Abstract
We study random Anderson Hamiltonians in Euclidean spaces with a long-range particle-media interaction potential
Acknowledgements
It is a pleasure to thank GĂŒnter Stolz and Ivan VeseliÄ for stimulating discussions of the long-range models. I also thank the team of the Isaac Newton Institute (Cambridge, UK) and the organizers of the program Periodic and Ergodic Spectral Problems (INI, 2015) for the warm hospitality and the opportunity to work in the unique atmosphere of the Institute, where a part of the present work has been completed.
References
[1] V. Chulaevsky, From fixed-energy localization analysis to dynamical localization: An elementary path, J. Stat. Phys. 154 (2014), no. 6, 1391â1429. 10.1007/s10955-014-0937-7Suche in Google Scholar
[2] V. Chulaevsky, Exponential scaling limit of the single-particle Anderson model via adaptive feedback scaling, J. Stat. Phys. 162 (2016), no. 3, 603â614. 10.1007/s10955-015-1438-zSuche in Google Scholar
[3] J.-M. Combes, P. D. Hislop and F. Klopp, An optimal Wegner estimate and its application to the global continuity of the integrated density of states for random Schrödinger operators, Duke Math. J. 140 (2007), no. 3, 469â498. 10.1215/S0012-7094-07-14032-8Suche in Google Scholar
[4] J. M. Combes and L. Thomas, Asymptotic behaviour of eigenfunctions for multiparticle Schrödinger operators, Comm. Math. Phys. 34 (1973), 251â270. 10.1007/BF01646473Suche in Google Scholar
[5] D. Damanik and P. Stollmann, Multi-scale analysis implies strong dynamical localization, Geom. Funct. Anal. 11 (2001), no. 1, 11â29. 10.1007/PL00001666Suche in Google Scholar
[6]
A. Elgart, M. Tautenhahn and I. VeseliÄ,
Localization via fractional moments for models on
[7] J. Fröhlich, F. Martinelli, E. Scoppola and T. Spencer, Constructive proof of localization in the Anderson tight binding model, Comm. Math. Phys. 101 (1985), no. 1, 21â46. 10.1007/BF01212355Suche in Google Scholar
[8] F. Germinet and A. Klein, Bootstrap multiscale analysis and localization in random media, Comm. Math. Phys. 222 (2001), no. 2, 415â448. 10.1007/s002200100518Suche in Google Scholar
[9] W. Kirsch, An invitation to random Schrödinger operators, Random Schrödinger Operators, Panor. SynthĂšses 25, Soc. Math. France, Paris (2008), 1â119. Suche in Google Scholar
[10] W. Kirsch, P. Stollmann and G. Stolz, Anderson localization for random Schrödinger operators with long range interactions, Comm. Math. Phys. 195 (1998), no. 3, 495â507. 10.1007/s002200050399Suche in Google Scholar
[11] I. M. Lifshitz, Energy spectrum structure and quantum states of disordered condensed systems, Soviet Phys. Uspekhi 7 (1965), 549â573. 10.1070/PU1965v007n04ABEH003634Suche in Google Scholar
[12] B. Simon and T. Wolff, Singular continuous spectrum under rank one perturbations and localization for random Hamiltonians, Comm. Pure Appl. Math. 39 (1986), no. 1, 75â90. 10.1002/cpa.3160390105Suche in Google Scholar
[13] P. Stollmann, Wegner estimates and localization for continuum Anderson models with some singular distributions, Arch. Math. (Basel) 75 (2000), no. 4, 307â311. 10.1007/s000130050508Suche in Google Scholar
[14] P. Stollmann, Caught by Disorder, Prog. Math. Phys. 20, BirkhÀuser, Boston, 2001. 10.1007/978-1-4612-0169-4Suche in Google Scholar
[15] H. von Dreifus and A. Klein, A new proof of localization in the Anderson tight binding model, Comm. Math. Phys. 124 (1989), no. 2, 285â299. 10.1007/BF01219198Suche in Google Scholar
[16] H. von Dreifus and A. Klein, Localization for random Schrödinger operators with correlated potentials, Comm. Math. Phys. 140 (1991), no. 1, 133â147. 10.1007/BF02099294Suche in Google Scholar
[17] F. Wegner, Bounds on the density of states in disordered systems, Z. Phys. B 44 (1981), no. 1â2, 9â15. 10.1007/BF01292646Suche in Google Scholar
© 2019 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- Wegner estimate for discrete Schrödinger operators with Gaussian random potentials
- A general maximum principle for mean-field forward-backward doubly stochastic differential equations with jumps processes
- BSDEs with right upper-semicontinuous reflecting obstacle and stochastic Lipschitz coefficient
- Fast decay of eigenfunction correlators in long-range continuous random alloys
- Inverting weak random operators
- The limit G-Law for the solutions of systems of linear algebraic equations with independent random coefficients under the G-Lindeberg condition
Artikel in diesem Heft
- Frontmatter
- Wegner estimate for discrete Schrödinger operators with Gaussian random potentials
- A general maximum principle for mean-field forward-backward doubly stochastic differential equations with jumps processes
- BSDEs with right upper-semicontinuous reflecting obstacle and stochastic Lipschitz coefficient
- Fast decay of eigenfunction correlators in long-range continuous random alloys
- Inverting weak random operators
- The limit G-Law for the solutions of systems of linear algebraic equations with independent random coefficients under the G-Lindeberg condition