Table of Contents
Journal of Operators
Volume 2014 (2014), Article ID 373754, 9 pages
http://dx.doi.org/10.1155/2014/373754
Research Article

On Partial Charge Transfer Processes in Multiparticle Systems on Graphs

Département De Mathématiques, Université De Reims, Moulin De La Housse, B.P. 1039, 51687 Cedex 2 Reims, France

Received 28 June 2014; Accepted 16 September 2014; Published 21 October 2014

Academic Editor: Lingju Kong

Copyright © 2014 Victor Chulaevsky. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. P. W. Anderson, “Absence of diffusion in certain random lattices,” Physical Review, vol. 109, no. 5, pp. 1492–1505, 1958. View at Publisher · View at Google Scholar · View at Scopus
  2. D. M. Basko, I. L. Aleiner, and B. L. Altshuler, “Metal-insulator transition in a weakly interacting many-electron system with localized single-particle states,” Annals of Physics, vol. 321, no. 5, pp. 1126–1205, 2005. View at Google Scholar
  3. I. V. Gornyi, A. D. Mirlin, and D. G. Polyakov, “Interacting electrons in disordered wires: anderson localization and low-T transport,” Physical Review Letters, vol. 95, Article ID 206603, 2005. View at Publisher · View at Google Scholar · View at Scopus
  4. V. Chulaevsky and Y. Suhov, “Eigenfunctions in a two-particle Anderson tight binding model,” Communications in Mathematical Physics, vol. 289, no. 2, pp. 701–723, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  5. V. Chulaevsky and Y. Suhov, “Multi-particle Anderson localisation: induction on the number of particles,” Mathematical Physics, Analysis and Geometry, vol. 12, no. 2, pp. 117–139, 2009. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  6. M. Aizenman and S. Warzel, “Localization bounds for multiparticle systems,” Communications in Mathematical Physics, vol. 290, no. 3, pp. 903–934, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  7. V. Chulaevsky, A. Boutet de Monvel, and Y. Suhov, “Dynamical localization for a multi-particle model with an alloy-type external random potential,” Nonlinearity, vol. 24, no. 5, pp. 1451–1472, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  8. A. Klein and S. T. Nguyen, “The bootstrap multiscale analysis of the multi-particle Anderson model,” Journal of Statistical Physics, vol. 151, no. 5, pp. 938–973, 2013. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  9. A. Klein and S. T. Nguyen, “Bootstrap multiscale analysis and localization for multi-particle continuous Anderson Hamiltonians,” 2013, http://arxiv.org/abs/1311.4220.
  10. M. Fauser and S. Warzel, “Multiparticle localization for disordered systems on continuous space via the fractional moment method,” http://arxiv.org/abs/1402.5832.
  11. F. Wegner, “Bounds on the density of states in disordered systems,” Zeitschrift für Physik B Condensed Matter and Quanta, vol. 44, no. 1-2, pp. 9–15, 1981. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  12. V. Chulaevsky, “On the regularity of the conditional distribution of the sample mean,” http://arxiv.org/abs/1304.6913.
  13. J. Fröhlich and T. Spencer, “Absence of diffusion in the Anderson tight binding model for large disorder or low energy,” Communications in Mathematical Physics, vol. 88, no. 2, pp. 151–184, 1983. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  14. M. Aizenman and S. Molchanov, “Localization at large disorder and at extreme energies: an elementary derivation,” Communications in Mathematical Physics, vol. 157, no. 2, pp. 245–278, 1993. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  15. V. Chulaevsky and Y. Suhov, “Wegner bounds for a two-particle tight binding model,” Communications in Mathematical Physics, vol. 283, no. 2, pp. 479–489, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  16. V. Chulaevsky and Y. Suhov, “Anderson localisation for an interacting two-particle quantum system on Z,” http://arxiv.org/abs/0705.0657.