Ekanga, Trésor Localization in the multi-particle tight-binding Anderson model at low energy. (English) Zbl 1445.47055 Rev. Math. Phys. 32, No. 3, Article ID 2050009, 35 p. (2020). MSC: 47N50 47B80 47A75 35P10 82B44 PDF BibTeX XML Cite \textit{T. Ekanga}, Rev. Math. Phys. 32, No. 3, Article ID 2050009, 35 p. (2020; Zbl 1445.47055) Full Text: DOI
Chulaevsky, Victor Towards localization in long-range continuous interactive Anderson models. (English) Zbl 1427.60141 Oper. Matrices 13, No. 1, 121-153 (2019). MSC: 60H25 37K55 82B44 PDF BibTeX XML Cite \textit{V. Chulaevsky}, Oper. Matrices 13, No. 1, 121--153 (2019; Zbl 1427.60141) Full Text: DOI
Bal, Guillaume Topological protection of perturbed edge states. (English) Zbl 1421.35305 Commun. Math. Sci. 17, No. 1, 193-225 (2019). MSC: 35Q41 47A53 60J70 35P25 PDF BibTeX XML Cite \textit{G. Bal}, Commun. Math. Sci. 17, No. 1, 193--225 (2019; Zbl 1421.35305) Full Text: DOI arXiv
de Oliveira, César R.; Pigossi, Mariane Proof of dynamical localization for perturbations of discrete 1D Schrödinger operators with uniform electric fields. (English) Zbl 07052009 Math. Z. 291, No. 3-4, 1525-1541 (2019). MSC: 47B39 47N50 81Q15 PDF BibTeX XML Cite \textit{C. R. de Oliveira} and \textit{M. Pigossi}, Math. Z. 291, No. 3--4, 1525--1541 (2019; Zbl 07052009) Full Text: DOI
Arnold, Douglas N.; David, Guy; Filoche, Marcel; Jerison, David; Mayboroda, Svitlana Computing spectra without solving eigenvalue problems. (English) Zbl 1420.81009 SIAM J. Sci. Comput. 41, No. 1, B69-B92 (2019). Reviewer: Mária Lukáčová (Mainz) MSC: 81Q05 65N25 81-08 82B44 PDF BibTeX XML Cite \textit{D. N. Arnold} et al., SIAM J. Sci. Comput. 41, No. 1, B69--B92 (2019; Zbl 1420.81009) Full Text: DOI
Lu, Jianfeng; Steinerberger, Stefan Detecting localized eigenstates of linear operators. (English) Zbl 1425.35128 Res. Math. Sci. 5, No. 3, Paper No. 33, 14 p. (2018). Reviewer: Pavel Burda (Praha) MSC: 35P20 35J10 65F15 82B44 47A75 60H25 PDF BibTeX XML Cite \textit{J. Lu} and \textit{S. Steinerberger}, Res. Math. Sci. 5, No. 3, Paper No. 33, 14 p. (2018; Zbl 1425.35128) Full Text: DOI arXiv
de Oliveira, César R.; Pigossi, Mariane Point spectrum and SULE for time-periodic perturbations of discrete 1D Schrödinger operators with electric fields. (English) Zbl 06969157 J. Stat. Phys. 173, No. 1, 140-162 (2018). MSC: 47B39 47N50 81Q15 PDF BibTeX XML Cite \textit{C. R. de Oliveira} and \textit{M. Pigossi}, J. Stat. Phys. 173, No. 1, 140--162 (2018; Zbl 06969157) Full Text: DOI
David, Guy; Filoche, Marcel; Jerison, David; Mayboroda, Svitlana A free boundary problem for the localization of eigenfunctions. (English) Zbl 1380.49001 Astérisque 392. Paris: Société Mathématique de France (SMF) (ISBN 978-2-85629-863-3/pbk). ii, 203 p. (2017). Reviewer: Vicenţiu D. Rădulescu (Craiova) MSC: 49-02 49Q20 49J40 35B30 35B65 35P05 49R05 PDF BibTeX XML Cite \textit{G. David} et al., A free boundary problem for the localization of eigenfunctions. Paris: Société Mathématique de France (SMF) (2017; Zbl 1380.49001)
