Satija, Indubala I.; Wilkinson, Michael Nests and chains of Hofstadter butterflies. (English) Zbl 1514.82146 J. Phys. A, Math. Theor. 53, No. 8, Article ID 085703, 18 p. (2020). MSC: 82C26 28A80 PDF BibTeX XML Cite \textit{I. I. Satija} and \textit{M. Wilkinson}, J. Phys. A, Math. Theor. 53, No. 8, Article ID 085703, 18 p. (2020; Zbl 1514.82146) Full Text: DOI arXiv
Albert, Victor V.; Pascazio, Saverio; Devoret, Michel H. General phase spaces: from discrete variables to rotor and continuum limits. (English) Zbl 1383.81119 J. Phys. A, Math. Theor. 50, No. 50, Article ID 504002, 29 p. (2017). MSC: 81S30 70G10 81V80 82B20 34C15 82D80 PDF BibTeX XML Cite \textit{V. V. Albert} et al., J. Phys. A, Math. Theor. 50, No. 50, Article ID 504002, 29 p. (2017; Zbl 1383.81119) Full Text: DOI arXiv
Eliashvili, M.; Tsitsishvili, G.; Japaridze, G. The quantum group and Harper equation on a honeycomb lattice. (English. Russian original) Zbl 1352.82005 J. Math. Sci., New York 216, No. 4, 522-526 (2016); translation from Sovrem. Mat. Prilozh. 94 (2014). Reviewer: Nasir N. Ganikhodjaev (Kuantan) MSC: 82B20 81R50 17B37 35Q82 35Q40 PDF BibTeX XML Cite \textit{M. Eliashvili} et al., J. Math. Sci., New York 216, No. 4, 522--526 (2016; Zbl 1352.82005); translation from Sovrem. Mat. Prilozh. 94 (2014) Full Text: DOI
Kulikov, A. N.; Kulikov, D. A. Bifurcations in a boundary-value problem of nanoelectronics. (English. Russian original) Zbl 1331.35039 J. Math. Sci., New York 208, No. 2, 211-221 (2015); translation from Probl. Mat. Anal. 80, 57-65 (2015). MSC: 35B32 35K35 35K58 35B35 PDF BibTeX XML Cite \textit{A. N. Kulikov} and \textit{D. A. Kulikov}, J. Math. Sci., New York 208, No. 2, 211--221 (2015; Zbl 1331.35039); translation from Probl. Mat. Anal. 80, 57--65 (2015) Full Text: DOI
Jones-Smith, Katherine; Wallace, Connor Hofstadter’s Cocoon. (English) Zbl 1314.81181 Int. J. Theor. Phys. 54, No. 1, 219-226 (2015). MSC: 81V70 78A35 PDF BibTeX XML Cite \textit{K. Jones-Smith} and \textit{C. Wallace}, Int. J. Theor. Phys. 54, No. 1, 219--226 (2015; Zbl 1314.81181) Full Text: DOI arXiv
Hulton, S.; Mestel, B. D. Renormalization of fluctuations for a generalized Harper equation for periodic continued fractions. (English) Zbl 1351.37172 Dyn. Syst. 30, No. 1, 85-121 (2015). MSC: 37E20 47B39 39A12 PDF BibTeX XML Cite \textit{S. Hulton} and \textit{B. D. Mestel}, Dyn. Syst. 30, No. 1, 85--121 (2015; Zbl 1351.37172) Full Text: DOI
Li, Dan Harper operator, Fermi curves and Picard-Fuchs equation. (English) Zbl 1302.74199 Lett. Math. Phys. 104, No. 5, 613-624 (2014). MSC: 74S25 PDF BibTeX XML Cite \textit{D. Li}, Lett. Math. Phys. 104, No. 5, 613--624 (2014; Zbl 1302.74199) Full Text: DOI arXiv
Kulikov, A. N.; Kulikov, D. A. Formation of wavy nanostructures on the surface of flat substrates by ion bombardment. (Russian, English) Zbl 1274.82111 Zh. Vychisl. Mat. Mat. Fiz. 52, No. 5, 930-945 (2012); translation in Comput. Math. Math. Phys. 52, No. 5, 800-814 (2012). MSC: 82D80 PDF BibTeX XML Cite \textit{A. N. Kulikov} and \textit{D. A. Kulikov}, Zh. Vychisl. Mat. Mat. Fiz. 52, No. 5, 930--945 (2012; Zbl 1274.82111); translation in Comput. Math. Math. Phys. 52, No. 5, 800--814 (2012) Full Text: DOI
