Li, Jing Reducibility for Schrödinger operator with finite smooth and time-quasi-periodic potential. (English) Zbl 1440.35222 Chin. Ann. Math., Ser. B 41, No. 3, 419-440 (2020). Reviewer: Michael Perelmuter (Kyïv) MSC: 35P05 37K55 81Q15 PDF BibTeX XML Cite \textit{J. Li}, Chin. Ann. Math., Ser. B 41, No. 3, 419--440 (2020; Zbl 1440.35222) Full Text: DOI
Parnovski, Leonid; Shterenberg, Roman Perturbation theory for almost-periodic potentials. I: One-dimensional case. (English) Zbl 1415.34131 Commun. Math. Phys. 366, No. 3, 1229-1257 (2019). Reviewer: Jiři Lipovský (Hradec Kralove) MSC: 34L40 34E05 34E10 34L05 PDF BibTeX XML Cite \textit{L. Parnovski} and \textit{R. Shterenberg}, Commun. Math. Phys. 366, No. 3, 1229--1257 (2019; Zbl 1415.34131) Full Text: DOI arXiv
Zheng, Guang-Hui Mathematical analysis of plasmonic resonance for 2-D photonic crystal. (English) Zbl 1410.35241 J. Differ. Equations 266, No. 8, 5095-5117 (2019). MSC: 35Q82 82D80 35B44 35J05 82D20 PDF BibTeX XML Cite \textit{G.-H. Zheng}, J. Differ. Equations 266, No. 8, 5095--5117 (2019; Zbl 1410.35241) Full Text: DOI arXiv
Chen, Bochao; Gao, Yixian; Jiang, Shan; Li, Yong Quasi-periodic solutions to nonlinear beam equations on compact Lie groups with a multiplicative potential. (English) Zbl 1385.53037 J. Differ. Equations 264, No. 11, 6959-6993 (2018). MSC: 53C30 35R03 35B15 74B20 PDF BibTeX XML Cite \textit{B. Chen} et al., J. Differ. Equations 264, No. 11, 6959--6993 (2018; Zbl 1385.53037) Full Text: DOI
Karpeshina, Yulia; Lee, Young-Ran; Shterenberg, Roman; Stolz, Günter Ballistic transport for the Schrödinger operator with limit-periodic or quasi-periodic potential in dimension two. (English) Zbl 1371.35238 Commun. Math. Phys. 354, No. 1, 85-113 (2017). MSC: 35Q41 35P05 81Q10 PDF BibTeX XML Cite \textit{Y. Karpeshina} et al., Commun. Math. Phys. 354, No. 1, 85--113 (2017; Zbl 1371.35238) Full Text: DOI
Zhao, Zhiyan Ballistic motion in one-dimensional quasi-periodic discrete Schrödinger equation. (English) Zbl 1366.34019 Commun. Math. Phys. 347, No. 2, 511-549 (2016). Reviewer: Daniela Danciu (Craiova) MSC: 34A33 34D05 PDF BibTeX XML Cite \textit{Z. Zhao}, Commun. Math. Phys. 347, No. 2, 511--549 (2016; Zbl 1366.34019) Full Text: DOI arXiv
Damanik, David; Goldstein, Michael; Lukic, Milivoje The spectrum of a Schrödinger operator with small quasi-periodic potential is homogeneous. (English) Zbl 1350.34067 J. Spectr. Theory 6, No. 2, 415-427 (2016). Reviewer: Ekin Uğurlu (Ankara) MSC: 34L40 34L05 PDF BibTeX XML Cite \textit{D. Damanik} et al., J. Spectr. Theory 6, No. 2, 415--427 (2016; Zbl 1350.34067) Full Text: DOI
Luque, Alejandro; Peralta-Salas, Daniel Motion of charged particles in ABC magnetic fields. (English) Zbl 1284.34080 SIAM J. Appl. Dyn. Syst. 12, No. 4, 1889-1947 (2013). MSC: 34C60 34C20 37J30 37J40 37D45 78A35 34C23 34C28 34D20 PDF BibTeX XML Cite \textit{A. Luque} and \textit{D. Peralta-Salas}, SIAM J. Appl. Dyn. Syst. 12, No. 4, 1889--1947 (2013; Zbl 1284.34080) Full Text: DOI arXiv
