Skip to main content
SpringerLink
Log in

Nonlocal Quantum Kinetic Theory and the Formation of Correlations

  • Chapter
  • First Online:
Many-body Approaches at Different Scales

  • 868 Accesses

Abstract

The quantum version of the Boltzmann equation remains still the basis of modern transport theories. Extensions become necessary for transient-time effects like the femtosecond response and for strongly correlated systems. At short time scales higher correlations have no time to develop yet and femto-second laser excitation of collective modes in semiconductors as well as quenches of cold atoms in optical lattices can be described even analytically by fluctuations of the meanfield. For plasma systems exposed to a sudden switching, analytical results are available from the time-dependent Fermi’s Golden Rule in good agreement with the results of two-time Green’s functions solving the Kadanoff and Baym equation. At later times when correlations develop, a kinetic equation of nonlocal and non-instantaneous character unifies the achievements of the transport in dense quantum gases with the Landau theory of quasiclassical transport in Fermi systems. The numerical solution is not more expensive than solving the Boltzmann equation since large cancellations in the off-shell motion appear which are hidden usually in non-Markovian behaviors. The quasiparticle drift of Landau’s equation is connected with a dissipation governed by a nonlocal and non-instant scattering integral in the spirit of Enskog corrections. These corrections are expressed in terms of shifts in space and time that characterize non-locality of the scattering process. In this way quantum transport is possible to recast into a quasi-classical picture. The balance equations for the density, momentum, energy and entropy include besides quasiparticle also the correlated two-particle contributions beyond the Landau theory. The medium effects on binary collisions are shown to mediate the latent heat, i.e., an energy conversion between correlation and thermal energy.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

References

  1. S. Trotzky, Y. Chen, A. Flesch, I.P. McCulloch, U. Schöllwock, J. Eisert, I. Bloch, Nat. Phys. 8(4), 325 (2012). https://doi.org/10.1038/nphys2232

  2. R. Huber, F. Tauser, A. Brodschelm, A. Leitenstorfer, Phys. Status Solidi B 234(1), 207 (2002). https://doi.org/10.1002/1521-3951(200211)234:1<207::AID-PSSB207>3.0.CO;2-Z

  3. R. Huber, C. Kübler, S. Tübel, A. Leitenstorfer, Q.T. Vu, H. Haug, F. Köhler, M.C. Amann, Phys. Rev. Lett. 94, 027401 (2005). https://doi.org/10.1103/PhysRevLett.94.027401