Efimov, G. V. Quantum particle in a random medium. (English. Russian original) Zbl 1336.81031 Theor. Math. Phys. 185, No. 1, 1433-1444 (2015); translation from Teor. Mat. Fiz. 185, No. 1, 86-98 (2015). MSC: 81Q05 81R20 82B44 82D30 35J08 PDF BibTeX XML Cite \textit{G. V. Efimov}, Theor. Math. Phys. 185, No. 1, 1433--1444 (2015; Zbl 1336.81031); translation from Teor. Mat. Fiz. 185, No. 1, 86--98 (2015) Full Text: DOI
Hislop, Peter D.; Krishna, M. Eigenvalue statistics for random Schrödinger operators with non rank one perturbations. (English) Zbl 1331.35342 Commun. Math. Phys. 340, No. 1, 125-143 (2015). Reviewer: Eugene Postnikov (Kursk) MSC: 35Q82 82B44 82B20 35P99 PDF BibTeX XML Cite \textit{P. D. Hislop} and \textit{M. Krishna}, Commun. Math. Phys. 340, No. 1, 125--143 (2015; Zbl 1331.35342) Full Text: DOI arXiv
Geng, Jiansheng; You, Jiangong; Zhao, Zhiyan Localization in one-dimensional quasi-periodic nonlinear systems. (English) Zbl 1293.35335 Geom. Funct. Anal. 24, No. 1, 116-158 (2014). MSC: 35Q82 35Q55 82B44 37K55 PDF BibTeX XML Cite \textit{J. Geng} et al., Geom. Funct. Anal. 24, No. 1, 116--158 (2014; Zbl 1293.35335) Full Text: DOI
Sabri, Mostafa Anderson localization for a multi-particle quantum graph. (English) Zbl 1292.82021 Rev. Math. Phys. 26, No. 1, Article ID 1350020, 52 p. (2014). MSC: 82B44 47B80 34B45 PDF BibTeX XML Cite \textit{M. Sabri}, Rev. Math. Phys. 26, No. 1, Article ID 1350020, 52 p. (2014; Zbl 1292.82021) Full Text: DOI arXiv
Duchêne, V.; Vukićević, I.; Weinstein, M. I. Scattering and localization properties of highly oscillatory potentials. (English) Zbl 1292.34083 Commun. Pure Appl. Math. 67, No. 1, 83-128 (2014). Reviewer: Bilender P. Allahverdiev (Isparta) MSC: 34L25 34L40 35P25 35Q41 47E05 PDF BibTeX XML Cite \textit{V. Duchêne} et al., Commun. Pure Appl. Math. 67, No. 1, 83--128 (2014; Zbl 1292.34083) Full Text: DOI
Chulaevsky, Victor; Suhov, Yuri Multi-scale analysis for random quantum systems with interaction. (English) Zbl 1280.81003 Progress in Mathematical Physics 65. New York, NY: Birkhäuser/Springer (ISBN 978-1-4614-8225-3/hbk; 978-1-4614-8226-0/ebook). xi, 238 p. (2014). Reviewer: Piotr Garbaczewski (Opole) MSC: 81-02 82C44 82D30 82B44 47B80 60H25 60B20 60K37 37K60 35J08 81Q50 81Q10 81V70 PDF BibTeX XML Cite \textit{V. Chulaevsky} and \textit{Y. Suhov}, Multi-scale analysis for random quantum systems with interaction. New York, NY: Birkhäuser/Springer (2014; Zbl 1280.81003) Full Text: DOI
Germinet, François; Taarabt, Amal Spectral properties of dynamical localization for Schrödinger operators. (English) Zbl 1278.81076 Rev. Math. Phys. 25, No. 9, Article ID 1350016, 28 p. (2013). MSC: 81Q10 82B44 35J10 35P05 PDF BibTeX XML Cite \textit{F. Germinet} and \textit{A. Taarabt}, Rev. Math. Phys. 25, No. 9, Article ID 1350016, 28 p. (2013; Zbl 1278.81076) Full Text: DOI arXiv