Jitomirskaya, S.; Marx, C. A. Analytic quasi-periodic Schrödinger operators and rational frequency approximants. (English) Zbl 1263.47037 Geom. Funct. Anal. 22, No. 5, 1407-1443 (2012). Reviewer: Aleksey Kostenko (Donetsk) MSC: 47B37 34L40 81Q10 PDF BibTeX XML Cite \textit{S. Jitomirskaya} and \textit{C. A. Marx}, Geom. Funct. Anal. 22, No. 5, 1407--1443 (2012; Zbl 1263.47037) Full Text: DOI arXiv
Marin, L. Dynamical bounds for Sturmian Schrödinger operators. (English) Zbl 1201.81052 Rev. Math. Phys. 22, No. 8, 859-879 (2010). MSC: 81Q10 47B36 35Q41 82D20 37C55 PDF BibTeX XML Cite \textit{L. Marin}, Rev. Math. Phys. 22, No. 8, 859--879 (2010; Zbl 1201.81052) Full Text: DOI arXiv
Gosse, Laurent Impurity bands and quasi-Bloch waves for a one-dimensional model of modulated crystal. (English) Zbl 1140.81398 Nonlinear Anal., Real World Appl. 9, No. 3, 927-948 (2008). MSC: 81Q20 81Q05 35J10 37C55 81Q50 82D25 PDF BibTeX XML Cite \textit{L. Gosse}, Nonlinear Anal., Real World Appl. 9, No. 3, 927--948 (2008; Zbl 1140.81398) Full Text: DOI
Eliasson, L. H.; Kuksin, S. B. Four lectures on KAM for the nonlinear Schrödinger equation. (English) Zbl 1140.37021 Craig, Walter (ed.), Hamiltonian dynamical systems and applications. Proceedings of the NATO Advanced Study Institute on Hamiltonian dynamical systems and applications, Montreal, Canada, June, 18-29, 2007. Berlin: Springer (ISBN 978-1-4020-6963-5/pbk; 978-1-4020-6962-8/hbk). NATO Science for Peace and Security Series B: Physics and Biophysics, 179-212 (2008). Reviewer: Hu Chuangan (Tianjin) MSC: 37K55 35Q55 PDF BibTeX XML Cite \textit{L. H. Eliasson} and \textit{S. B. Kuksin}, in: Hamiltonian dynamical systems and applications. Proceedings of the NATO Advanced Study Institute on Hamiltonian dynamical systems and applications, Montreal, Canada, June, 18-29, 2007. Berlin: Springer. 179--212 (2008; Zbl 1140.37021)
Chan, Jackson Method of variations of potential of quasi-periodic Schrödinger equations. (English) Zbl 1165.82014 Geom. Funct. Anal. 17(2007), No. 5, 1416-1478 (2008). Reviewer: Cesare Tronci (Lausanne) MSC: 82B44 39A70 47B39 81Q10 47N55 PDF BibTeX XML Cite \textit{J. Chan}, Geom. Funct. Anal. 17, No. 5, 1416--1478 (2008; Zbl 1165.82014) Full Text: DOI
Gosse, Laurent The numerical spectrum of a one-dimensional Schrödinger operator with two competing periodic potentials. (English) Zbl 1131.81006 Commun. Math. Sci. 5, No. 2, 485-493 (2007). MSC: 81Q05 81Q20 34L40 PDF BibTeX XML Cite \textit{L. Gosse}, Commun. Math. Sci. 5, No. 2, 485--493 (2007; Zbl 1131.81006) Full Text: DOI Euclid
Chang, Lihong; Li, Xing Anti-plane problems for doubly periodic parallelogrammic array of cylindrical inclusions in piezoelectric composite material. (Chinese. English summary) Zbl 1104.74305 J. Ningxia Univ., Nat. Sci. Ed. 27, No. 2, 165-168, 193 (2006). MSC: 74F15 74E30 78A48 30C20 PDF BibTeX XML Cite \textit{L. Chang} and \textit{X. Li}, J. Ningxia Univ., Nat. Sci. Ed. 27, No. 2, 165--168, 193 (2006; Zbl 1104.74305)