  4. V.M. Axt, T. Kuhn, Rep. Prog. Phys. 67(4), 433 (2004). https://doi.org/10.1088/0034-4885/67/4/R01

  5. K. Morawetz, P. Lipavský, M. Schreiber, Phys. Rev. B 72, 233203 (2005). https://doi.org/10.1103/PhysRevB.72.233203

  6. K. Morawetz, Phys. Rev. B 90, 075303 (2014). https://doi.org/10.1103/PhysRevB.90.075303

  7. L. Bányai, Q.T. Vu, B. Mieck, H. Haug, Phys. Rev. Lett. 81, 882 (1998). https://doi.org/10.1103/PhysRevLett.81.882

  8. P. Gartner, L. Bányai, H. Haug, Phys. Rev. B 60, 14234 (1999). https://doi.org/10.1103/PhysRevB.60.14234

  9. Q.T. Vu, H. Haug, Phys. Rev. B 62, 7179 (2000). https://doi.org/10.1103/PhysRevB.62.7179

  10. M. Kira, S.W. Koch, Phys. Rev. Lett. 93, 076402 (2004). https://doi.org/10.1103/PhysRevLett.93.076402

  11. L. Boltzmann, Wien. Ber. 66, 275 (1872)

    Google Scholar 

  12. S. Chapman, T.C. Cowling, The mathematical theory of nonuniform gases (Cambridge University Press, Cambridge, 1939)

    MATH  Google Scholar 

  13. D. Enskog, Kinetiske Theorie der Vorgänge in mäßig verdünnten Gasen (Almqvist & Wiksells, Uppsala, 1917)

    MATH  Google Scholar 

  14. J.G. Kirkwood, J. Chem. Phys. 14(3), 180 (1946). https://doi.org/10.1063/1.1724117

  15. N.N. Bogoliubov, J. Phys. (USSR) 10, 256 (1946), Translated in [125]

    Google Scholar 

  16. I. Prigogine, Nonequilibrium Statistical Mechanics (Wiley, New York, 1962)

    MATH  Google Scholar 

  17. N.N. Bogolyubov, K.P. Gurov, Zh Eksp, Teor. Fiz. 17, 614 (1947)

    Google Scholar 

  18. H. Mori, S. Ono, Progr. Theor. Phys. 8(3), 327 (1952). https://doi.org/10.1143/ptp/8.3.327

  19. G. Baym, C. Pethick, Landau Fermi Liquid Theory (Wiley, New York, 1991)

    Book  Google Scholar 

  20. S. Chapman, T.C. Cowling, The Mathematical Theory of Nonuniform Gases, 3rd edn. (Cambridge University Press, Cambridge, 1990)

    MATH  Google Scholar 

  21. F.J. Alexander, A.L. Garcia, B.J. Alder, Phys. Rev. Lett. 74, 5212 (1995). https://doi.org/10.1103/PhysRevLett.74.5212

  22. L. Waldmann, Z. Naturforsch. A 15, 19 (1960)

    Google Scholar 

  23. R.F. Snider, J. Math. Phys. 5(11), 1580 (1964). https://doi.org/10.1063/1.1931191

  24. K. Bärwinkel, Z. Naturforsch. A 24, 38 (1969)

    Google Scholar 

  25. M.W. Thomas, R.F. Snider, J. Stat. Phys. 2(1), 61 (1970). https://doi.org/10.1007/BF01009711

  26. R.F. Snider, B.C. Sanctuary, J. Chem. Phys. 55(4), 1555 (1971). https://doi.org/10.1063/1.1676279

  27. J.C. Rainwater, R.F. Snider, J. Chem. Phys. 65(11), 4958 (1976). https://doi.org/10.1063/1.432972

  28. R. Balescu, Equilibrium and Nonequilibrium Statistical Mechanis (Wiley, New York, 1975)

    MATH  Google Scholar 

  29. J.A. McLennan, Introduction to nOnequilibrium Statistical Mechanics (Prentice Hall, Englewood Cliffs, 1989)

    Google Scholar 

  30. F. Laloë, J. Phys. (Paris) 50(14), 1851 (1989). https://doi.org/10.1051/jphys:0198900500140185100

  31. P.J. Nacher, G. Tastevin, F. Laloë, J. Phys. (Paris) 50(14), 1907 (1989). https://doi.org/10.1051/jphys:0198900500140190700

  32. D. Loss, J. Stat. Phys. 61(1), 467 (1990). https://doi.org/10.1007/BF01013976

  33. M. De Haan, Physica A 170(3), 571 (1991). https://doi.org/10.1016/0378-4371(91)90007-Y

  34. F. Laloë, W.J. Mullin, J. Stat. Phys. 59(3), 725 (1990). https://doi.org/10.1007/BF01025848

  35. P.J. Nacher, G. Tastevin, F. Laloë, Ann. Phys. (Berlin) 503(1–3), 149 (1991). https://doi.org/10.1002/andp.19915030114