Gebert, Martin; Müller, Peter Localization for random block operators. (English) Zbl 1282.47060 Demuth, Michael (ed.) et al., Mathematical physics, spectral theory and stochastic analysis. Basel: Birkhäuser/Springer (ISBN 978-3-0348-0590-2/hbk; 978-3-0348-0591-9/ebook). Operator Theory: Advances and Applications 232. Advances in Partial Differential Equations, 229-246 (2013). Reviewer: Guy Jumarie (Montréal) MSC: 47B80 47A75 82B44 35Q55 PDF BibTeX XML Cite \textit{M. Gebert} and \textit{P. Müller}, Oper. Theory: Adv. Appl. 232, 229--246 (2013; Zbl 1282.47060) Full Text: DOI arXiv
Alimov, Sh. A. Generalized localization of Riesz means of spectral expansions of distributions. (English. Russian original) Zbl 1260.35081 Dokl. Math. 86, No. 2, 597-599 (2012); translation from Dokl. Akad. Nauk. 446, No. 1, 7-9 (2012). Reviewer: Dian K. Palagachev (Bari) MSC: 35P05 35P10 35J10 47F05 PDF BibTeX XML Cite \textit{Sh. A. Alimov}, Dokl. Math. 86, No. 2, 597--599 (2012; Zbl 1260.35081); translation from Dokl. Akad. Nauk. 446, No. 1, 7--9 (2012) Full Text: DOI
Hislop, Peter D. Lectures on random Schrödinger operators. (English) Zbl 1156.81020 Villegas-Blas, Carlos (ed.), Fourth summer school in analysis and mathematical physics. Topics in spectral theory and quantum mechanics, Cuernavaca, México, May 2005. Providence, RI: American Mathematical Society (AMS) (ISBN 978-0-8218-4064-1/pbk). Contemporary Mathematics 476; Aportaciones Matemáticas, 41-131 (2008). MSC: 81Q10 35P05 47A55 35J10 82B44 35R60 81-01 PDF BibTeX XML Cite \textit{P. D. Hislop}, Contemp. Math. 476, 41--131 (2008; Zbl 1156.81020)
Germinet, François; Hislop, Peter D.; Klein, Abel Localization at low energies for attractive Poisson random Schrödinger operators. (English) Zbl 1149.35064 Dawson, Donald A. (ed.) et al., Probability and mathematical physics. A volume in honor of Stanislav Molchanov. Proceedings of a conference in honor of Stanislav Molchanov’s 65th birthday, Montreal, Canada, June 27–July 1, 2005. Providence, RI: American Mathematical Society (AMS) (ISBN 978-0-8218-4089-4/pbk). CRM Proceedings and Lecture Notes 42, 153-165 (2007). Reviewer: Vassilis G. Papanicolaou (Athena) MSC: 35P05 81Q10 35J10 60H25 PDF BibTeX XML Cite \textit{F. Germinet} et al., in: Probability and mathematical physics. A volume in honor of Stanislav Molchanov. Proceedings of a conference in honor of Stanislav Molchanov's 65th birthday, Montreal, Canada, June 27--July 1, 2005. Providence, RI: American Mathematical Society (AMS). 153--165 (2007; Zbl 1149.35064) Full Text: arXiv
Schenk, Olaf; Bollhöfer, Matthias; Römer, Rudolf A. On large-scale diagonalization techniques for the Anderson model of localization. (English) Zbl 1116.65046 SIAM J. Sci. Comput. 28, No. 3, 963-983 (2006). MSC: 65F15 65F50 82B44 05C85 PDF BibTeX XML Cite \textit{O. Schenk} et al., SIAM J. Sci. Comput. 28, No. 3, 963--983 (2006; Zbl 1116.65046) Full Text: DOI arXiv
Chen, Kingwood; Molchanov, Stanislav; Vainberg, Boris Localization on Avron-Exner-Last graphs. I: Local perturbations. (English) Zbl 1104.81038 Berkolaiko, Gregory (ed.) et al., Quantum graphs and their applications. Proceedings of an AMS-IMS-SIAM joint summer research conference on quantum graphs and their applications, Snowbird, UT, USA, June 19–23, 2005. Providence, RI: American Mathematical Society (AMS) (ISBN 0-8218-3765-6/pbk). Contemporary Mathematics 415, 81-91 (2006). MSC: 81Q05 58J50 35J10 35P99 81Q15 34D10 82D20 PDF BibTeX XML Cite \textit{K. Chen} et al., Contemp. Math. 415, 81--91 (2006; Zbl 1104.81038)