Abderramán Marrero, J.; Rachidi, M. Application of the companion factorization to linear non-autonomous area-preserving maps. (English) Zbl 1248.15013 Linear Multilinear Algebra 60, No. 2, 201-217 (2012). Reviewer: Juan Ramon Torregrosa Sanchez (Valencia) MSC: 15A23 15A86 47B39 65F30 39A70 39A05 PDF BibTeX XML Cite \textit{J. Abderramán Marrero} and \textit{M. Rachidi}, Linear Multilinear Algebra 60, No. 2, 201--217 (2012; Zbl 1248.15013) Full Text: DOI
Helffer, Bernard; Pankrashkin, Konstantin Semiclassical reduction for magnetic Schrödinger operator with periodic zero-range potentials and applications. (English) Zbl 1185.35043 Asymptotic Anal. 63, No. 1-2, 1-27 (2009). Reviewer: Nils Ackermann (México) MSC: 35J10 35P05 47G30 47N50 81Q20 PDF BibTeX XML Cite \textit{B. Helffer} and \textit{K. Pankrashkin}, Asymptotic Anal. 63, No. 1--2, 1--27 (2009; Zbl 1185.35043) Full Text: DOI arXiv
Ye, Bin; Xu, Wenbo; Gu, Binjie Robust quantum computation of the quantum kicked Harper model and dissipative decoherence. (Chinese. English summary) Zbl 1174.81314 Acta Phys. Sin. 57, No. 2, 689-695 (2008). MSC: 81P68 65C05 PDF BibTeX XML Cite \textit{B. Ye} et al., Acta Phys. Sin. 57, No. 2, 689--695 (2008; Zbl 1174.81314)
Jorba, Àngel; Tatjer, Joan Carles; Núnẽz, Carmen; Obaya, Rafael Old and new results on strange nonchaotic attractors. (English) Zbl 1149.37303 Int. J. Bifurcation Chaos Appl. Sci. Eng. 17, No. 11, 3895-3928 (2007). MSC: 37C60 37D25 37C70 81Q05 39A12 PDF BibTeX XML Cite \textit{À. Jorba} et al., Int. J. Bifurcation Chaos Appl. Sci. Eng. 17, No. 11, 3895--3928 (2007; Zbl 1149.37303) Full Text: DOI
Mestel, B. D.; Osbaldestin, A. H. Golden mean renormalization for a generalized Harper equation: the Ketoja-Satija orchid. (English) Zbl 1064.47036 J. Math. Phys. 45, No. 12, 5042-5075 (2004). MSC: 47B39 35J10 37N20 39A10 47B36 81Q05 PDF BibTeX XML Cite \textit{B. D. Mestel} and \textit{A. H. Osbaldestin}, J. Math. Phys. 45, No. 12, 5042--5075 (2004; Zbl 1064.47036) Full Text: DOI
Datta, S.; Jäger, T.; Keller, G.; Ramaswamy, R. On the dynamics of the critical Harper map. (English) Zbl 1069.37068 Nonlinearity 17, No. 6, 2315-2323 (2004). Reviewer: Jerzy Ombach (Kraków) MSC: 37N20 37M25 37A20 37B25 54H20 PDF BibTeX XML Cite \textit{S. Datta} et al., Nonlinearity 17, No. 6, 2315--2323 (2004; Zbl 1069.37068) Full Text: DOI
Papp, Erhardt; Micu, Codruṫa Deriving exact energy solutions to the symmetrized \(q\)-difference Harper equation. (English) Zbl 1244.39009 Phys. Rev. E (3) 65, No. 4, Article ID 046234, 8 p. (2002). MSC: 39A13 PDF BibTeX XML Cite \textit{E. Papp} and \textit{C. Micu}, Phys. Rev. E (3) 65, No. 4, Article ID 046234, 8 p. (2002; Zbl 1244.39009) Full Text: DOI
Barker, Laurence The discrete fractional Fourier transform and Harper’s equation. (English) Zbl 1030.42006 Mathematika 47, No. 1-2, 281-297 (2000). Reviewer: Stefan G.Samko (Faro) MSC: 42A38 47B39 PDF BibTeX XML Cite \textit{L. Barker}, Mathematika 47, No. 1--2, 281--297 (2000; Zbl 1030.42006) Full Text: DOI
Krasovsky, I. V. On the discriminant of Harper’s equation. (English) Zbl 0969.47026 Lett. Math. Phys. 52, No. 2, 155-163 (2000). Reviewer: Ryszard Szwarc (Wrocław) MSC: 47B39 PDF BibTeX XML Cite \textit{I. V. Krasovsky}, Lett. Math. Phys. 52, No. 2, 155--163 (2000; Zbl 0969.47026) Full Text: DOI arXiv