  36. P.J. Nacher, G. Tastevin, F. Laloë, J. Phys. I (Paris) 1(2), 181 (1991). https://doi.org/10.1051/jp1:1991124

  37. R.F. Snider, J. Stat. Phys. 80(5), 1085 (1995). https://doi.org/10.1007/BF02179865

  38. R.F. Snider, W.J. Mullin, F. Laloë, Physica A 218(1), 155 (1995). https://doi.org/10.1016/0378-4371(95)00124-P

  39. V. Špička, P. Lipavský, K. Morawetz, Phys. Rev. B 55, 5084 (1997). https://doi.org/10.1103/PhysRevB.55.5084

  40. V. Špička, P. Lipavský, K. Morawetz, Phys. Rev. B 55, 5095 (1997). https://doi.org/10.1103/PhysRevB.55.5095

  41. V. Špička, P. Lipavský, K. Morawetz, Phys. Lett. A 240(3), 160 (1998). https://doi.org/10.1016/S0375-9601(98)00061-9

  42. P. Lipavský, K. Morawetz, V. Špička, Ann. Phys. Fr. 26(1), 1 (2001). https://doi.org/10.1051/anphys:200101001

  43. K. Morawetz, P. Lipavský, V. Špička, Ann. Phys. 294(2), 135 (2001). https://doi.org/10.1006/aphy.2001.6197

  44. K. Morawetz, P. Lipavský, V. Špička, N.H. Kwong, Phys. Rev. C 59, 3052 (1999). https://doi.org/10.1103/PhysRevC.59.3052

  45. I.B. Levinson, Zh. Eksp. Teor. Fiz. 57, 660 (1969), [Sov. Phys. JETP 30, 362 (1970)]

    Google Scholar 

  46. H.S. Köhler, K. Morawetz, Phys. Rev. C 64, 024613 (2001). https://doi.org/10.1103/PhysRevC.64.024613

  47. K. Morawetz, V. Špička, P. Lipavský, Phys. Lett. A 246(3), 311 (1998). https://doi.org/10.1016/S0375-9601(98)00356-9

  48. G. Zwicknagel, C. Toeppfer, P.G. Reinhard, in Physics of Strongly Coupled Plasmas, ed. by W.D. Kraeft, M. Schlanges, H. Haberland, T. Bornath (World Scientific, Singapore, 1995), p. 45

    Google Scholar 

  49. K. Morawetz, H.S. Köhler, Eur. Phys. J. A 4(3), 291 (1999). https://doi.org/10.1007/s100500050233

  50. A. Flesch, M. Cramer, I.P. McCulloch, U. Schollwöck, J. Eisert, Phys. Rev. A 78, 033608 (2008). https://doi.org/10.1103/PhysRevA.78.033608

  51. N. Syassen, D.M. Bauer, M. Lettner, T. Volz, D. Dietze, J.J. García-Ripoll, J.I. Cirac, G. Rempe, S. Dürr, Science 320(5881), 1329 (2008). https://doi.org/10.1126/science.1155309

  52. N.D. Mermin, Phys. Rev. B 1, 2362 (1970). https://doi.org/10.1103/PhysRevB.1.2362

  53. A.K. Das, J. Phys. F 5(11), 2035 (1975). https://doi.org/10.1088/0305-4608/5/11/015

  54. K. Morawetz, Phys. Rev. E 88, 022148 (2013). https://doi.org/10.1103/PhysRevE.88.022148

  55. W. Jones, N.H. March, Theoretical Solid-State Physics. Non-equilibrium and Disorder, vol. 2 (Dover, New York, 1986). ISBN 9780486650166

    Google Scholar 

  56. K. El Sayed, S. Schuster, H. Haug, F. Herzel, K. Henneberger, Phys. Rev. B 49, 7337 (1994). https://doi.org/10.1103/PhysRevB.49.7337

