{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,24]],"date-time":"2026-04-24T02:10:30Z","timestamp":1776996630161,"version":"3.51.4"},"reference-count":25,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2021,12,7]],"date-time":"2021-12-07T00:00:00Z","timestamp":1638835200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"},{"start":{"date-parts":[[2021,12,7]],"date-time":"2021-12-07T00:00:00Z","timestamp":1638835200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.springer.com\/tdm"}],"funder":[{"DOI":"10.13039\/100000086","name":"Directorate for Mathematical and Physical Sciences","doi-asserted-by":"publisher","award":["DMS-2012286"],"award-info":[{"award-number":["DMS-2012286"]}],"id":[{"id":"10.13039\/100000086","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000086","name":"Directorate for Mathematical and Physical Sciences","doi-asserted-by":"publisher","award":["DMS-1763179"],"award-info":[{"award-number":["DMS-1763179"]}],"id":[{"id":"10.13039\/100000086","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000086","name":"Directorate for Mathematical and Physical Sciences","doi-asserted-by":"publisher","award":["CHE-2037263"],"award-info":[{"award-number":["CHE-2037263"]}],"id":[{"id":"10.13039\/100000086","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000879","name":"Alfred P. Sloan Foundation","doi-asserted-by":"publisher","id":[{"id":"10.13039\/100000879","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Sci Comput"],"published-print":{"date-parts":[[2022,1]]},"DOI":"10.1007\/s10915-021-01682-x","type":"journal-article","created":{"date-parts":[[2021,12,7]],"date-time":"2021-12-07T17:02:33Z","timestamp":1638896553000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Fast Localization of Eigenfunctions via Smoothed Potentials"],"prefix":"10.1007","volume":"90","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6255-5165","authenticated-orcid":false,"given":"Jianfeng","family":"Lu","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Cody","family":"Murphey","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Stefan","family":"Steinerberger","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2021,12,7]]},"reference":[{"key":"1682_CR1","doi-asserted-by":"crossref","unstructured":"Altmann, R., Henning, P., Peterseim, D.: Quantitative Anderson localization of Schrodinger eigenstates under disorder potentials. to appear in Mathematical Models and Methods in Applied Sciences (2020). arXiv:1803.09950","DOI":"10.1142\/S0218202520500190"},{"key":"1682_CR2","unstructured":"Altmann, R., Henning, P., Peterseim, D.: Localization and Delocalization of Ground States of Bose\u2013Einstein Condensates Under Disorder (2020). arXiv:2006.00773"},{"issue":"6","key":"1682_CR3","doi-asserted-by":"publisher","first-page":"B1211","DOI":"10.1137\/19M1252594","volume":"41","author":"R Altmann","year":"2019","unstructured":"Altmann, R., Peterseim, D.: Localized computation of eigenstates of random Schr\u00f6dinger operators. SIAM J. Sci. Comput. 41(6), B1211\u2013B1227 (2019)","journal-title":"SIAM J. Sci. Comput."},{"key":"1682_CR4","doi-asserted-by":"publisher","first-page":"1492","DOI":"10.1103\/PhysRev.109.1492","volume":"109","author":"PW Anderson","year":"1958","unstructured":"Anderson, P.W.: Absence of diffusion in certain random lattices. Phys. Rev. 109, 1492\u20131505 (1958)","journal-title":"Phys. Rev."},{"issue":"5","key":"1682_CR5","doi-asserted-by":"publisher","first-page":"056602","DOI":"10.1103\/PhysRevLett.116.056602","volume":"116","author":"D Arnold","year":"2016","unstructured":"Arnold, D., David, G., Jerison, D., Mayboroda, S., Filoche, M.: Effective confining potential of quantum states in disordered media. Phys. Rev. Lett. 116(5), 056602 (2016)","journal-title":"Phys. Rev. Lett."