Papp, E.; Micu, C. Symmetry properties of exact energy solutions to the Harper equation and related \(q\)-normalizations. (English) Zbl 0963.39024 J. Phys. A, Math. Gen. 33, No. 37, 6615-6626 (2000). Reviewer: Katsuya Ishizaki (Saitama) MSC: 39A13 81Q70 82B10 PDF BibTeX XML Cite \textit{E. Papp} and \textit{C. Micu}, J. Phys. A, Math. Gen. 33, No. 37, 6615--6626 (2000; Zbl 0963.39024) Full Text: DOI
Barker, Laurence; Candan, Çağatay; Hakioğlu, Tuğrul; Kutay, M. Alper; Ozaktas, Haldun M. The discrete harmonic oscillator, Harper’s equation, and the discrete fractional Fourier transform. (English) Zbl 0991.39007 J. Phys. A, Math. Gen. 33, No. 11, 2209-2222 (2000). MSC: 39A12 34C10 65T50 PDF BibTeX XML Cite \textit{L. Barker} et al., J. Phys. A, Math. Gen. 33, No. 11, 2209--2222 (2000; Zbl 0991.39007) Full Text: DOI Link
Micu, C.; Papp, E. Non-polynomial solutions to the \(q\)-difference form of the Harper equation. (English) Zbl 0905.39001 J. Phys. A, Math. Gen. 31, No. 12, 2881-2887 (1998). MSC: 39A10 81V10 PDF BibTeX XML Cite \textit{C. Micu} and \textit{E. Papp}, J. Phys. A, Math. Gen. 31, No. 12, 2881--2887 (1998; Zbl 0905.39001) Full Text: DOI
Bellissard, Jean; Camacho, Carlos J.; Barelli, Armelle; Claro, Francisco Exact random walk distributions using noncommutative geometry. (English) Zbl 0942.82010 J. Phys. A, Math. Gen. 30, No. 21, L707-L709 (1997). MSC: 82B41 58B32 60G50 PDF BibTeX XML Cite \textit{J. Bellissard} et al., J. Phys. A, Math. Gen. 30, No. 21, L707--L709 (1997; Zbl 0942.82010) Full Text: DOI arXiv
Rüdinger, Andreas; Piéchon, Frédéric Hofstadter rules and generalized dimensions of the spectrum of Harper’s equation. (English) Zbl 0917.39003 J. Phys. A, Math. Gen. 30, No. 1, 117-128 (1997). MSC: 39A10 81Q05 81Q20 39A12 81V70 PDF BibTeX XML Cite \textit{A. Rüdinger} and \textit{F. Piéchon}, J. Phys. A, Math. Gen. 30, No. 1, 117--128 (1997; Zbl 0917.39003) Full Text: DOI arXiv
Ketoja, Jukka A.; Satija, Indubala I. Harper equation, the dissipative standard map and strange nonchaotic attractors: Relationship between an eigenvalue problem and iterated maps. (English) Zbl 0925.58057 Physica D 109, No. 1-2, 70-80 (1997). MSC: 37D45 39A10 PDF BibTeX XML Cite \textit{J. A. Ketoja} and \textit{I. I. Satija}, Physica D 109, No. 1--2, 70--80 (1997; Zbl 0925.58057) Full Text: DOI
Janssen, T. Aperiodic Schrödinger operators. Electrons and phonons in aperiodic crystals. (English) Zbl 0883.47087 Moody, Robert V. (ed.), The mathematics of long-range aperiodic order. Proceedings of the NATO Advanced Study Institute, Waterloo, Ontario, Canada, August 21–September 1, 1995. Dordrecht: Kluwer Academic Publishers. NATO ASI Ser., Ser. C, Math. Phys. Sci. 489, 269-306 (1997). Reviewer: M.Demuth (Clausthal) MSC: 47N50 81Q10 81Q05 PDF BibTeX XML Cite \textit{T. Janssen}, NATO ASI Ser., Ser. C, Math. Phys. Sci. 489, 269--306 (1997; Zbl 0883.47087)