  57. K. Morawetz (ed.), Nonequilibrium Physics at Short Time Scales (Formation of Correlations (Springer, Berlin, 2004)

    Google Scholar 

  58. R.A. Craig, Ann. Phys. 40(3), 416 (1966). https://doi.org/10.1016/0003-4916(66)90143-6

  59. B. Bezzerides, D.F. DuBois, Phys. Rev. 168, 233 (1968). https://doi.org/10.1103/PhysRev.168.233

  60. H. Stolz, R. Zimmermann, Phys. Status Solidi B 94(1), 135 (1979). https://doi.org/10.1002/pssb.2220940114

  61. D. Kremp, W.D. Kraeft, A.J.D. Lambert, Physica A 127(1), 72 (1984). https://doi.org/10.1016/0378-4371(84)90120-1

  62. M. Schmidt, G. Röpke, Phys. Status Solidi B 139(2), 441 (1987). https://doi.org/10.1002/pssb.2221390212

  63. H.S. Köhler, R. Malfliet, Phys. Rev. C 48, 1034 (1993). https://doi.org/10.1103/PhysRevC.48.1034

  64. V. Špička, P. Lipavský, Phys. Rev. B 52, 14615 (1995). https://doi.org/10.1103/PhysRevB.52.14615

  65. K. Bärwinkel, in Proceedings of the 14th International Symposium on Rarefied Gas Dynamics, ed. by H. Oguchi (University of Tokyo Press, Tokyo, 1984). ISBN 9784130681094

    Google Scholar 

  66. R.F. Snider, J. Stat. Phys. 63(3), 707 (1991). https://doi.org/10.1007/BF01029207

  67. N.H. March, R. Santamaria, Int. J. Quantum Chem. 39(4), 585 (1991). https://doi.org/10.1002/qua.560390405

  68. N.H. March, Phys. Rev. A 56, 1025 (1997). https://doi.org/10.1103/PhysRevA.56.1025

  69. H.S. Köhler, Phys. Rev. C 51, 3232 (1995). https://doi.org/10.1103/PhysRevC.51.3232

  70. M. Schmidt, G. Röpke, H. Schulz, Ann. Phys. 202(1), 57 (1990). https://doi.org/10.1016/0003-4916(90)90340-T

  71. K. Morawetz, G. Roepke, Phys. Rev. E 51, 4246 (1995). https://doi.org/10.1103/PhysRevE.51.4246

  72. P. Lipavský, V. Špička, K. Morawetz, Phys. Rev. E 59, R1291 (1999). https://doi.org/10.1103/PhysRevE.59.R1291

  73. V. Špička, K. Morawetz, P. Lipavský, Phys. Rev. E 64, 046107 (2001). https://doi.org/10.1103/PhysRevE.64.046107

  74. K. Morawetz, V. Špička, P. Lipavský, G. Kortemeyer, C. Kuhrts, R. Nebauer, Phys. Rev. Lett. 82, 3767 (1999). https://doi.org/10.1103/PhysRevLett.82.3767

  75. K. Morawetz, Phys. Rev. C 62, 044606 (2000). https://doi.org/10.1103/PhysRevC.62.044606

  76. K. Morawetz, M. Płoszajczak, V.D. Toneev, Phys. Rev. C 62, 064602 (2000). https://doi.org/10.1103/PhysRevC.62.064602

  77. K. Morawetz, P. Lipavský, J. Normand, D. Cussol, J. Colin, B. Tamain, Phys. Rev. C 63, 034619 (2001). https://doi.org/10.1103/PhysRevC.63.034619

  78. K. Morawetz, Phys. Rev. E 96, 032106 (2017). https://doi.org/10.1103/PhysRevE.96.032106

  79. K. Morawetz, Interacting Systems far From Equilibrium (Quantum Kinetic Theory (Oxford University Press, Oxford, 2017)

    MATH  Google Scholar 

  80. J. Tõke, B. Lott, S.P. Baldwin, B.M. Quednau, W.U. Schröder, L.G. Sobotka, J. Barreto, R.J. Charity, D.G. Sarantites, D.W. Stracener, R.T. de Souza, Phys. Rev. Lett. 75, 2920 (1995). https://doi.org/10.1103/PhysRevLett.75.2920

  81. S.P. Baldwin, B. Lott, B.M. Szabo, B.M. Quednau, W.U. Schröder, J. Tõke, L.G. Sobotka, J. Barreto, R.J. Charity, L. Gallamore, D.G. Sarantites, D.W. Stracener, R.T. de Souza, Phys. Rev. Lett. 74, 1299 (1995). https://doi.org/10.1103/PhysRevLett.74.1299

  82. W. Skulski, B. Djerroud, D.K. Agnihotri, S.P. Baldwin, J. Tõke, X. Zhao, W.U. Schröder, L.G. Sobotka, R.J. Charity, J. Dempsey, D.G. Sarantites, B. Lott, W. Loveland, K. Aleklett, Phys. Rev. C 53, R2594 (1996). https://doi.org/10.1103/PhysRevC.53.R2594

