An explicit skew-shift Schr\"odinger operator with positive Lyapunov exponent at small coupling
作者： Helge Krüger
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摘要: I give an example of a skew-shift Schrodinger operator with positive Lyapunov exponent in the spectrum for all coupling constant frequency. This is first this kind. The proof based on CMV operators given by skew-shift. Further results these are derived.
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arxiv.org参考文章(14)
Jean Bourgain, Green's Function Estimates for Lattice Schrödinger Operators and Applications. ,(2004)
Helge Krüger, On the spectrum of skew-shift Schrödinger operators arXiv: Spectral Theory. ,(2010)
Barry Simon, OPUC on one foot Bulletin of the American Mathematical Society. ,vol. 42, pp. 431- 460 ,(2005) , 10.1090/S0273-0979-05-01075-X
J. Bourgain, Estimates on Green’s functions, localization and the quantum kicked rotor model Annals of Mathematics. ,vol. 156, pp. 249- 294 ,(2002) , 10.2307/3597190
Jean Bourgain, Michael Goldstein, Wilhelm Schlag, Anderson Localization for Schrödinger Operators on ℤ with Potentials Given by the Skew–Shift Communications in Mathematical Physics. ,vol. 220, pp. 583- 621 ,(2001) , 10.1007/PL00005570
V. A. Chulaevsky, Ya. G. Sinai, Anderson localization for the 1-D discrete Schrödinger operator with two-frequency potential Communications in Mathematical Physics. ,vol. 125, pp. 91- 112 ,(1989) , 10.1007/BF01217771
Michael Goldstein, Wilhelm Schlag, Holder continuity of the integrated density of states for quasi-periodic Schrodinger equations and averages of shifts of subharmonic functions Annals of Mathematics. ,vol. 154, pp. 155- 203 ,(2001) , 10.2307/3062114
Helge Krüger, Probabilistic Averages of Jacobi Operators Communications in Mathematical Physics. ,vol. 295, pp. 853- 875 ,(2010) , 10.1007/S00220-010-1014-Y
Helge Krüger, Localization for Random Operators with Non-monotone Potentials with Exponentially Decaying Correlations Annales Henri Poincaré. ,vol. 13, pp. 543- 598 ,(2012) , 10.1007/S00023-011-0130-3
J. Bourgain, M. Goldstein, On nonperturbative localization with quasi-periodic potential Annals of Mathematics. ,vol. 152, pp. 835- 879 ,(2000) , 10.2307/2661356