Johnson, Russell; Mantellini, Francesca Non-autonomous differential equations. (English) Zbl 1046.34002 Macki, Jack W. (ed.) et al., Dynamical systems. Lectures given at the C.I.M.E. summer school, Cetraro, Italy, June 19–26, 2000. Berlin: Springer (ISBN 3-540-40786-3/pbk). Lect. Notes Math. 1822, 173-229 (2003). Reviewer: Yuri V. Rogovchenko (Famagusta) MSC: 34-02 34D08 34D09 37B55 37C10 34F05 35K20 PDF BibTeX XML Cite \textit{R. Johnson} and \textit{F. Mantellini}, Lect. Notes Math. 1822, 173--229 (2003; Zbl 1046.34002)
Damanik, David Absence of eigenvalues for a class of Schrödinger operators on the strip. (English) Zbl 1033.81031 Forum Math. 14, No. 5, 797-806 (2002). Reviewer: Tuncay Aktosun (Mississippi State) MSC: 81Q10 47B39 39A12 PDF BibTeX XML Cite \textit{D. Damanik}, Forum Math. 14, No. 5, 797--806 (2002; Zbl 1033.81031) Full Text: DOI
Bentosela, François; Briet, Philippe; Pastur, Leonid Absolutely continuous spectrum and scattering in the surface Maryland model. (English) Zbl 1026.47024 Journées “Équations aux dérivées partielles”, Plestin-les-Grèves, France, 5 au 8 juin 2001. Exposés Nos. I-XIV. Nantes: Université de Nantes. Exp. No. 10, 15 p. (2001). Reviewer: Messoud Efendiev (Berlin) MSC: 47B39 82B44 35J10 PDF BibTeX XML Cite \textit{F. Bentosela} et al., in: Journées ``Équations aux dérivées partielles'', Plestin-les-Grèves, France, 5 au 8 juin 2001. Exposés Nos. I-XIV. Nantes: Université de Nantes. Exp. No. 10, 15 p. (2001; Zbl 1026.47024) Full Text: Numdam EuDML
Nichols, J. M.; Virgin, L. N. Practical evaluation of invariant measures for the chaotic response of a two-frequency excited mechanical oscillator. (English) Zbl 1004.70020 Nonlinear Dyn. 26, No. 1, 67-86 (2001). MSC: 70K55 70K40 37N05 PDF BibTeX XML Cite \textit{J. M. Nichols} and \textit{L. N. Virgin}, Nonlinear Dyn. 26, No. 1, 67--86 (2001; Zbl 1004.70020) Full Text: DOI
Bourgain, J.; Jitomirskaya, S. Anderson localization for the band model. (English) Zbl 1039.81018 Milman, V. D. (ed.) et al., Geometric aspects of functional analysis. Proceedings of the Israel seminar (GAFA) 1996–2000. Berlin: Springer (ISBN 3-540-41070-8/pbk). Lect. Notes Math. 1745, 67-79 (2000). Reviewer: Messoud A. Efendiev (Berlin) MSC: 81Q10 39A70 82B44 47B39 47N50 PDF BibTeX XML Cite \textit{J. Bourgain} and \textit{S. Jitomirskaya}, Lect. Notes Math. 1745, 67--79 (2000; Zbl 1039.81018)
Broer, Henk; Simó, Carles Hill’s equation with quasi-periodic forcing: resonance tongues, instability pockets and global phenomena. (English) Zbl 0917.34019 Bol. Soc. Bras. Mat., Nova Sér. 29, No. 2, 253-293 (1998). MSC: 34B30 34C29 34C23 34C27 PDF BibTeX XML Cite \textit{H. Broer} and \textit{C. Simó}, Bol. Soc. Bras. Mat., Nova Sér. 29, No. 2, 253--293 (1998; Zbl 0917.34019) Full Text: DOI
Surace, Steve A finite range operator with a quasi-periodic potential. (English) Zbl 0838.47018 Differ. Integral Equ. 9, No. 1, 213-237 (1996). MSC: 47B25 47F05 47N20 PDF BibTeX XML Cite \textit{S. Surace}, Differ. Integral Equ. 9, No. 1, 213--237 (1996; Zbl 0838.47018)