  83. S. Chattopadhyay, Phys. Rev. C 52, R480 (1995). https://doi.org/10.1103/PhysRevC.52.R480

  84. S. Chattopadhyay, Phys. Rev. C 53, R1065 (1996). https://doi.org/10.1103/PhysRevC.53.R1065

  85. E. Suraud, S. Ayik, J. Stryjewski, M. Belkacem, Nucl. Phys. A 519(1), 171 (1990). https://doi.org/10.1016/0375-9474(90)90624-U

  86. S. Ayik, C. Grégoire, Nucl. Phys. A 513(1), 187 (1990). https://doi.org/10.1016/0375-9474(90)90348-P

  87. J. Randrup, B. Remaud, Nucl. Phys. A 514(2), 339 (1990). https://doi.org/10.1016/0375-9474(90)90075-W

  88. S. Ayik, E. Suraud, M. Belkacem, D. Boilley, Nucl. Phys. A 545(1), 35 (1992). https://doi.org/10.1016/0375-9474(92)90444-O

  89. M. Colonna, G.F. Burgio, P. Chomaz, M. Di Toro, J. Randrup, Phys. Rev. C 47, 1395 (1993). https://doi.org/10.1103/PhysRevC.47.1395

  90. M. Colonna, P. Chomaz, J. Randrup, Nucl. Phys. A 567(3), 637 (1994). https://doi.org/10.1016/0375-9474(94)90029-9

  91. P. Reinhard, E. Suraud, S. Ayik, Ann. Phys. 213(1), 204 (1992). https://doi.org/10.1016/0003-4916(92)90289-X

  92. P. Reinhard, E. Suraud, Ann. Phys. 216(1), 98 (1992). https://doi.org/10.1016/0003-4916(52)90043-2

  93. R. Balian, M. Vénéroni, Ann. Phys. 164(2), 334 (1985). https://doi.org/10.1016/0003-4916(85)90020-X

  94. H. Flocard, Ann. Phys. 191(2), 382 (1989). https://doi.org/10.1016/0003-4916(89)90323-0

  95. T. Troudet, D. Vautherin, Phys. Rev. C 31, 278 (1985). https://doi.org/10.1103/PhysRevC.31.278

  96. The INDRA Collaboration, F. Bocage, J. Colin, M. Louvel, G. Auger, C. Bacri, N. Bellaize, B. Borderie, R. Bougault, R. Brou, P. Buchet, J.L. Charvet, A. Chbihi, D. Cussol, R. Dayras, N.D. Cesare, A. Demeyer, D. Doré, D. Durand, J.D. Frankland, E. Galichet, E. Genouin-Duhamel, E. Gerlic, D. Guinet, P. Lautesse, J.L. Laville, J.F. Lecolley, R. Legrain, N.L. Neindre, O. Lopez, A.M. Maskay, L. Nalpas, A.D. Nguyen, M. Pârlog, J. Péter, E. Plagnol, M.F. Rivet, E. Rosato, F. Saint-Laurent, S. Salou, J. Steckmeyer, M. Stern, G. Tăbăcaru, B. Tamain, O. Tirel, L. Tassan-Got, E. Vient, M. Vigilante, C. Volant, J.P. Wieleczko, C.L. Brun, A. Genoux-Lubain, G. Rudolf, L. Stuttgé, Nucl. Phys. A 676(1), 391 (2000). https://doi.org/10.1016/S0375-9474(00)00193-7