Sjöstrand, Johannes Complex integral transforms, diffraction, resonances, and phase space tunneling. (English) Zbl 0884.35004 Jerison, David (ed.) et al., The legacy of Norbert Wiener: a centennial symposium. In honor of the 100th anniversary of Norbert Wiener’s birth, October 8-14, 1994, Cambridge, MA, USA. Providence, RI: American Mathematical Society. Proc. Symp. Pure Math. 60, 355-371 (1997). Reviewer: B.Helffer (Orsay) MSC: 35A27 35P20 35A22 PDF BibTeX XML Cite \textit{J. Sjöstrand}, Proc. Symp. Pure Math. 60, 355--371 (1997; Zbl 0884.35004)
Buslaev, V. S.; Fedotov, A. A. The Harper equation: Monodromization without quasiclassics. (English. Russian original) Zbl 0866.34071 St. Petersbg. Math. J. 8, No. 2, 231-254 (1997); translation from Algebra Anal. 8, No. 2, 65-97 (1996). MSC: 34L40 81Q05 34E20 PDF BibTeX XML Cite \textit{V. S. Buslaev} and \textit{A. A. Fedotov}, St. Petersbg. Math. J. 8, No. 2, 65--97 (1996; Zbl 0866.34071); translation from Algebra Anal. 8, No. 2, 65--97 (1996)
Buslaev, V. S.; Fedotov, A. A. The Harper equation: Monodromization without quasiclassics. (Russian) Zbl 0849.34066 Algebra Anal. 8, No. 2, 65-97 (1996). Reviewer: L.A.Sakhnovich (Odessa) MSC: 34L40 81Q05 34E20 PDF BibTeX XML Cite \textit{V. S. Buslaev} and \textit{A. A. Fedotov}, Algebra Anal. 8, No. 2, 65--97 (1996; Zbl 0849.34066)
Buslaev, V.; Fedotov, A. Spectral properties of the monodromy matrix for Harper equation. (English) Zbl 0874.39006 Journ. Équ. Dériv. Partielles, St.-Jean-de-Monts 1996, Exp. No. 4, 11 p. (1996). Reviewer: R.Vaillancourt (Ottawa) MSC: 39A11 39A10 PDF BibTeX XML Cite \textit{V. Buslaev} and \textit{A. Fedotov}, Journ. Équ. Dériv. Partielles, St.-Jean-de-Monts 1996, Exp. No. 4, 11 p. (1996; Zbl 0874.39006) Full Text: Numdam EuDML
Tan, Yong Total bandwidth for Harper equation: Correction to renormalization analysis. (English) Zbl 0859.34076 J. Phys. A, Math. Gen. 28, No. 14, 4163-4173 (1995). MSC: 34L40 81Q05 PDF BibTeX XML Cite \textit{Y. Tan}, J. Phys. A, Math. Gen. 28, No. 14, 4163--4173 (1995; Zbl 0859.34076) Full Text: DOI
Borac, Silviu Algebraic techniques in the study of particle systems in a magnetic field. (English) Zbl 0873.46039 Berlin: TU Berlin, FB Math. 40 p. (1995). Reviewer: M.Gorzelańczyk (Wrocław) MSC: 46N50 46L10 PDF BibTeX XML Cite \textit{S. Borac}, Algebraic techniques in the study of particle systems in a magnetic field. Berlin: TU Berlin, FB Math. (1995; Zbl 0873.46039)
Buslaev, Vladimir; Fedotov, Alexander The functional structure of the monodromy matrix for Harper’s equation. (English) Zbl 0816.34058 Demuth, Michael (ed.) et al., Mathematical results in quantum mechanics: International conference in Blossin (Germany), May 17-21, 1993. Basel: Birkhäuser Verlag. Oper. Theory, Adv. Appl. 70, 321-342 (1994). Reviewer: Jiang Furu (Shanghai) MSC: 34L40 81Q05 34E20 PDF BibTeX XML Cite \textit{V. Buslaev} and \textit{A. Fedotov}, in: Mathematical results in quantum mechanics: International conference in Blossin (Germany), May 17-21, 1993. Basel: Birkhäuser Verlag. 321--342 (1994; Zbl 0816.34058)
Buslaev, V.; Fedotov, A. Monodromization and the Harper equation. (English) Zbl 0880.34082 Sémin. Équ. Dériv. Partielles, Éc. Polytech., Cent. Math., Palaiseau Sémin. 1993-1994, Exp. No. 21, 21 p. (1994). Reviewer: V.C.Boffi (Roma) MSC: 34L05 34L40 34M99 PDF BibTeX XML Cite \textit{V. Buslaev} and \textit{A. Fedotov}, Sémin. Équ. Dériv. Partielles, Éc. Polytech., Cent. Math. Laurent Schwartz, Palaiseau, Exp. No. 21, 21\,p. (1994; Zbl 0880.34082) Full Text: EuDML
