Dynamical Localization for Unitary Anderson Models

Springer Science and Business Media LLC - Tập 12 Số 4 - Trang 381-444 - 2009
Eman Hamza1, Alain Joye2, Günter Stolz3
1Department of Physics, Faculty of Science, Cairo University, Cairo, Egypt
2Institut Fourier
3Department of Mathematics, University of Alabama at Birmingham, Birmingham, USA

Tóm tắt

Từ khóa


Tài liệu tham khảo

Aizenman, M.: Localization at weak disorder: some elementary bounds. Rev. Math. Phys. 6, 1163 (1994)

Aizenman, M., Graf, G.-M.: Localization bounds for an electron gas. J. Phys., A, Math. Gen. 31, 6783 (1998)

Aizenman, M., Elgart, A., Naboko, S., Schenker, J., Stolz, G.: Moment analysis for localization in random Schrödinger operators. Invent. Math. 163, 343–413 (2006)

Aizenman, M., Molchanov, S.: Localization at large disorder and at extreme energies: an elementary derivation. Commun. Math. Phys. 157, 245–278 (1993)

Aizenman, M., Schenker, J., Friedrich, R., Hundertmark, D.: Finite-volume fractional-moment criteria for Anderson localization. Commun. Math. Phys. 224, 219–253 (2001)

Ao, P.: Absence of localization in energy space of a Bloch electron driven by a constant electric force. Phys. Rev., B 41, 3998–4001 (1989)

Asch, J., Duclos, P., Exner, P.: Stability of driven systems with growing gaps, quantum rings, and Wannier ladders. J. Stat. Phys. 92, 1053–1070 (1998)

Asch, J., Bentosela, F., Duclos, P., Nenciu, G.: On the dynamics of crystal electrons, high momentum regime. J. Math. Anal. Appl. 256, 99–114 (2001)

Bellissard, J.: Stability and instability in quantum mechanics. In: Albeverio, S., Blanchard, P. (eds.) Trends and Developments in the Eighties, pp. 1–106. World Scientific, Singapore (1985)

Bellissard, J.: Stability and chaotic behaviour in quantum rotators. In: Albeverio, S., Casati, G., Merlini, D. (eds.) Stochastic Processes in Classical and Quantum Systems. Springer, New York (1986)

Blatter, G., Browne, D.: Zener tunneling and localization in small conducting rings. Phys. Rev., B 37, 3856 (1988)

Bourget, O.: Singular continuous Floquet operator for periodic quantum systems. J. Math. Anal. Appl. 301(1), 65–83 (2005)

Bourget, O., Howland, J.S., Joye, A.: Spectral analysis of unitary band matrices. Commun. Math. Phys. 234, 191–227 (2003)

Boutet de Monvel, A., Naboko, S., Stollmann, P., Stolz, G.: Localization near fluctuation boundaries via fractional moments and applications. J. Anal. Math. 100, 83–116 (2006)

Bunimovich, L., Jauslin, H.R., Lebowitz, J.L., Pellegrinotti, A., Nielaba, P.: Diffusive energy growth in classical and quantum driven oscillators. J. Stat. Phys. 62, 793 (1991)

Carmona, R., Klein, A., Martinelli, F.: Anderson localization for Bernoulli and other singular potentials. Commun. Math. Phys. 108, 41–66 (1987)

Carmona, R., Lacroix, J.: Spectral theory of random Schrödinger operators. In: Probability and its Applications. Birkhäuser, Boston (1990)

Casati, G., Ford, J., Guarneri, I., Vivaldi, F.: Search for randomness in the kicked quantum rotator. Phys. Rev., A 34(2), 1413 (1986)

Combes, J.M., Thomas, L.: Asymptotic behaviour of eigenfunctions for multiparticle Schrödinger operators. Commun. Math. Phys. 34, 251–270 (1973)

Guarneri, I.: Spectral properties of quantum diffusion on discrete lattices. Europhys. Lett. 10, 95–100 (1989)

Combescure, M.: Spectral properties of a periodically kicked quantum Hamiltonian. J. Stat. Phys. 59, 679 (1990)