  97. The INDRA Collaboration, E. Plagnol, J. Łukasik, G. Auger, C.O. Bacri, N. Bellaize, F. Bocage, B. Borderie, R. Bougault, R. Brou, P. Buchet, J.L. Charvet, A. Chbihi, J. Colin, D. Cussol, R. Dayras, A. Demeyer, D. Doré, D. Durand, J.D. Frankland, E. Galichet, E. Genouin-Duhamel, E. Gerlic, D. Guinet, P. Lautesse, J.L. Laville, J.F. Lecolley, R. Legrain, N. Le Neindre, O. Lopez, M. Louvel, A.M. Maskay, L. Nalpas, A.D. Nguyen, M. Pârlog, J. Péter, M.F. Rivet, E. Rosato, F. Saint-Laurent, S. Salou, J.C. Steckmeyer, M. Stern, G. Tăbăcaru, B. Tamain, L. Tassan-Got, O. Tirel, E. Vient, C. Volant, J.P. Wieleczko, Phys. Rev. C 61, 014606 (1999). https://doi.org/10.1103/PhysRevC.61.014606

  98. The INDRA Collaboration, J. Lecolley, E. Galichet, D.C.R. Guinet, R. Bougault, F. Gulminelli, G. Auger, C. Bacri, F. Bocage, B. Borderie, R. Brou, P. Buchet, J. Charvet, A. Chbihi, J. Colin, D. Cussol, R. Dayras, A. Demeyer, D. Doré, D. Durand, J.D. Frankland, E. Genouin-Duhamel, E. Gerlic, P. Lautesse, J. Laville, T. Lefort, R. Legrain, N. LeNeindre, O. Lopez, M. Louvel, A. Maskay, L. Nalpas, A.D. Nguyen, M. Parlog, J. Péter, E. Plagnol, M. Rivet, E. Rosato, F. Saint-Laurent, J. Steckmeyer, M. Stern, G. Tăbăcaru, B. Tamain, L. Tassan-Got, O. Tirel, E. Vient, C. Volant, J.P. Wieleczko, Nucl. Instr. Meth. Phys. Res. A 441(3), 517 (2000). https://doi.org/10.1016/S0168-9002(99)00831-1

  99. V. Ambegaokar, in Superconductivity, vol. 1, ed. by R.D. Parks (Dekker, New York, 1969), chap. 5, p. 259

    Google Scholar 

  100. K. Morawetz, P. Lipavský, J. Koláček, E.H. Brandt, M. Schreiber, Int. J. Mod. Phys. B 21(13n14), 2348 (2007). https://doi.org/10.1142/S0217979207043713

  101. G. Rickayzen, J. Phys. C 2(7), 1334 (1969). https://doi.org/10.1088/0022-3719/2/7/325

  102. J. Bok, J. Klein, Phys. Rev. Lett. 20, 660 (1968). https://doi.org/10.1103/PhysRevLett.20.660

  103. T.D. Morris, J.B. Brown, Physica 55, 760 (1971). https://doi.org/10.1016/0031-8914(71)90330-2

  104. P. Lipavský, J. Koláček, J.J. Mareš, K. Morawetz, Phys. Rev. B 65, 012507 (2001). https://doi.org/10.1103/PhysRevB.65.012507

  105. H.F. Budd, J. Vannimenus, Phys. Rev. Lett. 31, 1218 (1973). https://doi.org/10.1103/PhysRevLett.31.1218

  106. K. Morawetz, N.H. March, R.H. Squire, Phys. Lett. A 372(10), 1707 (2008). https://doi.org/10.1016/j.physleta.2007.10.025

  107. P. Lipavský, K. Morawetz, J. Koláček, J.J. Mareš, E.H. Brandt, M. Schreiber, Phys. Rev. B 69, 024524 (2004). https://doi.org/10.1103/PhysRevB.69.024524

  108. P. Lipavský, K. Morawetz, J. Koláček, J.J. Mareš, E.H. Brandt, M. Schreiber, Phys. Rev. B 71, 024526 (2005). https://doi.org/10.1103/PhysRevB.71.024526

  109. P. Lipavský, K. Morawetz, J. Koláček, J.J. Mareš, E.H. Brandt, M. Schreiber, Phys. Rev. B 70, 104518 (2004). https://doi.org/10.1103/PhysRevB.70.104518

  110. K. Kumagai, K. Nozaki, Y. Matsuda, Phys. Rev. B 63, 144502 (2001). https://doi.org/10.1103/PhysRevB.63.144502

  111. P. Lipavský, J. Koláček, K. Morawetz, E.H. Brandt, Phys. Rev. B 66, 134525 (2002). https://doi.org/10.1103/PhysRevB.66.134525

