Communications in Mathematical Physics - Volume 233 by M. Aizenman (Chief Editor)

By M. Aizenman (Chief Editor)

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Math. Phys. : Localization of one dimensional, continuum, BernoulliAnderson models. Duke Math. J. : Operators with singular continuous spectrum: IV. Hausdorff dimension, rank-one perturbations and localization. J. d’Analyse Math. : Absence of Localization in Random-Dimer Model. Phys. Rev. Lett. : Noncommuting random products. Trans. Am. Math. Soc. : Bootstrap Multiscale Analysis and Localization in Random Media. Commun. Math. Phys. : Spectral properties of quantum diffusion on discrete lattices.

We note that H2,2 is a Hilbert space with norm · 2,2 given by ϕ 2 2,2 = Tr k ϕ, ak∗ [ak , ϕ] + Tr ϕ 2 = [ak , ϕ] 2 2 + ϕ 2 2 , (2) k where · 2 denotes the Hilbert-Schmidt norm. e. matrices with only finitely many non-zero entries) in the standard harmonic oscillator basis form a dense subspace of H2,2 . The variational equation of the functional (1) is d 2 k=1 ak∗ , [ak , ϕ] = −θV (ϕ) . (3) We regard this equation as an equality between two Hilbert-Schmidt operators on L2 Rd . Thus, a solution ϕ to Eq.

Spectral properties of quantum diffusion on discrete lattices. Europhys. , 10, 95–100 (1989); On an estimate concerning quantum diffusion in the presence of a fractal spectrum. Europhys. Lett. : Intermittent lower bound on quantum diffusion. Lett. Math. Phys. : Delocalization in polymer models. Preprint. : Global bounds for the Lyapunov exponent and the integrated density of states of random Schr¨odinger operators in one dimension. J. Phys. : Electronic structure and vertical transport in random dimer GaAs-Alx Ga1−x As superlattices.

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