Erdős, László; Solovej, Jan Philip Uniform Lieb-Thirring inequality for the three-dimensional Pauli operator with a strong non-homogeneous magnetic field. (English) Zbl 1054.81016 Ann. Henri Poincaré 5, No. 4, 671-741 (2004). Reviewer: Hiroshi Tamura (Kanazawa) MSC: 81Q05 81Q10 81Q15 PDF BibTeX XML Cite \textit{L. Erdős} and \textit{J. P. Solovej}, Ann. Henri Poincaré 5, No. 4, 671--741 (2004; Zbl 1054.81016) Full Text: DOI arXiv
Dorlas, T. C.; Pulé, J. V. Invariant measures for one-dimensional Anderson localisation. (English) Zbl 1054.60106 Markov Process. Relat. Fields 9, No. 4, 567-578 (2003). MSC: 60K40 37L40 82B23 82B44 PDF BibTeX XML Cite \textit{T. C. Dorlas} and \textit{J. V. Pulé}, Markov Process. Relat. Fields 9, No. 4, 567--578 (2003; Zbl 1054.60106)
Combes, J.-M.; Hislop, P. D.; Klopp, F. Local and global continuity of the integrated density of states. (English) Zbl 1060.47042 Karpeshina, Yulia (ed.) et al., Advances in differential equations and mathematical physics. Proceedings of the 9th UAB international conference, University of Alabama, Birmingham, AL, USA, March 26–30, 2002. Providence, RI: American Mathematical Society (AMS) (ISBN 0-8218-3296-4). Contemp. Math. 327, 61-74 (2003). Reviewer: Takashi Ichinose (Kanazawa) MSC: 47B80 81Q10 81Q15 82B44 60H25 35R60 35Q40 PDF BibTeX XML Cite \textit{J. M. Combes} et al., Contemp. Math. 327, 61--74 (2003; Zbl 1060.47042)
Stepin, S. A.; Arzhanov, A. A. On the localization of the spectrum in a problem in singular perturbation theory. (English. Russian original) Zbl 1058.34116 Russ. Math. Surv. 57, No. 3, 608-610 (2002); translation from Usp. Mat. Nauk 57, No. 3, 161-162 (2002). Reviewer: E. V. Shchetinina (Samara) MSC: 34L20 34L40 34E15 PDF BibTeX XML Cite \textit{S. A. Stepin} and \textit{A. A. Arzhanov}, Russ. Math. Surv. 57, No. 3, 608--610 (2002; Zbl 1058.34116); translation from Usp. Mat. Nauk 57, No. 3, 161--162 (2002) Full Text: DOI
Grecchi, Vincenzo; Martinez, André; Sacchetti, Andrea Destruction of the beating effect for a nonlinear Schrödinger equation. (English) Zbl 1001.81011 Commun. Math. Phys. 227, No. 1, 191-209 (2002). MSC: 81Q05 35Q55 81V55 47N50 81Q20 81Q15 PDF BibTeX XML Cite \textit{V. Grecchi} et al., Commun. Math. Phys. 227, No. 1, 191--209 (2002; Zbl 1001.81011) Full Text: DOI
Kleespies, Frank; Stollmann, Peter Lifshitz asymptotics and localization for random quantum waveguides. (English) Zbl 0976.81008 Rev. Math. Phys. 12, No. 10, 1345-1365 (2000). Reviewer: Vladimir V.Kisil (Leeds) MSC: 81Q15 47B80 47N50 PDF BibTeX XML Cite \textit{F. Kleespies} and \textit{P. Stollmann}, Rev. Math. Phys. 12, No. 10, 1345--1365 (2000; Zbl 0976.81008) Full Text: DOI