},{"key":"1682_CR6","doi-asserted-by":"publisher","first-page":"1186","DOI":"10.1080\/03605302.2019.1626420","volume":"44","author":"D Arnold","year":"2019","unstructured":"Arnold, D., David, G., Filoche, M., Jerison, D., Mayboroda, S.: Localization of eigenfunctions via an effective potential. Commun. Partial Differ. Equ. 44, 1186\u20131216 (2019)","journal-title":"Commun. Partial Differ. Equ."},{"issue":"1","key":"1682_CR7","doi-asserted-by":"publisher","first-page":"B69","DOI":"10.1137\/17M1156721","volume":"41","author":"D Arnold","year":"2019","unstructured":"Arnold, D., David, G., Filoche, M., Jerison, D., Mayboroda, S.: Computing spectra without solving eigenvalue problems. SIAM J. Sci. Comput. 41(1), B69\u2013B92 (2019)","journal-title":"SIAM J. Sci. Comput."},{"key":"1682_CR8","doi-asserted-by":"publisher","first-page":"12835","DOI":"10.1038\/s41598-019-48905-8","volume":"9","author":"Y Chalopin","year":"2019","unstructured":"Chalopin, Y., Piazza, F., Mayboroda, S., Weisbuch, C., Filoche, M.: Universality of fold-encoded localized vibrations in enzymes. Sci. Rep. 9, 12835 (2019)","journal-title":"Sci. Rep."},{"key":"1682_CR9","doi-asserted-by":"crossref","unstructured":"David, G., Filoche, M., Mayboroda, S.: The Landscape Law for the Integrated Density of States (2021). arXiv:1909.10558","DOI":"10.1016\/j.aim.2021.107946"},{"issue":"2","key":"1682_CR10","doi-asserted-by":"publisher","first-page":"129","DOI":"10.1090\/S0273-0979-1983-15154-6","volume":"9","author":"C Fefferman","year":"1983","unstructured":"Fefferman, C.: The uncertainty principle. Bull. Am. Math. Soc. 9(2), 129\u2013206 (1983)","journal-title":"Bull. Am. Math. Soc."},{"key":"1682_CR11","doi-asserted-by":"publisher","first-page":"965","DOI":"10.1016\/j.jsv.2006.07.036","volume":"299","author":"S Felix","year":"2007","unstructured":"Felix, S., Asch, M., Filoche, M., Sapoval, B.: Localization and increased damping in irregular acoustic cavities. J. Sci. Vib. 299, 965\u2013976 (2007)","journal-title":"J. Sci. Vib."},{"issue":"37","key":"1682_CR12","doi-asserted-by":"publisher","first-page":"14761","DOI":"10.1073\/pnas.1120432109","volume":"109","author":"M Filoche","year":"2012","unstructured":"Filoche, M., Mayboroda, S.: Universal mechanism for Anderson and weak localization. Proc. Natl. Acad. Sci. USA 109(37), 14761\u201314766 (2012)","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"1682_CR13","doi-asserted-by":"crossref","unstructured":"Filoche, M., Mayboroda, S.: The landscape of Anderson localization in a disordered medium. Fractal geometry and dynamical systems in pure and applied mathematics. II. Fractals in applied mathematics, 113\u2013121, Cont. Math., 601, AMS, Providence, RI, 2013","DOI":"10.1090\/conm\/601\/11916"},{"key":"1682_CR14","doi-asserted-by":"publisher","first-page":"144204","DOI":"10.1103\/PhysRevB.95.144204","volume":"95","author":"M Filoche","year":"2017","unstructured":"Filoche, M., Piccardo, M., Wu, Y.-R., Li, C.-K., Weisbuch, C., Mayboroda, S.: Localization landscape theory of disorder in semiconductors I: theory and modeling. Phys. Rev. B 95, 144204 (2017)","journal-title":"Phys. Rev. B"},{"issue":"2","key":"1682_CR15","doi-asserted-by":"publisher","first-page":"429","DOI":"10.1007\/s00220-018-3124-x","volume":"359","author":"E Harrell","year":"2018","unstructured":"Harrell, E., Maltsev, A.: On Agmon metrics and exponential localization for quantum graphs. Commun. Math. Phys. 359(2), 429\u2013448 (2018)","journal-title":"Commun. Math. Phys."},{"key":"1682_CR16","doi-asserted-by":"publisher","first-page":"768","DOI":"10.1088\/1361-6544\/aafa89","volume":"32","author":"PW Jones","year":"2019","unstructured":"Jones, P.W., Steinerberger, S.: Localization of Neumann eigenfunctions near irregular boundaries. Nonlinearity 32, 768\u2013776 (2019)","journal-title":"Nonlinearity"},{"issue":"3","key":"1682_CR17","doi-asserted-by":"publisher","first-page":"1017","DOI":"10.1137\/15M1028510","volume":"14","author":"R Kornhuber","year":"2016","unstructured":"Kornhuber, R., Yserentant, H.: Numerical homogenization of elliptic multiscale problems by subspace decomposition. Multiscale Model. Simul. 