Generalized Kotani’s trick for unitary operators
Tài liệu tham khảo
Abakumov, 2013, Cyclicity in rank-1 perturbation problems, J. London Math. Soc., 88, 523, 10.1112/jlms/jdt028
Asch, 2010, Localization properties of the Chalker-Coddington model, Ann. Henri Poincaré, 11, 1341, 10.1007/s00023-010-0056-1
Bourget, 2002, Singular continuous Floquet operator for systems with increasing gaps, J. Math. Anal. Appl., 276, 28, 10.1016/S0022-247X(02)00277-9
Bourget, 2005, Singular continuous Floquet operator for periodic quantum systems, J. Math. Anal. Appl., 301, 65, 10.1016/j.jmaa.2004.07.008
Carmona, 1983, One-dimensional Schrödinger operators with random or deterministic potentials: New spectral types, J. Func. Anal., 51, 229, 10.1016/0022-1236(83)90027-7
Combescure, 1990, Spectral properties of a periodically kicked quantum Hamiltonian, J. Stat. Phys., 59, 679, 10.1007/BF01025846
Combescure, 1992, Recurrent versus diffusive dynamics for a kicked quantum oscillator, Ann. Inst. H. Poincaré A: Phys. Théor., 57, 67
de Oliveira, 1994, On kicked systems modulated along the Thue-Morse sequence, J. Phys. A: Math. Gen., 27, L847, 10.1088/0305-4470/27/22/001
de Oliveira, 2007, A Floquet operator with purely point spectrum and energy instability, Ann. H. Poincaré, 8, 1255, 10.1007/s00023-007-0334-8
del Rio, 1996, Operators with singular continuous spectrum. IV. Hausdorff dimensions, rank one perturbations, and localization, J. Anal. Math., 69, 153, 10.1007/BF02787106
del Rio, 2008, Spectral averaging techniques for Jacobi matrices, J. Math. Phys., 49, 023507, 10.1063/1.2840910
del Rio, 2007, Sturm-Liouville operators in the half axis with local perturbations, J. Math. Anal. Appl., 329, 557, 10.1016/j.jmaa.2006.07.015
Falconer, 1990
Gesztesy, 2004, SL(2, C), exponential Herglotz representations, and spectral averaging, S. Petersburg Math. J., 15, 393, 10.1090/S1061-0022-04-00814-3
Hamza, 2006, Localization for random unitary operators, Lett. Math. Phys., 75, 255, 10.1007/s11005-005-0044-4
Jones, 2004, Asymptotic growth of Cauchy transforms, Ann. Acad. Sci. Fenn. Math., 29, 99
Joye, 2005, Fractional Moment Estimates for Random Unitary Operators, Lett. Math. Phys., 72, 51, 10.1007/s11005-005-3256-8
Kotani, 1982, Lyapunov indices determine absolutely continuous spectra of stationary random one-dimensional Schrödinger operators, 225
Kotani, 1984, Lyapunov exponents and spectra for one dimensional random Schrödinger operators, Contemporary Math. (AMS), 50, 277, 10.1090/conm/050/841099
Marx, 2011, Continuity of spectral averaging, Proc. Amer. Math. Soc., 139, 283, 10.1090/S0002-9939-2010-10629-9
Mattila, 1995
McCaw, 2005, Pure point spectrum for the time evolution of a periodically rank-N kicked Hamiltonian, J. Math. Phys., 46, 24
Milek, 1990, Singular continuous quasi-energy spectrum in the kicked rotator with separable perturbation: possibility of the onset of quantum chaos, Phys. Rev. A, 42, 3213, 10.1103/PhysRevA.42.3213
Rogers, 1970
Rudin, 1987, 239
Simon, 1995, Spectral analysis of rank one perturbations and applications, 109, 10.1090/crmp/008/04
Simon, 2004, Analogs of the m-function in the theory of orthogonal polynomials on the unit circle, J. Comput. Appl. Math., 171, 411, 10.1016/j.cam.2004.01.022
Simon, 2005, Trace Ideals and Their Applications, 120
Simon, 1986, Singular continuous spectrum under rank one perturbations and localization for random Hamiltonians, Commun. Pure Appl. Math., 39, 75, 10.1002/cpa.3160390105