Elsner, Ulrich; Mehrmann, Volker; Milde, Frank; Römer, Rudolf A.; Schreiber, Michael The Anderson model of localization: A challenge for modern eigenvalue methods. (English) Zbl 0945.65038 SIAM J. Sci. Comput. 20, No. 6, 2089-2102 (1999). Reviewer: E.Kreyszig (Ottawa) MSC: 65F15 65F50 82B44 82B80 PDF BibTeX XML Cite \textit{U. Elsner} et al., SIAM J. Sci. Comput. 20, No. 6, 2089--2102 (1999; Zbl 0945.65038) Full Text: DOI
Kirsch, W. Wegner estimates and Anderson localization for alloy-type potentials. (English) Zbl 0863.35069 Math. Z. 221, No. 3, 507-512 (1996). Reviewer: W.Kirsch (Bochum) MSC: 35P05 35J10 PDF BibTeX XML Cite \textit{W. Kirsch}, Math. Z. 221, No. 3, 507--512 (1996; Zbl 0863.35069) Full Text: DOI EuDML
Simon, Barry Spectral analysis of rank one perturbations and applications. (English) Zbl 0824.47019 Feldman, J. (ed.) et al., Mathematical quantum theory II: Schrödinger operators. Proceedings of the Canadian Mathematical Society annual seminar on mathematical quantum theory held in Vancouver, Canada, August 4-14, 1993. Providence, RI: American Mathematical Society. CRM Proc. Lect. Notes. 8, 109-149 (1995). MSC: 47B15 47A10 47A55 34L05 81Q10 34F05 PDF BibTeX XML Cite \textit{B. Simon}, in: Mathematical quantum theory II: Schrödinger operators. Proceedings of the Canadian Mathematical Society annual seminar on mathematical quantum theory held in Vancouver, Canada, August 4-14, 1993. Providence, RI: American Mathematical Society. 109--149 (1995; Zbl 0824.47019)
Aizenman, Michael Localization at weak disorder: some elementary bounds. (English) Zbl 0843.47039 Rev. Math. Phys. 6, No. 5a, 1163-1182 (1994). MSC: 82B44 47N55 81Q10 35J10 PDF BibTeX XML Cite \textit{M. Aizenman}, Rev. Math. Phys. 6, No. 5a, 1163--1182 (1994; Zbl 0843.47039) Full Text: DOI
Klopp, Frédéric Localization for semiclassical continuous random Schrödinger operators. II: The random displacement model. (English) Zbl 0820.60043 Helv. Phys. Acta 66, No. 7-8, 810-841 (1993). MSC: 60H25 81Q10 82B44 PDF BibTeX XML Cite \textit{F. Klopp}, Helv. Phys. Acta 66, No. 7--8, 810--841 (1993; Zbl 0820.60043)
Hempel, Rainer Eigenvalue asymptotics related to impurities in crystals. (English) Zbl 0789.35121 Robert, D. (ed.), Méthodes semi-classiques, Volume 2. Colloque international (Nantes, juin 1991). Paris: Société Mathématique de France, Astérisque. 210, 183-196 (1992). Reviewer: N.E.Ratanov (Chelyabinsk) MSC: 35P05 81Q10 82D25 PDF BibTeX XML Cite \textit{R. Hempel}, in: Méthodes semi-classiques, Volume 2. Colloque international (Nantes, juin 1991). Paris: Société Mathématique de France. 183--196 (1992; Zbl 0789.35121) Full Text: Link
Il’in, V. A. Componentwise equiconvergence with a trigonometric series of expansions with respect to root vector-functions of the Schrödinger operator with non-Hermitian matrix potential all elements of which are only summable. (Russian) Zbl 0741.34053 Differ. Uravn. 27, No. 11, 1862-1879 (1991). Reviewer: L.Pastur (Khar’kov) MSC: 34L10 34L40 42C15 42C25 PDF BibTeX XML Cite \textit{V. A. Il'in}, Differ. Uravn. 27, No. 11, 1862--1879 (1991; Zbl 0741.34053)
