Vertically extended Frenkel-Kontorova model: A real space renormalization group study

Physical Review B - Condensed Matter and Materials Physics

Volumn 72, Issue 12, 2005, Pages

  Rodríguez Laguna, Javier ^a   Santalla, Silvia N ^b  

^a UNIVERSIDAD COMPLUTENSE DE MADRID   (Spain)

^b UNIVERSIDAD CARLOS III DE MADRID   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 29744443512     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.72.125412     Document Type: Article

References (36)

1. O. M. Braun and Y. S. Kivshar, The Frenkel-Kontorova Model (Springer, New York, 2004).
2. P. M. Chaikin and T. C. Lubensky, Principles of Condensed Matter Physics (Cambridge University Press, Cambridge, U.K., 1995).
3. J. Frenkel and T. Kontorova, Phys. Z. Sowjetunion PHZSAL 0369-9811 13, 1 (1938);
4. J. Frenkel and T. Kontorova, J. Phys. (USSR) JOPYA6 0368-3400 1, 137 (1939).
5. F. C. Frank and J. H. van der Merwe, Proc. R. Soc. London, Ser. A PRLAAZ 1364-5021 198, 205 (1949);
6. F. C. Frank and J. H. van der Merwe, Proc. R. Soc. London, Ser. A PRLAAZ 1364-5021 198, 216 (1949);
7. F. C. Frank and J. H. van der Merwe, Proc. R. Soc. London, Ser. A PRLAAZ 1364-5021 200, 125 (1949);
8. F. C. Frank and J. H. van der Merwe, Proc. R. Soc. London, Ser. A PRLAAZ 1364-5021 201, 261 (1950).
9. W. Chou and B. Griffiths, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.34.6219 34, 9, 6219 (1986).
10. S. Aubry, Physica D PDNPDT 0167-2789 10.1016/0167-2789(83)90129-X 7, 240 (1983);
11. S. Aubry, J. Phys. C JPSOAW 0022-3719 10.1088/0022-3719/16/13/012 16, 2497 (1983);
12. S. Aubry, J. Phys. (Paris) JOPQAG 0302-0738 44, 147 (1983).
13. M. Peyrard and S. Aubry, J. Phys. C JPSOAW 0022-3719 10.1088/0022-3719/ 16/9/005 16, 1593 (1983).
14. O. Biham and D. Mukamel, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.39.5326 39, 5326 (1989).
15. S. C. Ying, Phys. Rev. B PLRBAQ 0556-2805 10.1103/PhysRevB.3.4160 3, 4160 (1971).
16. J. E. Sacco, A. Widom, and J. B. Sokoloff, J. Stat. Phys. JSTPBS 0022-4715 10.1007/BF01011165 21, 497 (1979).
17. O. M. Braun and Y. S. Kivshar, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.44.7694 44, 7694 (1991).
18. P. Bak, D. Mukamel, J. Villain, and K. Wentowsaka, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.19.1610 19, 1610 (1979).
19. I. Markov and A. Trayanov, J. Phys. C JPSOAW 0022-3719 10.1088/0022-3719/21/13/012 21, 2475 (1988);
20. I. Markov and A. Trayanov, J. Phys.: Condens. Matter JCOMEL 0953-8984 10.1088/0953-8984/2/33/009 2, 6965 (1990).
21. S. Little and A. Zangwill, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.46.7981 46, 7981 (1992);
22. S. Little and A. Zangwill, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.49.16659 49, 16659 (1994).
23. W. Chou, J. Stat. Phys. JSTPBS 0022-4715 10.1007/BF01022992 50, 207 (1988).
24. Density Matrix Renormalization, edited by, I. Peschel,,, X. Wang,,, M. Kaulke, and, K. Hallberg, (Springer, New York, 1998).
25. D. Bimberg, M. Grundmann, and N. N. Ledentsov, Quantum Dot Heterostructures (Wiley, New York, 1999).
26. I. Daruka and A.-L. Barabási, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.79.3708 79, 3708 (1997).
27. V. A. Shchukin and D. Bimberg, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.71.1125 71, 1125 (1999).
28. A.-L. Barabási, Appl. Phys. Lett. APPLAB 0003-6951 10.1063/1.118920 70, 2565 (1997).
29. C. Ratsch and A. Zangwill, Surf. Sci. SUSCAS 0039-6028 10.1016/0039-6028(93)90250-N 293, 123 (1993).
30. E. Korutcheva, A. M. Turiel, and I. Markov, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.61.16890 61, 24, 16890 (2000).
31. S. N. Santalla, J. Rodríguez-Laguna, C. Kanyinda-Malu, and R. M. de la Cruz, poster at the conference Trends in Nanotechnology, Salamanca (Spain), 2003. Available at http://moria.uc3m.es/~noema/investigacion/ semiatomistico.html
32. R. A. Cunninghame-Green, Minimax Algebra (Springer, New York, 1979).
33. W. H. Press, Numerical Recipes in C (Cambridge University Press, Cambridge, U.K., 1997).
34. M. A. Martín-Delgado, J. Rodríguez-Laguna, and G. Sierra, Nucl. Phys. B NUPBBO 0550-3213 10.1016/S0550-3213(01)00073-6 601, 569 (2001)
35. See talks from the Density Matrix Renormalization Meeting, Leiden, August 2004 at http://dmrg.info/workshop.
36. Other potentials with similar features, such as the Morse potential or the one proposed by Markov (Ref.), give the same qualitative physics.