--- _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 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. Journal of Spectral Theory. 2019;9(3):921-965. doi:10.4171/jst/267 apa: Dietlein, A. M., 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. European Mathematical Society Publishing House. https://doi.org/10.4171/jst/267 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.” Journal of Spectral Theory. European Mathematical Society Publishing House, 2019. https://doi.org/10.4171/jst/267. 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,” Journal of Spectral Theory, 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.” Journal of Spectral Theory, vol. 9, no. 3, European Mathematical Society Publishing House, 2019, pp. 921–65, doi:10.4171/jst/267. 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' ...