Astrauskas, A.; Molchanov, S. A. The ground state of a random stationary medium in the mean field approximation. (English) Zbl 0768.60057 New trends in probability and statistics. Vol. 1, Proc. 23rd Bakuriani Colloq. in Honour of Yu. V. Prokhorov, Bakuriani/USSR 1990, 668-682 (1991). MSC: 60H25 82B44 PDF BibTeX XML Cite \textit{A. Astrauskas} and \textit{S. A. Molchanov}, in: New trends in probability and statistics. Vol. 1. Proceedings of the XXIII Bakuriani colloquium in Honour of Yu. V. Prokhorov, Bakuriani, Georgia, 24 February - 4 March, 1990. Utrecht: VSP; Vilnius: Mokslas. 668--682 (1991; Zbl 0768.60057)
Thaller, Bernd The Dirac equation. (English) Zbl 0765.47023 Texts and Monographs in Physics. Berlin: Springer-Verlag. xvii, 357 p. (1991). Reviewer: M.Demuth (Potsdam) MSC: 47N50 47A40 81T60 47-02 81-02 47B25 81Q05 PDF BibTeX XML Cite \textit{B. Thaller}, The Dirac equation. Berlin: Springer-Verlag (1991; Zbl 0765.47023)
Il’in, V. A. Component-wise equiconvergence with a trigonometric series of expansions in eigenfunctions and associated functions of a Schrödinger operator with a nonhermite potential matrix of summable elements. (English. Russian original) Zbl 0789.34071 Differ. Equations 27, No. 11, 1307-1321 (1991); translation from Differ. Uravn. 27, No. 11, 1862-1879 (1991). MSC: 34L10 34L40 42C15 42C25 PDF BibTeX XML Cite \textit{V. A. Il'in}, Differ. Equations 27, No. 11, 1307--1321 (1991; Zbl 0789.34071); translation from Differ. Uravn. 27, No. 11, 1862--1879 (1991)
Briet, Ph.; Combes, J. M.; Duclos, P. Spectral stability under tunneling. (English) Zbl 0702.35189 Commun. Math. Phys. 126, No. 1, 133-156 (1989). Reviewer: D.Robert MSC: 35P15 35J10 81Q15 PDF BibTeX XML Cite \textit{Ph. Briet} et al., Commun. Math. Phys. 126, No. 1, 133--156 (1989; Zbl 0702.35189) Full Text: DOI
Souillard, Bernard Spectral properties of discrete and continuous random Schrödinger operators: A review. (English) Zbl 0659.60089 Random media, IMA Vol. Math. Appl. 7, 279-291 (1987). Reviewer: Y.Prahalad MSC: 60H25 81Q99 49R50 PDF BibTeX XML
Kotani, S.; Simon, B. Localization in general one-dimensional random systems. II: Continuum Schrödinger operators. (English) Zbl 0637.60080 Commun. Math. Phys. 112, No. 1, 103-119 (1987). Reviewer: L.Pastur MSC: 60H25 35R60 34B20 PDF BibTeX XML Cite \textit{S. Kotani} and \textit{B. Simon}, Commun. Math. Phys. 112, 103--119 (1987; Zbl 0637.60080) Full Text: DOI
Spencer, Thomas C. The Schrödinger equation with a random potential. A mathematical review. (English) Zbl 0655.60050 Critical phenomena, random systems, gauge theories, Proc. Summer Sch. Theor. Phys., Sess. 43, Les Houches/France 1984, Pt. 2, 895-942 (1986). Reviewer: R.Manthey MSC: 60H25 81P20 81Q15 35J10 PDF BibTeX XML
Bougerol, Philippe; Lacroix, Jean Products of random matrices with applications to Schrödinger operators. (English) Zbl 0572.60001 Progress in Probability and Statistics, Vol. 8. Boston - Basel - Stuttgart: Birkhäuser. X, 283 p. DM 88.00 (1985). Reviewer: T.Kaijser MSC: 60-02 60B15 60B12 60K35 82D30 PDF BibTeX XML Backlinks: MO