{"issue":"3","page":"921-965","day":"01","intvolume":"         9","publication_identifier":{"issn":["1664-039X"]},"language":[{"iso":"eng"}],"date_created":"2022-03-18T12:36:42Z","title":"Perturbations of continuum random Schrödinger operators with applications to Anderson orthogonality and the spectral shift function","article_processing_charge":"No","department":[{"_id":"LaEr"}],"abstract":[{"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.","lang":"eng"}],"oa":1,"oa_version":"Preprint","date_published":"2019-03-01T00:00:00Z","type":"journal_article","publisher":"European Mathematical Society Publishing House","article_type":"original","_id":"10879","year":"2019","doi":"10.4171/jst/267","quality_controlled":"1","author":[{"id":"317CB464-F248-11E8-B48F-1D18A9856A87","last_name":"Dietlein","first_name":"Adrian M","full_name":"Dietlein, Adrian M"},{"last_name":"Gebert","first_name":"Martin","full_name":"Gebert, Martin"},{"full_name":"Müller, Peter","first_name":"Peter","last_name":"Müller"}],"external_id":{"arxiv":["1701.02956"],"isi":["000484709400006"]},"date_updated":"2023-09-08T11:35:31Z","user_id":"c635000d-4b10-11ee-a964-aac5a93f6ac1","status":"public","acknowledgement":"M.G. was supported by the DFG under grant GE 2871/1-1.","isi":1,"publication_status":"published","main_file_link":[{"open_access":"1","url":"https://arxiv.org/abs/1701.02956"}],"scopus_import":"1","keyword":["Random Schrödinger operators","spectral shift function","Anderson orthogonality"],"volume":9,"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>","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>.","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>","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.","short":"A.M. Dietlein, M. Gebert, P. Müller, Journal of Spectral Theory 9 (2019) 921–965.","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>."},"month":"03","publication":"Journal of Spectral Theory"}