- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Physical Review E

Export citation

Export citation

Choose format for download:

Download Citation
  • Access by Xinjiang University

Kinetic equation approach to the description of quantum surface diffusion: Non-Markovian effects versus jump dynamics

V. V. Ignatyuk

  • Institute for Condensed Matter Physics, 1 Svientsitskii Street, 79011 Lviv, Ukraine

PDF

Phys. Rev. E 80, 041133 – Published 30 October, 2009

DOI: https://doi.org/10.1103/PhysRevE.80.041133

Abstract

We consider surface diffusion of a single particle, which performs site-to-site underbarrier hopping, fulfils intrasite motion between the ground and the first-excited states within a quantum well, and interacts with surface phonons. We obtain a chain of quantum-kinetic equations for one-particle distribution functions and nonequilibrium hopping probabilities. The generalized diffusion coefficients are derived, and the generic non-Markovian diffusion equation is written down both for the infinite lattice model and in the continuous media limit. In the latter case, the one-particle distribution function obeys the telegrapher’s equation, which could give us a nonmonotonic behavior of the intermediate distribution functions at large spatial gradients. In a weak-coupling limit, if the energy of level splitting is comparable with the temperature, there are also pronounced oscillations of the generalized diffusion coefficients. The recrossing/multiple crossing phenomena, a problem of long tails of the generalized diffusion coefficients, as well as a mapping into the next- to the nearest-neighbors hopping regime, are discussed.

View figure in article

Article Text

References (39)

  1. S. Miret-Artés and E. Pollak, J. Phys.: Condens. Matter 17, S4133 (2005).
  2. I. C. da Cunha Lima, A. Troper, and S. C. Ying, Phys. Rev. B 41, 11798 (1990).
  3. T. Ala-Nissila, R. Ferrando, and S. C. Ying, Adv. Phys. 51, 949 (2002).
  4. P. Ohresser, H. Bulou, S. S. Dhesi, C. Boeglin, B. Lazarovits, E. Gaudry, I. Chado, J. Faerber, and F. Scheurer, Phys. Rev. Lett. 95, 195901 (2005).
  5. R. Martínez-Casado, A. Sanz, and S. Miret-Artés, J. Chem. Phys. 129, 184704 (2008).
  6. P. D. Reilly, R. A. Harris, and K. B. Whaley, Phys. Rev. B 47, 5721 (1993).
  7. R. F. Kiefl, R. Kadono, J. H. Brewer, G. M. Luke, H. K. Yen, M. Celio, and E. J. Ansaldo, Phys. Rev. Lett. 62, 792 (1989).
  8. R. Kadono, J. Imazato, T. Matsuzaki, K. Nishiyama, K. Nagamine, T. Yamazaki, D. Richter, and J.-M. Welter, Phys. Rev. B 39, 23 (1989).
  9. D. N. Zubarev, V. G. Morozov, and G. Röpke, Statistical Mechanics of Nonequilibrium Processes (Fizmatlit, Moscow, 2002).
  10. V. G. Morozov (unpublished).
  11. R. Ferrando, R. Spadacini, G. E. Tommei, and G. Caratti, Physica A 195, 506 (1993).
  12. R. Ferrando, R. Spadacini, G. E. Tommei, and G. Caratti, Surf. Sci. 311, 411 (1994).
  13. G. Wahnström, K. Haug, and H. Metiu, Chem. Phys. Lett. 148, 158 (1988).
  14. D. H. Zhang, J. C. Light, and Soo-Y. Lee, J. Chem. Phys. 111, 5741 (1999).
  15. P. Hänggi, P. Talkner, and M. Borkovec, Rev. Mod. Phys. 62, 251 (1990).
  16. E. Pollak and P. Talkner, Phys. Rev. E 51, 1868 (1995).
  17. T. Taniike and K. Yamashita, Chem. Phys. 304, 159 (2004).
  18. K. A. Fichthorn and P. G. Balan, J. Chem. Phys. 101, 10028 (1994).
  19. P. P. Kostrobii, Yu. K. Rudavskii, V. V. Ignatyuk, and M. V. Tokarchuk, Condens. Matter Phys. 6, 409 (2003).
  20. P. D. Reilly, R. A. Harris, and K. B. Whaley, J. Chem. Phys. 95, 8599 (1991).
  21. P. D. Reilly, R. A. Harris, and K. B. Whaley, J. Chem. Phys. 97, 6975 (1992).
  22. Yu. Kagan and M. I. Klinger, J. Phys. C 7, 2791 (1974).
  23. W. Ho, J. Chem. Phys. 117, 11033 (2002).
  24. I. M. Mryglod, I. P. Omelyan, and M. V. Tokarchuk, Mol. Phys. 84, 235 (1995).
  25. I. M. Mryglod, I. P. Omelyan, and R. Folk, J. Phys.: Condens. Matter 15, S83 (2003).
  26. S. Cazzato, T. Scopigno, T. Bryk, I. Mryglod, and G. Ruocco, Phys. Rev. B 77, 094204 (2008).
  27. V. V. Ignatyuk, I. M. Mryglod, and M. V. Tokarchuk, Low Temp. Phys. 25, 857 (1999).
  28. D. Dou, J. Casas-Vazquez, and G. Lebon, Extended Irreversible Thermodynamics (Springer-Verlag, Berlin, 1998).
  29. V. V. Ignatyuk, M. V. Tokarchuk, and P. P. Kostrobij, Condens. Matter Phys. 9, 55 (2006).
  30. V. Pouthier and J. C. Light, J. Chem. Phys. 113, 1204 (2000).
  31. Z. Chvoj, J. Phys.: Condens. Matter 12, 2135 (2000).
  32. R. Kubo, M. Toda, and N. Hashitsume, Statistical Physics II (Springer-Verlag, Berlin, 1991).
  33. T. Holstein, Ann. Phys. 8, 325 (1959).
  34. C. P. Flynn and A. M. Stoneham, Phys. Rev. B 1, 3966 (1970).
  35. T. R. Mattsson and G. Wahnström, Phys. Rev. B 56, 14944 (1997).
  36. H. Okuyama, T. Ueda, T. Aruga, and M. Nishijima, Phys. Rev. B 63, 233403 (2001).
  37. S. C. Badescu, S. C. Ying, and T. Ala-Nissila, Phys. Rev. Lett. 86, 5092 (2001).
  38. Yu. Kagan and L. A. Maksimov, Zh. Eksp. Teor. Fiz. 65, 622 (1973) [Sov. Phys. JETP 38, 307 (1974)].
  39. Yu. Kagan and N. V. Prokofiev, Zh. Eksp. Teor. Fiz. 96, 2209 (1989) [Sov. Phys. JETP 69, 1250 (1989)].

Outline

Information

Phys. Rev. E 80, 041133– Published 30 October, 2009
  • Received 23 May 2009

© 2009 American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation