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Theoretical Approaches to Quantum Monte Carlo Methods

  • 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 substantially extend the analysis of the previous chapters to two-component partially ionized Coulomb systems with positive and negative charges and a mass ratio M varying between one and two thousand. While low values of the mass ratio M are directly relevant for semiconductors, we do not consider any special solid state properties here, but focus on the fundamental aspects of Coulomb correlations in two-component plasmas which depend on M. In this way, we may cover the case of mass-symmetric plasmas on the one hand and the case of heavy-ion plasmas on the other as special cases.

References

  1. B.J. Berne, G. Ciccotti, D.F. Coker (eds.), Classical and Quantum Dynamics of Condensed Phase (World Scientific, Singapore, 1998)Google Scholar
  2. K. Binder, G. Cicotti (eds.), The Monte Carlo and Molecular Dynamics of Condensed Matter Systems (SIF, Bologna, 1996)Google Scholar
  3. M. Bonitz, D. Semkat (eds.), Introduction to Computational Methods for Many Body Systems (Rinton Press, Princeton, 2006)zbMATHGoogle Scholar
  4. M. Bonitz et al., J. Phys. B: Condensed. Matter 8, 6057 (1996)ADSGoogle Scholar
  5. J. Bosse, K.N. Pathak, G.S. Singh, Phys. Rev. E 84, 042101 (2011)ADSCrossRefGoogle Scholar
  6. R.E. Caflisch, Acta Numerica 7, 1 (1998)ADSCrossRefGoogle Scholar
  7. D. Ceperley, J. Stat. Phys. 63, 1237 (1991)ADSCrossRefGoogle Scholar
  8. D. Ceperley, Phys. Rev. Let. 69, 331 (1992)ADSCrossRefGoogle Scholar
  9. D.M. Ceperley, Rev. Mod. Phys. 65, 279 (1995)ADSCrossRefGoogle Scholar
  10. D.M. Ceperley, in The Monte Carlo and Molecular Dynamics of Condensed Matter Systems, ed. by K. Binder, G. Cicotti (SIF, Bologna, 1996), pp. 447–482Google Scholar
  11. S.A. Chin, Phys. Lett. A 226, 344 (1997)ADSMathSciNetCrossRefGoogle Scholar
  12. S.A. Chin, Phys. Rev. E 91, 031301 (2015). (R)Google Scholar
  13. T. Dornheim, S. Groth, A. Filinov, M. Bonitz, New J. Phys. 17, 073017 (2015)ADSCrossRefGoogle Scholar
  14. T. Dornheim, T. Schoof, S. Groth, A. Filinov, M. Bonitz, J. Chem. Phys. 143, 204101 (2015)ADSCrossRefGoogle Scholar
  15. T. Dornheim, S. Groth, T. Sjostrom, F.D. Malone, W.M.C. Foulkes, M. Bonitz, Phys. Rev. Lett. 117, 156403 (2016)ADSCrossRefGoogle Scholar
  16. C. Dorso, S. Duarte, J. Randrup, Phys. Lett B 188, 287 (1987); 215, 611 (1988)Google Scholar
  17. C. Dorso, S. Duarte, J. Randrup, Excited electron dynamics modeling of warm matter, Phys. Lett. B 188, 287 (1987); 215, 611 (1988)Google Scholar
  18. J.L. DuBois , B.J. Alder, E.W. Brown (2014), arXiv: 1409.3262
  19. W. Ebeling, F. Schautz, Phys. Rev. E 56, 3498 (1997)ADSCrossRefGoogle Scholar
  20. W. Ebeling, A. Filinov, M. Bonitz, V. Filinov, T. Pohl, J. Phys. A Math. Gen. 39, 4309 (2006)ADSCrossRefGoogle Scholar
  21. R. Egger, W. Häusler, C.H. Mak, H. Grabert, Phys. Rev. Lett. 82, 3320 (1999)ADSCrossRefGoogle Scholar
  22. A.V. Eletskii, A.N. Starostin, M.D. Taran, Physics-Uspekhi 48, 281 (2005)ADSCrossRefGoogle Scholar
  23. A.V. Emelianov, A.V. Eremin, E.E. YuV Petrushevich, A.N. Sivkova, M.D. Starostin, V.E.Fortov Taran, ETP Lett. 94(7), 530 (2011)ADSGoogle Scholar
  24. R.P. Feynman, A.R. Hibbs, Quantum Mechanics and Path Integrals (McGraw-Hill, New York, 1965)zbMATHGoogle Scholar