Treshchev, Dmitrij V. On the reducibility of the one-dimensional Schrödinger equation with quasi-periodic potential. (English) Zbl 0838.34052 Kozlov, V. V. (ed.), Dynamical systems in classical mechanics. Transl., Ser. 2, Am. Math. Soc. 168(25), 129-140 (1995). Reviewer: J.Pöschel (Zürich) MSC: 34C27 34L40 PDF BibTeX XML Cite \textit{D. V. Treshchev}, Transl., Ser. 2, Am. Math. Soc. 168, 129--140 (1995; Zbl 0838.34052)
Kunz, H. Adiabatic charge transport and topological invariants for electrons in a quasi-periodic potential and a magnetic field. (English) Zbl 0823.58044 Helv. Phys. Acta 66, No. 3, 264-335 (1993). MSC: 58Z05 82B44 81Q10 81V70 82C70 PDF BibTeX XML Cite \textit{H. Kunz}, Helv. Phys. Acta 66, No. 3, 264--335 (1993; Zbl 0823.58044)
Soshnikov, Alexander Difference almost-periodic Schrödinger operators: Corollaries of localization. (English) Zbl 0772.34060 Commun. Math. Phys. 153, No. 3, 465-477 (1993). MSC: 34L40 34C27 39A70 47E05 PDF BibTeX XML Cite \textit{A. Soshnikov}, Commun. Math. Phys. 153, No. 3, 465--477 (1993; Zbl 0772.34060) Full Text: DOI
Eliasson, L. H. Floquet solutions for the 1-dimensional quasi-periodic Schrödinger equation. (English) Zbl 0753.34055 Commun. Math. Phys. 146, No. 3, 447-482 (1992). MSC: 34L40 34C25 81Q05 PDF BibTeX XML Cite \textit{L. H. Eliasson}, Commun. Math. Phys. 146, No. 3, 447--482 (1992; Zbl 0753.34055) Full Text: DOI
Goldsheid, I. Ya.; Sorets, E. Lyapunov exponents of the Schrödinger equation with quasi-periodic potential on a strip. (English) Zbl 0759.39001 Commun. Math. Phys. 145, No. 3, 507-513 (1992). Reviewer: S.Balint (Timişoara) MSC: 39A10 PDF BibTeX XML Cite \textit{I. Ya. Goldsheid} and \textit{E. Sorets}, Commun. Math. Phys. 145, No. 3, 507--513 (1992; Zbl 0759.39001) Full Text: DOI
Pastur, Leonid; Figotin, Alexander Spectra of random and almost-periodic operators. (English) Zbl 0752.47002 Grundlehren der Mathematischen Wissenschaften. 297. Berlin etc.: Springer-Verlag. viii, 587 p. (1992). Reviewer: J.F.Toland (Bath) MSC: 47-02 35J10 47N20 47F05 PDF BibTeX XML Cite \textit{L. Pastur} and \textit{A. Figotin}, Spectra of random and almost-periodic operators. Berlin etc.: Springer-Verlag (1992; Zbl 0752.47002)
Chulaevskii, V. A.; Sinai, Ya. G. The exponential localization and structure of the spectrum for 1D quasi- periodic discrete Schrödinger operators. (English) Zbl 0742.34074 Rev. Math. Phys. 3, No. 3, 241-284 (1991). MSC: 34L40 34L10 47E05 PDF BibTeX XML Cite \textit{V. A. Chulaevskii} and \textit{Ya. G. Sinai}, Rev. Math. Phys. 3, No. 3, 241--284 (1991; Zbl 0742.34074) Full Text: DOI
Sorets, Eugene; Spencer, Thomas Positive Lyapunov exponents for Schrödinger operators with quasi- periodic potentials. (English) Zbl 0745.34046 Commun. Math. Phys. 142, No. 3, 543-566 (1991). Reviewer: Y.Kivshar (Düsseldorf) MSC: 34D08 39A11 34L40 PDF BibTeX XML Cite \textit{E. Sorets} and \textit{T. Spencer}, Commun. Math. Phys. 142, No. 3, 543--566 (1991; Zbl 0745.34046) Full Text: DOI
