. Sadykova, W. Ebeling, I.M. Tkachenko, Eur. Phys. J. D 61, 117–130 (2011)ADSCrossRefGoogle Scholar
  79. V.P. Silin, A.A. Rukhadse, Electromagnetic Properties of plasmas(in Russ.) (Atomisdat, Moskva, 1961)Google Scholar
  80. J. Taruna, J. Piekarewicz, M.A. Pèrez-Garcìa, Virtues and flaws of the Pauli potential, J. Phys. A: Math. Theor. 41(3) (2008)Google Scholar
  81. W. Thirring, Lehrbuch der Mathematischen Physik. 4 Quantenmechanik großer Systeme Springer 1980Google Scholar
  82. I.A. Valuev, I.V. Morozov, Extension of the wave packet molecular dynamics. J. Phys. Conf. Series 653, 012153 (2015)CrossRefGoogle Scholar
  83. D.N. Zubarev, V. Morozov, G. Röpke, Statistical Mechanics of Nonequilibrium Processes, vol. 1–2 (Wiley-VCH, Weinheim, 1997)Google Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Werner Ebeling
    • 1
    Email author
  • Vladimir E. Fortov
    • 2
  • Vladimir Filinov
    • 3
  1. 1.Institut für PhysikHumboldt Universität BerlinBerlinGermany
  2. 2.Russian Academy of SciencesMoscowRussia
  3. 3.Joint Institute for High TemperaturesRussian Academy of SciencesMoscowRussia

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