  112. P. Lipavský, J. Koláček, K. Morawetz, E.H. Brandt, T.J. Yang (eds.), Bernoulli Potential in Superconductors, vol. 733, Lecture Notes in Physics (Springer, Berlin, 2008). ISBN 9783540734550. https://doi.org/10.1007/978-3-540-73456-7

  113. C. Amovilli, N.H. March, Phys. Rev. A 69(5), 054302 (2004). https://doi.org/10.1103/PhysRevA.69.054302

  114. N.H. March, G.G.N. Angilella, R. Pucci, Int. J. Mod. Phys. B 27, 1330021 (2013). https://doi.org/10.1142/S0217979213300211

  115. Y.B. Ivanov, J. Knoll, D.N. Voskresensky, Phys. Atomic Nuclei 66(10), 1902 (2003). https://doi.org/10.1134/1.1619502

  116. A. Peshier, Phys. Rev. D 70, 034016 (2004). https://doi.org/10.1103/PhysRevD.70.034016

  117. W.M. Alberico, S. Chiacchiera, H. Hansen, A. Molinari, M. Nardi, Eur. Phys. J. A 38(1), 97 (2008). https://doi.org/10.1140/epja/i2008-10648-8

  118. C. Moustakidis, V.P. Psonis, K. Chatzisavvas, C.P. Panos, S.E. Massen, Phys. Rev. E 81, 011104 (2010). https://doi.org/10.1103/PhysRevE.81.011104

  119. E. Suraud, P.G. Reinhard, New J. Phys. 16(6), 063066 (2014). https://doi.org/10.1088/1367-2630/16/6/063066

  120. S.K. Baur, E.J. Mueller, Phys. Rev. A 82, 023626 (2010). https://doi.org/10.1103/PhysRevA.82.023626

  121. J.G. Kirkwood, E. Monroe, Boggs. J. Chem. Phys. 10(6), 394 (1942). https://doi.org/10.1063/1.1723737

  122. B.B. Laird, A.D.J. Haymet, Phys. Rev. A 45, 5680 (1992). https://doi.org/10.1103/PhysRevA.45.5680

  123. D. Nayar, C. Chakravarty, Phys. Chem. Chem. Phys. 15, 14162 (2013). https://doi.org/10.1039/C3CP51114F

  124. M. Puoskari, Physica A 272(3), 509 (1999). https://doi.org/10.1016/S0378-4371(99)00262-9

  125. J.A. Hernando, L. Blum, Phys. Rev. E 62, 6577 (2000). https://doi.org/10.1103/PhysRevE.62.6577

  126. D. de Boer, G.E. Uhlenbeck (eds.), Studies in Statistical Mechanics, vol. 1 (North-Holland, Amsterdam, 1962)

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Münster University of Applied Sciences, Stegerwaldstrasse 39, 48565, Steinfurt, Germany

    K. Morawetz

  2. International Institute of Physics (IIP), Campus Universitário Lagoa Nova, Natal, 59078-970, Brazil

    K. Morawetz

  3. Max-Planck-Institute for the Physics of Complex Systems, 01187, Dresden, Germany

    K. Morawetz

Authors
  1. K. Morawetz
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to K. Morawetz .

Editor information

Editors and Affiliations

  1. Dipartimento di Fisica e Astronomia, Università di Catania, Catania, Italy

    G.G.N Angilella

  2. Dipartimento di Chimica e Chimica Industriale, Università di Pisa, Pisa, Italy

    C. Amovilli

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer International Publishing AG, part of Springer Nature

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Morawetz, K. (2018). Nonlocal Quantum Kinetic Theory and the Formation of Correlations. In: Angilella, G., Amovilli, C. (eds) Many-body Approaches at Different Scales. Springer, Cham. https://doi.org/10.1007/978-3-319-72374-7_25

Download citation

Publish with us

Policies and ethics

Search

Navigation