14(3), 1017\u20131036 (2016)","journal-title":"Multiscale Model. Simul."},{"key":"1682_CR18","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.117.074301","volume":"117","author":"G Lefebvre","year":"2016","unstructured":"Lefebvre, G., Gondel, A., Dubois, M., Atlan, M., Feppon, F., Labbe, A., Gillot, C., Garelli, A., Ernoult, M., Filoche, M., Sebbah, P.: One single static measurement predicts wave localization in complex structures. Phys. Rev. Lett. 117, 074301 (2016)","journal-title":"Phys. Rev. Lett."},{"issue":"4","key":"1682_CR19","doi-asserted-by":"publisher","first-page":"47001","DOI":"10.1209\/0295-5075\/109\/47001","volume":"109","author":"M Leite Lyra","year":"2015","unstructured":"Leite Lyra, M., Mayboroda, S., Filoch, M.: Dual landscapes in Anderson localization on discrete lattices. Europhys. Lett. 109(4), 47001 (2015)","journal-title":"Europhys. Lett."},{"issue":"34","key":"1682_CR20","first-page":"1","volume":"5","author":"J Lu","year":"2018","unstructured":"Lu, J., Steinerberger, S.: Detecting localized eigenstates of linear operators. Res. Math. Sci. 5(34), 1\u201314 (2018)","journal-title":"Res. Math. Sci."},{"key":"1682_CR21","doi-asserted-by":"publisher","first-page":"14","DOI":"10.1103\/PhysRevB.95.144205","volume":"95","author":"M Piccardo","year":"2017","unstructured":"Piccardo, M., Li, C.-K., Wu, Y.-R., Speck, J., Bonef, B., Farrell, R., Filoche, M., Martinelli, L., Peretti, J., Weisbuch, C.: Localization landscape theory of disorder in semiconductors. II. Urbach tails of disordered quantum well layers. Phys. Rev. B 95, 14 (2017)","journal-title":"Phys. Rev. B"},{"key":"1682_CR22","doi-asserted-by":"publisher","first-page":"225","DOI":"10.1140\/epjst\/e2008-00763-2","volume":"161","author":"B Sapoval","year":"2008","unstructured":"Sapoval, B., Felix, S., Filoche, M.: Localisation and damping in resonators with complex geometry. Eur. Phys. J. Spec. Top. 161, 225\u2013232 (2008)","journal-title":"Eur. Phys. J. Spec. Top."},{"key":"1682_CR23","doi-asserted-by":"publisher","first-page":"143","DOI":"10.1512\/iumj.1994.43.43007","volume":"43","author":"Z Shen","year":"1994","unstructured":"Shen, Z.: On the Neumann problem for Schr\u00f6dinger operators in Lipschitz domains. Indiana Univ. Math. J. 43, 143\u2013176 (1994)","journal-title":"Indiana Univ. Math. J."},{"key":"1682_CR24","doi-asserted-by":"publisher","first-page":"2895","DOI":"10.1090\/proc\/13343","volume":"145","author":"S Steinerberger","year":"2017","unstructured":"Steinerberger, S.: Localization of quantum states and landscape functions. Proc. Am. Math. Soc. 145, 2895\u20132907 (2017)","journal-title":"Proc. Am. Math. Soc."},{"key":"1682_CR25","doi-asserted-by":"crossref","unstructured":"Steinerberger, S.: Regularized Potentials of Schrodinger Operators and a Local Landscape Function (2021). arXiv:2003.01091","DOI":"10.1080\/03605302.2020.1871366"}],"container-title":["Journal of Scientific Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-021-01682-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10915-021-01682-x\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10915-021-01682-x.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2022,1,17]],"date-time":"2022-01-17T23:20:12Z","timestamp":1642461612000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10915-021-01682-x"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,12,7]]},"references-count":25,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2022,1]]}},"alternative-id":["1682"],"URL":"https:\/\/doi.org\/10.1007\/s10915-021-01682-x","relation":{},"ISSN":["0885-7474","1573-7691"],"issn-type":[{"value":"0885-7474","type":"print"},{"value":"1573-7691","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,12,7]]},"assertion":[{"value":"18 November 2020","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"12 October 2021","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"7 December 2021","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}],"article-number":"38"}}