---
_id: '10879'
abstract:
- lang: eng
  text: We study effects of a bounded and compactly supported perturbation on multidimensional
    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 (2015),
    560–565]. 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(Hτ))χb in a and b.
    Here, Hτ 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∈Rd, and f is in a suitable class of functions of bounded variation with distributional
    derivative supported in the region of complete localisation for H.
acknowledgement: M.G. was supported by the DFG under grant GE 2871/1-1.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Adrian M
  full_name: Dietlein, Adrian M
  id: 317CB464-F248-11E8-B48F-1D18A9856A87
  last_name: Dietlein
- first_name: Martin
  full_name: Gebert, Martin
  last_name: Gebert
- first_name: Peter
  full_name: Müller, Peter
  last_name: Müller
citation:
  ama: Dietlein AM, Gebert M, Müller P. Perturbations of continuum random Schrödinger
    operators with applications to Anderson orthogonality and the spectral shift function.
    <i>Journal of Spectral Theory</i>. 2019;9(3):921-965. doi:<a href="https://doi.org/10.4171/jst/267">10.4171/jst/267</a>
  apa: Dietlein, A. M., Gebert, M., &#38; Müller, P. (2019). Perturbations of continuum
    random Schrödinger operators with applications to Anderson orthogonality and the
    spectral shift function. <i>Journal of Spectral Theory</i>. European Mathematical
    Society Publishing House. <a href="https://doi.org/10.4171/jst/267">https://doi.org/10.4171/jst/267</a>
  chicago: Dietlein, Adrian M, Martin Gebert, and Peter Müller. “Perturbations of
    Continuum Random Schrödinger Operators with Applications to Anderson Orthogonality
    and the Spectral Shift Function.” <i>Journal of Spectral Theory</i>. European
    Mathematical Society Publishing House, 2019. <a href="https://doi.org/10.4171/jst/267">https://doi.org/10.4171/jst/267</a>.
  ieee: A. M. Dietlein, M. Gebert, and P. Müller, “Perturbations of continuum random
    Schrödinger operators with applications to Anderson orthogonality and the spectral
    shift function,” <i>Journal of Spectral Theory</i>, vol. 9, no. 3. European Mathematical
    Society Publishing House, pp. 921–965, 2019.
  ista: Dietlein AM, Gebert M, Müller P. 2019. Perturbations of continuum random Schrödinger
    operators with applications to Anderson orthogonality and the spectral shift function.
    Journal of Spectral Theory. 9(3), 921–965.
  mla: Dietlein, Adrian M., et al. “Perturbations of Continuum Random Schrödinger
    Operators with Applications to Anderson Orthogonality and the Spectral Shift Function.”
    <i>Journal of Spectral Theory</i>, vol. 9, no. 3, European Mathematical Society
    Publishing House, 2019, pp. 921–65, doi:<a href="https://doi.org/10.4171/jst/267">10.4171/jst/267</a>.
  short: A.M. Dietlein, M. Gebert, P. Müller, Journal of Spectral Theory 9 (2019)
    921–965.
date_created: 2022-03-18T12:36:42Z
date_published: 2019-03-01T00:00:00Z
date_updated: 2023-09-08T11:35:31Z
day: '01'
department:
- _id: LaEr
doi: 10.4171/jst/267
external_id:
  arxiv:
  - '1701.02956'
  isi:
  - '000484709400006'
intvolume: '         9'
isi: 1
issue: '3'
keyword:
- Random Schrödinger operators
- spectral shift function
- Anderson orthogonality
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://arxiv.org/abs/1701.02956
month: '03'
oa: 1
oa_version: Preprint
page: 921-965
publication: Journal of Spectral Theory
publication_identifier:
  issn:
  - 1664-039X
publication_status: published
publisher: European Mathematical Society Publishing House
quality_controlled: '1'
scopus_import: '1'
status: public
title: Perturbations of continuum random Schrödinger operators with applications to
  Anderson orthogonality and the spectral shift function
type: journal_article
user_id: c635000d-4b10-11ee-a964-aac5a93f6ac1
volume: 9
year: '2019'
...