Generalized Kotani’s trick for unitary operators

Reports on Mathematical Physics - Tập 79 - Trang 151-163 - 2017
César R. de Oliveira1, Wagner Monteiro1
1Departamento de Matemática, Universidade Federal de São Carlos, Cx. P. 676, São Carlos, SP, 13560-970 Brazil

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