  25. A. Filinov, M. Bonitz, YuE Lozovik, J. Phys. A Math. Gen. 36, 5957 (2003)ADSCrossRefGoogle Scholar
  26. A. Filinov, V. Golubnychiy, M. Bonitz, W. Ebeling, J.W. Dufty, Phys. Rev. E 70, 46411 (2004)ADSCrossRefGoogle Scholar
  27. V. Filinov, J. Phys. A Math. Gen. 34, 1665 (2001)ADSCrossRefGoogle Scholar
  28. V. Filinov, P. Thomas, I. Varga, T. Meier, M. Bonitz, V. Fortov, S. Koch, Phys. Rev. B 65, 165124 (2002)ADSCrossRefGoogle Scholar
  29. V. Filinov, M. Bonitz, P. Levashov, V. Fortov, W. Ebeling, M. Schlanges, Contrib. Plasma Phys. 43, 290 (2003)ADSCrossRefGoogle Scholar
  30. V. Filinov, H. Fehske, M. Bonitz, V.E. Fortov, P.R. Levashov, Phys. Rev. E 75, 36401 (2007)ADSCrossRefGoogle Scholar
  31. V. Filinov, V. Fortov, M. Bonitz, Zh Moldabekov, Phys. Rev. E 91, 033108 (2015)ADSCrossRefGoogle Scholar
  32. V.S. Filinov, High Temp. 13, 1065 (1975); 14, 225 (1976)Google Scholar
  33. V.S. Filinov, J. Phys. A 34, 1665 (2001)ADSCrossRefGoogle Scholar
  34. V.S. Filinov, High Temp. 52, 615 (2014)CrossRefGoogle Scholar
  35. V.S. Filinov, M. Bonitz, V.E. Fortov, JETP Lett. 72, 245 (2000)ADSCrossRefGoogle Scholar
  36. V.S. Filinov, M. Bonitz, V.E. Fortov, JETP Lett. 72, 245 (2000); Pisma v ZhETF, 72, 361 (2000)Google Scholar
  37. V.S. Filinov, V.E. Fortov, M. Bonitz, D. Kremp, Phys. Lett. A 274, 228 (2000)ADSCrossRefGoogle Scholar
  38. V.S. Filinov, P.R. Levashov, V.E. Fortov, M. Bonitz, in Progress in Nonequilibrium Greens Functions, ed. by M. Bonitz (World Scientific Publ, Singapore, 2000), p. 513CrossRefGoogle Scholar
  39. V.S. Filinov, V.E. Fortov, M. Bonitz, P.R. Levashov, JETP Lett. 74, 384 2001); [Pisma v ZhETF 74, 422 (2001)]Google Scholar
  40. V.S. Filinov, M. Bonitz, W. Ebeling, V.E. Fortov, Plasma Phys. Control. Fusion 43, 743 (2001)ADSCrossRefGoogle Scholar
  41. V.S. Filinov, M. Bonitz, P.R. Levashov, V.E. Fortov, W. Ebeling, M. Schlanges, S.W. Koch, J. Phys. A Math. Gen. 36, 6069 (2003)ADSCrossRefGoogle Scholar
  42. V.S. Filinov, M. Bonitz, V.E. Fortov, W. Ebeling, P. Levashov, M. Schlanges, Contrib. Plasma Phys. 44, 388 (2004)ADSCrossRefGoogle Scholar
  43. V. Filinov, H. Fehske, M. Bonitz, V.E. Fortov, P.R. Levashov, Phys. Rev. E 75, 36401 (2007)ADSCrossRefGoogle Scholar
  44. V.M. Galitskii, V.V. Yakimets, Zh Eksp, Teor. Fiz. 51, 957 (1966). Sov. Phys. JETP 24, 637 (1967)ADSGoogle Scholar
  45. S. Groth, T. Schoof, T. Dornheim, M. Bonitz, Phys. Rev. B 93, 085102 (2016)ADSCrossRefGoogle Scholar
  46. W.K. Hastings, Biometrika 57(1), 97 (1970)MathSciNetCrossRefGoogle Scholar
  47. M.F. Herman, J. Chem. Phys. 76, 29495 (1982). A similar energy estimator has been derived by Herman, but that result neglects the spin statistics and does not contain the correct noninteracting limitGoogle Scholar
  48. K. Huang, Statistical Mechanics (Wiley, New York, 1963)Google Scholar
  49. R. Imada, J. Phys. Soc. Jpn. 53, 2861 (1984). However, we have found that this approach is not adequate for thermodynamic propertiesGoogle Scholar
  50. G. Kalman (ed.), Strongly Coupled Coulomb Systems (Pergamon Press, New York, 1998)Google Scholar
  51. G. Kelbg, Ann. Physik 12, 219 (1963); 13, 354; 14, 394 (1964); W. Ebeling, H.J. Homann, G. Kelbg, Beitr. Plasmaphys. 7, 233 (1967)Google Scholar
  52. J.C. Kimball, J. Phys. A Math. Gen. 8(9), 1513 (1975)ADSCrossRefGoogle Scholar
  53. D. Klakow, C. Toepffer, P.-G. Reinhard, Phys. Lett. A 192, 55 (1994). J. Chem. Phys. 101, 10766 (1994)ADSCrossRefGoogle Scholar
