Mixed lower bounds for quantum transport

Journal of Functional Analysis

Volumn 197, Issue 1, 2003, Pages 247-282

  Tcheremchantsev, Serguei ^a  

^a UNIVERSITÉ D'ORLÉANS   (France)

Author keywords

Generalized eigenfunctions; Lower bounds; Multifractal dimensions; Quantum transport; Spectral measure

Indexed keywords

EID: 0037428622     PISSN: 00221236     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0022-1236(02)00066-6     Document Type: Article

References (27)

1. J.M. Barbaroux, J.M. Combes, R. Montcho, Remarks on the relation between quantum dynamics and fractal spectra, J. Math. Anal. Appl. 213 (1997) 698-722.
2. J.M. Barbaroux, F. Germinet, S. Tcheremchantsev, Non-linear variation of diffusion exponents in quantum dynamics, C.R. Acad. Sci. Paris 330 (2000) 409-414.
3. J.M. Barbaroux, F. Germinet, S. Tcheremchantsev, Fractal dimensions and the phenomenon of intermittency in quantum dynamics, Duke Math. J. 110 (1) (2001) 161-193.
4. J.M. Barbaroux, F. Germinet, S. Tcheremchantsev, Generalized fractal dimensions: equivalencies and basic properties, J. Math. Pures Appl. 80 (2001) 977-1012.
5. J.M. Barbaroux, H. Schulz-Baldes, Anomalous quantum transport in the presence of self-similar spectra, Ann. Inst. Henri Poincaré 71 (N5) (1999) 1-21.
6. J.M. Barbaroux, S. Tcheremchantsev, Universal lower bounds in quantum dynamics, J. Funct. Anal. 168 (1999) 327-354.
7. M. Christ, A. Kiselev, Y. Last, Approximate eigenvectors and spectral theory, Proceedings of UABGIT 99 International Conference on Differential Equations and Mathematical Physics.
8. J.M. Combes, Connection between quantum dynamics and spectral properties of time evolution operators, in: W.F. Ames, E.M. Harrell, J.V. Herod (Eds.), Differential Equations with Applications to Mathematical Physics, Academic Press, Boston, 1993, pp. 59-69.
9. J.M. Combes, G. Mantica, Fractal dimensions and quantum evolution associated with sparse Jacobi matrices, in: S. Graffi, A. Martinez (Eds.), Long time behaviour of classical and quantum systems. Series on Concrete and Appl. Math. World Scientific, Singapore, 2001, Vol. 1, 107-123.
10. R. Del Rio, S. Jitomirskaya, Y. Last, B. Simon, Operators with singular continuous spectrum IV: Hausdorff dimensions, rank one perturbations and localization, J. Anal. Math. 69 (1996) 153-200.
11. K.J. Falconer, Techniques in Fractal Geometry, Wiley, New York, 1997.
12. F. Germinet, A. Kiselev, S. Tcheremchantsev, Transfer matrices and transport for 1D Schrödinger operators with singular spectrum, in preparation.
13. F. Germinet, S. Tcheremchantsev, Generalized fractal dimensions of compactly supported measures on the negative axis, submitted for publication.
14. I. Guarneri, Spectral properties of quantum diffusion on discrete lattices, Europhys. Lett. 10 (1989) 95-100.
15. I. Guarneri, On an estimate concerning quantum diffusion in the presence of a fractal spectrum, Europhys. Lett. 21 (1993) 729-733.
16. I. Guarneri, H. Schulz-Baldes, Lower bounds on wave-packet propagation by packing dimensions of spectral measures, Math. Phys. Electron J. 5 (1999) 1.
17. I. Guarneri, H. Schulz-Baldes, Intermittent lower bound on quantum diffusion, Lett. Math. Phys. 49 (1999) 317-324.
18. Y. Heurteaux, Estimations de la dimension inférieure et de la dimension supérieure des mesures, Ann. Inst. Henri Poincaré 34 (3) (1998) 309-338.
19. S. Jitomirskaya, Y. Last, Power law subordinacy and singular spectra I: half line operators, Acta Math. 183 (1999) 171-189.
20. A. Kiselev, Y. Last, Solutions, spectrum and dynamics for Schrödinger operators on infinite domains, Duke Math. J. 102 (2000) 125-150.
21. Y. Last, Quantum dynamics and decomposition of singular continuous spectra, J. Funct. Anal. 142 (1996) 406-445.
22. G. Mantica, Quantum intermittency in almost periodic systems derived from their spectral properties, Physica D 103 (1997) 576-589.
23. G. Mantica, Wave propagation in Almost periodic structures, Physica D 109 (1997) 113-127.
24. M. Reed, B. Simon, Methods of modern mathematical physics IV: Analysis of operators, Academic Press, New York, 1978.
25. p -norms of the Borel transform and the decomposition of measures, Proc. Amer. Math. Soc. 123 (1995) 3749-3755.
26. S. Tcheremchantsev, How to prove dynamical localization, Comm. Math. Phys. 221 (2001) 27-56.
27. S. Tcheremchantsev, in preparation.