Efficiency of quantum and classical transport on graphs

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 73, Issue 6, 2006, Pages

  Mülken, Oliver ^a   Blumen, Alexander ^a  

^a UNIVERSITY OF FREIBURG   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EIGENVALUES AND EIGENFUNCTIONS; GRAPH THEORY; MATHEMATICAL MODELS; NUMERICAL METHODS; STATISTICAL MECHANICS; TREES (MATHEMATICS);

DENSITY OF STATES (DOS); FINITE TREE GRAPHS; QUANTUM TRANSPORT; STRETCHED EXPONENTIAL LAW;

QUANTUM THEORY;

EID: 33745160430     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.73.066117     Document Type: Article

References (33)

1. J. M. Ziman, Principles of the Theory of Solids (Cambridge University Press, Cambridge, 1972);
2. N. W. Ashcroft and N. D. Mermin, Solid State Physics (Saunders College, Philadelphia, 1976).
3. V. M. Kenkre and P. Reineker, Exciton Dynamics in Molecular Crystals and Aggregates (Springer, Berlin, 1982);
4. A. S. Davydov, Theory of Molecular Excitons (McGraw-Hill, New York, 1962).
5. R. Albert and A.-L. Barabási, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.74.47 74, 47 (2002);
6. S. N. Dorogovtsev and J. F. F. Mendes, Adv. Phys. ADPHAH 0001-8732 10.1080/00018730110112519 51, 1079 (2002).
7. D. A. McQuarrie, Quantum Chemistry (Oxford University Press, Oxford, 1983).
8. M. Doi and S. F. Edwards, The Theory of Polymer Dynamics (Oxford University Press, Oxford, 1998).
9. N. van Kampen, Stochastic Processes in Physics and Chemistry (North-Holland, Amsterdam, 1990);
10. G. H. Weiss, Aspects and Applications of the Random Walk (North-Holland, Amsterdam, 1994).
11. M. L. Mehta, Random Matrices (Academic Press, San Diego, 1991);
12. B. Bollobás, Random Graphs (Academic Press, Orlando, 1985).
13. E. P. Wigner, Ann. Math. ANMAAH 0003-486X 10.2307/1970079 62, 548 (1955).
14. E. Farhi and S. Gutmann, Phys. Rev. A PLRAAN 1050-2947 10.1103/PhysRevA.58.915 58, 915 (1998).
15. O. Mülken and A. Blumen, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.71.016101 71, 016101 (2005).
16. O. Mülken, V. Bierbaum, and A. Blumen, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.2179427 124, 124905 (2006);
17. A. Blumen, V. Bierbaum, and O. Mülken, Physica A PHYADX 0378-4371 (to be published).
18. A. J. Bray and G. J. Rodgers, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.38.11461 38, 11461 (1988);
19. A. Blumen, A. Volta, A. Jurjiu, and T. Koslowski, J. Lumin. JLUMA8 0022-2313 111, 327 (2005).
20. I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and Products (Academic Press, New York 1980);
21. Handbook of Mathematical Functions, edited by, M. Abramowitz, and, I. A. Stegun, (Dover, New York, 1972).
22. S. Alexander, J. Bernasconi, W. R. Schneider, and R. Orbach, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.53.175 53, 175 (1981);
23. S. Alexander and R. Orbach, J. Phys. (Paris), Lett. JPSLBO 0302-072X 43, L625 (1982);
24. J. Klafter and A. Blumen, J. Chem. Phys. JCPSA6 0021-9606 10.1063/1.446743 80, 875 (1984);
25. S. Havlin and D. Ben-Avraham, Adv. Phys. ADPHAH 0001-8732 10.1080/00018738700101072 36, 695 (1987).
26. R. Ketzmerick, G. Petschel, and T. Geisel, Phys. Rev. Lett. PRLTAO 0031-9007 10.1103/PhysRevLett.69.695 69, 695 (1992);
27. J. Vidal, R. Mosseri, and J. Bellissard, J. Phys. A JPHAC5 0305-4470 32, 2361 (1999).
28. R. Monasson, Eur. Phys. J. B EPJBFY 1434-6028 10.1007/s100510051038 12, 555 (1999);
29. S. Jespersen, I. M. Sokolov, and A. Blumen, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.62.4405 62, 4405 (2000);
30. S. Jespersen and A. Blumen, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.62.6270 62, 6270 (2000).
31. B. J. Kim, H. Hong, and M. Y. Choi, Phys. Rev. B PRBMDO 0163-1829 10.1103/PhysRevB.68.014304 68, 014304 (2003).
32. O. Mülken and A. Blumen, Phys. Rev. E PLEEE8 1063-651X 10.1103/PhysRevE.71.036128 71, 036128 (2005).
33. P. W. Anderson, Rev. Mod. Phys. RMPHAT 0034-6861 10.1103/RevModPhys.50. 191 50, 191 (1978).