Bootstrap Multiscale Analysis and Localization¶in Random Media

Germinet, François; Klein, Abel

doi:10.1007/s002200100518

Cited by 217 publications

(445 citation statements)

References 34 publications

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“…[18]. Using a "bootstrap" approach in which the output of one multi-scale analysis serves as the input for another, Germinet and Klein have shown that this probability is O(e −L α ) with any α < 1 throughout the multi-scale regime [32]. A posteriori, we conclude from Theorem 1.2 that this bound may be replaced by O(e −νL ) with ν > 0 for the operators considered here.…”

Section: Theorem 51 Let H Be a Random Schrödinger Operator Which Samentioning

confidence: 70%

Moment analysis for localization in random Schrödinger operators

et al. 2005

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Abstract. We study localization effects of disorder on the spectral and dynamical properties of Schrödinger operators with random potentials. The new results include exponentially decaying bounds on the transition amplitude and related projection kernels, including in the mean. These are derived through the analysis of fractional moments of the resolvent, which are finite due to the resonance-diffusing effects of the disorder. The main difficulty which has up to now prevented an extension of this method to the continuum can be traced to the lack of a uniform bound on the Lifshitz-Krein spectral shift associated with the local potential terms. The difficulty is avoided here through the use of a weak-L 1 estimate concerning the boundary-value distribution of resolvents of maximally dissipative operators, combined with standard tools of relative compactness theory.

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Section: Theorem 51 Let H Be a Random Schrödinger Operator Which Samentioning

confidence: 70%

Moment analysis for localization in random Schrödinger operators

et al. 2005

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“…This notion means that wavepackets with energies in an energy interval I ⊂ R do not spread under the time evolution of the operator H ω , see, e.g., [17,42]. More precisely,…”

Section: Theorem 1 (Density Of States) Let U Be a Generalized Step Fmentioning

confidence: 99%

On the Lipschitz continuity of the integrated density of states for sign-indefinite potentials

Kostrykin

Veselić

2005

Math. Z.

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ABSTRACT. The present paper is devoted to the study of spectral properties of random Schrödinger operators. Using a finite section method for Toeplitz matrices, we prove a Wegner estimate for some alloy type models where the single site potential is allowed to change sign. The results apply to the corresponding discrete model, too. In certain disorder regimes we are able to prove the Lipschitz continuity of the integrated density of states and/or localization near spectral edges.

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“…The occurrence of localization is by now well established, e.g., [GoMP], [FrS], [FrMSS], [CKM], [S], [DrK], [KlLS], [AM], [FK1], [A], [Klo1], [CoH1], [CoH2], [FK2], [FK3], [W1], [GD], [KSS], [CoHT], [FLM], [ASFH], [DS], [GK1], [St], [W2], [Klo2], [DSS], [KlK2], [GK3], [U], [AENSS], [BouK] and many more. But delocalization is another story.…”

Section: Introductionmentioning

confidence: 99%

Dynamical delocalization in random Landau Hamiltonians

2007

Self Cite

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We prove the existence of dynamical delocalization for random Landau Hamiltonians near each Landau level. Since typically there is dynamical localization at the edges of each disordered-broadened Landau band, this implies the existence of at least one dynamical mobility edge at each Landau band, namely a boundary point between the localization and delocalization regimes, which we prove to converge to the corresponding Landau level as either the magnetic field goes to infinity or the disorder goes to zero.

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Bootstrap Multiscale Analysis and Localization¶in Random Media

Cited by 217 publications

References 34 publications

Moment analysis for localization in random Schrödinger operators

Moment analysis for localization in random Schrödinger operators

On the Lipschitz continuity of the integrated density of states for sign-indefinite potentials

Dynamical delocalization in random Landau Hamiltonians

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