Kunz, H. Topological invariants associated with quasi-periodic quantum Hamiltonians. (English) Zbl 0716.58028 Number theory and physics, Proc. Winter Sch., Les Houches/Fr. 1989, Springer Proc. Phys. 47, 157-161 (1990). Reviewer: W.Sarlet MSC: 35J10 81Q05 37J99 57R20 PDF BibTeX XML
Chulaevsky, V. A.; Sinai, Ya. G. Anderson localization and KAM-theory. (English) Zbl 0817.47045 Analysis, et cetera, Res. Pap. in Honor of J. Moser’s 60th Birthd., 237-249 (1990). Reviewer: N.D.Sengupta (Bombay) MSC: 47B39 47F05 58C25 58K99 PDF BibTeX XML
Chierchia, L.; Zehnder, E. Asymptotic expansions of quasiperiodic solutions. (English) Zbl 0695.34040 Ann. Sc. Norm. Super. Pisa, Cl. Sci., IV. Ser. 16, No. 2, 245-258 (1989). Reviewer: L.Chierchia MSC: 34C27 35C20 34C15 37-XX 34D30 30B10 PDF BibTeX XML Cite \textit{L. Chierchia} and \textit{E. Zehnder}, Ann. Sc. Norm. Super. Pisa, Cl. Sci., IV. Ser. 16, No. 2, 245--258 (1989; Zbl 0695.34040) Full Text: Numdam EuDML
Bellissard, J.; Iochum, B.; Scoppola, E.; Testard, D. Spectral properties of one dimensional quasi-crystals. (English) Zbl 0825.58010 Commun. Math. Phys. 125, No. 3, 527-543 (1989). MSC: 37E99 37A30 82D25 PDF BibTeX XML Cite \textit{J. Bellissard} et al., Commun. Math. Phys. 125, No. 3, 527--543 (1989; Zbl 0825.58010) Full Text: DOI
Spencer, Thomas Random and quasiperiodic Schrödinger operators. (English) Zbl 0676.47031 Proc. Int. Congr. Math., Berkeley/Calif. 1986, Vol. 2, 1312-1318 (1987). Reviewer: R.Salvi MSC: 47F05 39A70 35J10 PDF BibTeX XML
Delyon, François; Petritis, Dimitri Absence of localization in a class of Schrödinger operators with quasiperiodic potential. (English) Zbl 0604.35072 Commun. Math. Phys. 103, 441-444 (1986). Reviewer: M.Merigot MSC: 35Q99 35J10 47A10 35P05 PDF BibTeX XML Cite \textit{F. Delyon} and \textit{D. Petritis}, Commun. Math. Phys. 103, 441--444 (1986; Zbl 0604.35072) Full Text: DOI
Moser, Jürgen; Pöschel, Jürgen On the stationary Schrödinger equation with a quasi-periodic potential. (English) Zbl 0601.34016 Physica A 124, 535-542 (1984). MSC: 34L99 81Q05 PDF BibTeX XML Cite \textit{J. Moser} and \textit{J. Pöschel}, Physica A 124, 535--542 (1984; Zbl 0601.34016) Full Text: DOI
Figotin, A. L.; Pastur, L. A. An exactly solvable model of a multidimensional incommensurate structure. (English) Zbl 0582.35101 Commun. Math. Phys. 95, 401-425 (1984). MSC: 35Q99 35J10 35P05 PDF BibTeX XML Cite \textit{A. L. Figotin} and \textit{L. A. Pastur}, Commun. Math. Phys. 95, 401--425 (1984; Zbl 0582.35101) Full Text: DOI
Moser, Jürgen; Pöschel, Jürgen An extension of a result by Dinaburg and Sinai on quasi-periodic potentials. (English) Zbl 0533.34023 Comment. Math. Helv. 59, 39-85 (1984). MSC: 34L99 81Q15 PDF BibTeX XML Cite \textit{J. Moser} and \textit{J. Pöschel}, Comment. Math. Helv. 59, 39--85 (1984; Zbl 0533.34023) Full Text: DOI EuDML
Avron, Joseph E.; Simon, Barry Transient and recurrent spectrum. (English) Zbl 0488.47021 J. Funct. Anal. 43, 1-31 (1981). MSC: 47F05 47A10 47B25 PDF BibTeX XML Cite \textit{J. E. Avron} and \textit{B. Simon}, J. Funct. Anal. 43, 1--31 (1981; Zbl 0488.47021) Full Text: DOI