  54. Yu.L. Klimontovich, Statistical Theory of Open Systems (in Russian), Vol. I (1995); II (1999); III (Janus, Moscow, 2001)Google Scholar
  55. I.V. Kochetov, A.P. Napartovich, A.N. YuV Petrushevich, M.D.Taran Starostin, High Temp. 54(4), 563 (2016)CrossRefGoogle Scholar
  56. W.D. Kraeft, M. Schlanges (eds.), in Proceedings of the International Conference on Strongly Coupled Plasmas, World Scientific, Singapore (1996)Google Scholar
  57. G.P. Lepage, VEGAS: An Adaptive Multi-dimensional Integration Program, Cornell preprint CLNS 80–447 (1980)Google Scholar
  58. A.S. Larkin, V.S. Filinov, V.E. Fortov, Contrib. Plasma Phys. 56, 187 (2016)ADSCrossRefGoogle Scholar
  59. A.S.Larkin, V.S. Filinov, V.E. Fortov (2017), arXiv:1702.04091 [physics.plasm-ph]
  60. A.P. Lyubartsev, J. Phys. A Math. Gen. 38, 6659 (2005)ADSMathSciNetCrossRefGoogle Scholar
  61. J.M. McMahon, M.A. Morales, C. Pierleoni, D. Ceperley, Rev. Mod. Phys. 84, 1607 (2012)ADSCrossRefGoogle Scholar
  62. N. Metropolis, A. Rosenbluth, M. Rosenbluth, A. Teller, E. Teller, J. Chem. Phys. 21, 1087 (1953)ADSCrossRefGoogle Scholar
  63. B. Militzer, R. Pollock, Phys. Rev. E 61, 3470 (2000)ADSCrossRefGoogle Scholar
  64. M.E.J. Newman, G.T. Barkema, Monte Carlo Methods in Statistical Physics (Oxford University Press, USA, 1999)zbMATHGoogle Scholar
  65. J. Ortner, F. Schautz, W. Ebeling, Phys. Rev. E 56, 4665–4670 (1997)ADSCrossRefGoogle Scholar
  66. W.H. Press, G.R. Farrar, Comput. Phys. 4, 190 (1998)ADSCrossRefGoogle Scholar
  67. C. Robert, G. Casella, Monte Carlo Statistical Methods (Springer, New York, 2004)CrossRefzbMATHGoogle Scholar
  68. G.O. Roberts, A. Gelman, W.R. Gilks, Ann. Appl. Prob. 7(1), 110 (1997)CrossRefGoogle Scholar
  69. D. Ruelle, Statistical Mechanics: Rigorous Results (World Scientific Publishing Co (Pte. Ltd, Singapore, 1999)CrossRefGoogle Scholar
  70. T. Schoof, M. Bonitz, A.V. Filinov, D. Hochstuhl, J.W. Dufty, Contrib. Plasma Phys. 51(8), 687 (2011)ADSCrossRefGoogle Scholar
  71. T. Schoof, S. Groth, J. Vorberger, M. Bonitz, Phys. Rev. Lett. 115, 130402 (2015)ADSCrossRefGoogle Scholar
  72. T. Schoof, S. Groth, M. Bonitz, Contrib. Plasma Phys. 55, 136 (2015)ADSCrossRefGoogle Scholar
  73. M. Suzuki, Phys. Lett. A 146, 319 (1990)ADSMathSciNetCrossRefGoogle Scholar
  74. M. Suzuki, Phys. Lett. A 201, 425 (1995)ADSMathSciNetCrossRefGoogle Scholar
  75. A.N. Starostin, Yu.V. Petrushevich, Abstracts of Scientific-Coordination Workshop on Non-Ideal Plasma Physics, Moscow, Russia, 7–8 Dec 2016, http://www.ihed.ras.ru/npp2016/program/
  76. A.N. Starostin, A.B. Mironov, N.L. Aleksandrov, N.J. Fischc, R.M. Kulsrudc, Physica A 305, 287 (2002)ADSCrossRefGoogle Scholar
  77. M. Takahashi, M. Imada, J. Phys. Soc. Jpn. 53, 963–3765 (1984)ADSCrossRefGoogle Scholar
  78. V.I. Tatarskii, Sov. Phys. Uspekhi 26, 311 (1983)ADSCrossRefGoogle Scholar
  79. S. Weinzierl, NIKHEF Theory Group (2000), arXiv:hep-ph/0006269v1
  80. E.P. Wigner, Phys. Rev. 40, 749 (1932)ADSCrossRefGoogle Scholar
  81. V.M. Zamalin, G.E. Norman, V.S. Filinov, The Monte Carlo Method in Statistical Thermodynamics (Nauka, Moscow, 1977). (in Russian)Google Scholar
  82. B.V. Zelener, G.E. Norman, V.S. Filinov, Perturbation Theory and Pseudopotential in Statistical Thermodynamics (Nauka, Moscow, 1981). (in Russian)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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