World Scientific
Skip main navigation

Cookies Notification

We use cookies on this site to enhance your user experience. By continuing to browse the site, you consent to the use of our cookies. Learn More
×

System Upgrade on Tue, May 28th, 2024 at 2am (EDT)

Existing users will be able to log into the site and access content. However, E-commerce and registration of new users may not be available for up to 12 hours.
For online purchase, please visit us again. Contact us at customercare@wspc.com for any enquiries.

LOCALIZATION AT WEAK DISORDER: SOME ELEMENTARY BOUNDS

    https://doi.org/10.1142/S0129055X94000419Cited by:135 (Source: Crossref)

    An elementary proof is given of localization for linear operators H = Ho + λV, with Ho translation invariant, or periodic, and V (·) a random potential, in energy regimes which for weak disorder (λ → 0) are close to the unperturbed spectrum σ (Ho). The analysis is within the approach introduced in the recent study of localization at high disorder by Aizenman and Molchanov [4]; the localization regimes discussed in the two works being supplementary. Included also are some general auxiliary results enhancing the method, which now yields uniform exponential decay for the matrix elements <0|P[a,b]exp(−itH)|x> of the spectrally filtered unitary time evolution operators, with [a, b] in the relevant range.

    Dedicated to E. H. Lieb, in celebration of his sixtieth birthday