El Naschie, M. S. Semiconductors, Fermi statistics and multi-dimensional Cantor sets. (English) Zbl 0786.58025 Chaos Solitons Fractals 3, No. 4, 481-488 (1993). Reviewer: A.V.Aminova (Kazan’) MSC: 37A99 82D40 82D45 PDF BibTeX XML Cite \textit{M. S. El Naschie}, Chaos Solitons Fractals 3, No. 4, 481--488 (1993; Zbl 0786.58025) Full Text: DOI
Sjöstrand, Johannes Microlocal analysis for the periodic magnetic Schrödinger equation and related questions. (English) Zbl 0761.35090 Microlocal analysis and applications, Lect. 2nd Sess. CIME, Montecatini Terme/Italy 1989, Lect. Notes Math. 1495, 237-332 (1991). Reviewer: B.Helffer (Paris) MSC: 35Q40 35A27 81Q20 35-03 PDF BibTeX XML Cite \textit{J. Sjöstrand}, Lect. Notes Math. 1495, 237--332 (1991; Zbl 0761.35090)
Chulaevskij, Victor; Delyon, François Purely absolutely continuous spectrum for almost Mathieu operators. (English) Zbl 0714.34129 J. Stat. Phys. 55, No. 5-6, 1279-1284 (1989). MSC: 34L40 34B30 34L05 PDF BibTeX XML Cite \textit{V. Chulaevskij} and \textit{F. Delyon}, J. Stat. Phys. 55, No. 5--6, 1279--1284 (1989; Zbl 0714.34129) Full Text: DOI
Helffer, B.; Sjöstrand, J. Equation de Schrödinger avec champ magnétique et équation de Harper. (The Schrödinger equation with magnetic field and the Harper equation). (French) Zbl 0699.35189 Schrödinger operators, Proc. Nord. Summer Sch. Math., Sandbjerg Slot, Sønderborg/Denmark 1988, Lect. Notes Phys. 345, 118-197 (1989). Reviewer: V.I.Ivrij MSC: 35P05 35S05 35J10 PDF BibTeX XML
Helffer, B.; Sjöstrand, J. On the link between the Schrödinger operator with magnetic field and Harper’s equation. (English) Zbl 0684.35074 Partial differential equations, Proc. Symp., Hozhau/GDR 1988, Teubner- Texte Math. 112, 139-156 (1989). Reviewer: V.Bach MSC: 35P05 35Q99 35S15 60G25 PDF BibTeX XML
Helffer, B.; Sjöstrand, J. Analyse semi-classique pour l’équation de Harper (avec application à l’équation de Schrödinger avec champ magnétique). (Semiclassical analysis for the Harper equation (with application to the magnetic Schrödinger equation)). (French) Zbl 0714.34130 Mém. Soc. Math. Fr., Nouv. Sér. 34, 113 p. (1988). Reviewer: C.Zuily MSC: 34L40 35P15 34L15 81Q20 35B20 35J10 PDF BibTeX XML Cite \textit{B. Helffer} and \textit{J. Sjöstrand}, Mém. Soc. Math. Fr., Nouv. Sér. 34, 113 p. (1988; Zbl 0714.34130) Full Text: DOI Numdam EuDML
Helffer, B.; Sjöstrand, J. Structure cantorienne du spectre de l’opérateur de Harper. (Cantor structure of the spectrum of the Harper operator). (French) Zbl 0709.34066 Cah. Math., Oran 1988, No. 2, 31-37 (1988). Reviewer: B.Helffer MSC: 34L05 35P20 81Q10 PDF BibTeX XML Cite \textit{B. Helffer} and \textit{J. Sjöstrand}, Cah. Math., Oran 1988, No. 2, 31--37 (1988; Zbl 0709.34066)
Helffer, B.; Sjöstrand, J. Équation de Schrödinger avec champ magnétique et équation de Harper. (Schrödinger equation with magnetic field and Harper’s equation). (French) Zbl 0641.35015 Journ. Équ. Dériv. Partielles, St.-Jean-De-Monts 1987, Exp. No. 6, 9 p. (1987). MSC: 35J10 35Q99 PDF BibTeX XML Full Text: Numdam EuDML