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Some Rigorous Results for the Anderson Model

Simon, Barry and Taylor, Michael and Wolff, Tom (1985) Some Rigorous Results for the Anderson Model. Physical Review Letters, 54 (14). pp. 1589-1592. ISSN 0031-9007. http://resolver.caltech.edu/CaltechAUTHORS:20180417-104515007

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Abstract

We discuss two results for the Anderson model of random quantum Hamiltonians: (1) smoothness of the density of states in the one-dimensional model, even in many cases where the potential distribution is not smooth; and (2) a criterion for localization which, among other consequences, implies that certain estimates of Fröhlich and Spencer yield a dense point spectrum for the multidimensional model at large randomness or large energies.


Item Type:Article
Related URLs:
URLURL TypeDescription
https://doi.org/10.1103/PhysRevLett.54.1589DOIArticle
ORCID:
AuthorORCID
Simon, Barry0000-0003-2561-8539
Additional Information:© 1985 American Physical Society. (Received 10 January 1985) Two of us (B.S. and M.T.) would like to thank T. Spencer for valuable discussions related to theorem 1, and one of us (B.S.) would like to thank S. Kotani and T. Spencer for useful discussions related to theorems 2 and 3. This research was partially supported by the National Science Foundation under Grants No. MCS-81-20833, No. MCS-82-01766A01, and No. DMS-84-07099.
Funders:
Funding AgencyGrant Number
NSFMCS-81-20833
NSFMCS-82-01766A01
NSFDMS-84-07099
Classification Code:PACS numbers: 71.55.Jv, 71.20.+c
Record Number:CaltechAUTHORS:20180417-104515007
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20180417-104515007
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:85900
Collection:CaltechAUTHORS
Deposited By: George Porter
Deposited On:17 Apr 2018 23:16
Last Modified:17 Apr 2018 23:16

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