Scale-free uncertainty principles and Wegner estimates for random breather potentials

Nakić, Ivica; Täufer, Matthias; Tautenhahn, Martin; Veselić, Ivan

doi:10.1016/j.crma.2015.08.005

Cited by 17 publications

(24 citation statements)

References 14 publications

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“…Remark 4.4. In [NTTV,TV15a] we establish the Wegner bound for a much more general class of random potentials. Here, for the sake of simplicity, we have restricted ourselves to the case of the standard random breather model.…”

Section: Random Schrödinger Operatorsmentioning

confidence: 99%

Harmonic Analysis and Random Schrödinger Operators

Täufer

Tautenhahn

Veselić

2016

Operator Theory: Advances and Applications

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Section: Random Schrödinger Operatorsmentioning

confidence: 99%

Harmonic Analysis and Random Schrödinger Operators

Täufer

Tautenhahn

Veselić

2016

Operator Theory: Advances and Applications

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“…Let us summarize previous results on random breather Schrödinger operators: They have been introduced in the mathematical literature in [5], a non-trivial Wegner estimates was proven in [6], Lifschitz tail estimates were established in [9] and [17], and a flexible Wegner estimate was given in [11], which covers also standard random breather potentials…”

Section: Introductionmentioning

confidence: 99%

Wegner estimate for Landau-breather Hamiltonians

Täufer

Veselić

2016

Journal of Mathematical Physics

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“…The second result is a scale-free unique continuation principle for averaged local traces of nonnegative functions of infinite-volume ergodic random Schrödinger operators in Lemma 5.2. It follows from a scale-free unique continuation principle for spectral projections of finitevolume random Schrödinger operators [Kle13,NTTV15] by a suitable limit procedure. We are not aware that this consequence has been noticed elsewhere.…”

Section: Introductionmentioning

confidence: 99%

Perturbations of continuum random Schrödinger operators with applications to Anderson orthogonality and the spectral shift function

2019

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We study effects of a bounded and compactly supported perturbation on multi-dimensional continuum random Schrödinger operators in the region of complete localisation. Our main emphasis is on Anderson orthogonality for random Schrödinger operators. Among others, we prove that Anderson orthogonality does occur for Fermi energies in the region of complete localisation with a non-zero probability. This partially confirms recent non-rigorous findings [V. Khemani et al., Nature Phys. 11, 560-565 (2015)]. The spectral shift function plays an important role in our analysis of Anderson orthogonality. We identify it with the index of the corresponding pair of spectral projections and explore the consequences thereof. All our results rely on the main technical estimate of this paper which guarantees separate exponential decay of the disorder-averaged Schatten p-norm of χa(f (H) − f (H τ ))χ b in a and b. Here, H τ is a perturbation of the random Schrödinger operator H, χa is the multiplication operator corresponding to the indicator function of a unit cube centred about a ∈ R d , and f is in a suitable class of functions of bounded variation with distributional derivative supported in the region of complete localisation for H.

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Scale-free uncertainty principles and Wegner estimates for random breather potentials

Cited by 17 publications

References 14 publications

Harmonic Analysis and Random Schrödinger Operators

Harmonic Analysis and Random Schrödinger Operators

Wegner estimate for Landau-breather Hamiltonians

Perturbations of continuum random Schrödinger operators with applications to Anderson orthogonality and the spectral shift function

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