Combescure, M.: Recurrent versus diffusive dynamics for a kicked quantum oscillator. Ann. Inst. Henri Poincaré 57, 67–87 (1992)

Damanik, D., Stollmann, P.: Multiscale analysis implies strong dynamical localization. Geom. Funct. Anal. 11, 11–29, (2001)

DeBièvre, S., Forni, G.; Transport properties of kicked and quasiperiodic Hamiltonians. J. Stat. Phys. 90, 1201–1223 (1998)

Demko, S.: Inverses of band matrices and local convergence of spline projections. SIAM J. Numer. Anal. 14, 616–619 (1977)

de Oliveira, C.R.: On kicked systems modulated along the Thue-Morse sequence. J. Phys. A 27, 847–851 (1994)

de Oliveira, C.R., Simsen, M.S.: A floquet operator with purely point spectrum and energy instability. Ann. Henri Poincaré 7, 1255–1277 (2008)

Duclos, P., Soccorsi, E., Stovicek, P., Vittot, M.: On the stability of periodically time-dependent quantum systems. Rev. Math. Phys. 20, 6 (2008)

del Rio, R., Jitomirskaya, S., Last, Y., Simon, B.: Operators with singular continuous spectrum IV: Hausdorff dimensions, rank one perturbations and localization. J. Anal. Math. 69, 153 (1996)

Enss, V., Veselic, K.; Bound states and propagating states for time dependent Hamiltonians. Ann. Inst. Henri Poincaré, Ser. A 39, 159–191 (1983)

Germinet, F., DeBièvre, S.: Dynamical localization for discrete and continuous random Schrödinger operators. Commun. Math. Phys. 194, 323 (1998)

Germinet, F., Klein, A.: A characterization of the Anderson metal-insulator transport transition. Duke Math. J. 124, 309–351 (2004)

Graf, G.M.: Anderson localization and the space-time characteristic of continuum states. J. Stat. Phys. 75, 337–346 (1994)

Hamza, E.: Localization properties for the unitary Anderson model. PhD thesis, University of Alabama at Birmingham, 2007. https://www.mhsl.uab.edu/dt/2008r/hamza.pdf

Hamza, E., Joye, A., Stolz, G.: Localization for random unitary operators. Lett. Math. Phys. 75, 255–272 (2006)

Hamza, E., Stolz, G.: Lyapunov exponents for unitary Anderson models. J. Math. Phys. 48, 043301 (2007)

Howland, J.: Scattering theory for Hamiltonians periodic in time. Indiana Univ. Math. J. 28, 471–494 (1979)

Howland, J.: Quantum stability. In: Baslev, E. (ed.) Lecture Notes in Physics, vol. 403, pp. 100–122 (1992)

Jauslin, H.R., Lebowitz, J.L.: Spectral and stability aspects of quantum chaos. Chaos 1, 114–121 (1991)

Joye, A.: Density of states and Thouless formula for random unitary band matrices. Ann. Henri Poincaré 5, 347–379 (2004)

Joye, A.: Fractional moment estimates for random unitary band matrices. Lett. Math. Phys. 72, 51–64 (2005)

Kato, T.: Perturbation Theory for Linear Operators. Springer, New York (1982)

Kunz, H., Souillard, B.: Sur le spectre des opérateurs aux différences finies aléatoires. Commun. Math. Phys 78, 201 (1980)

Lenstra, D., van Haeringen, W.: Elastic scattering in a normal-metal loop causing resistive electronic behavior. Phys. Rev. Lett. 57, 1623–1626 (1986)

McCaw, J., McKellar, B.H.J.: Pure point spectrum for the time evolution of a periodically rank-N kicked Hamiltonian. J. Math. Phys. 46, 032108 (2005)

Pinsky, M.A.: Introduction to Fourier Analysis and Wavelets. Brooks/Cole, Florence (2002)

Rudin, W.: Real and Complex Analysis, 2nd edn. McGraw-Hill, New York (1987)

Ryu, J.-W., Hur, G., Kim, S.W.: Quantum localization in open chaotic systems. Phys. Rev., E, 037201 (2008)

Simon, B.: Orthogonal Polynomials on the Unit Circle, Part 1. American Mathematical Society, Providence (2005)

Simon, B.: Orthogonal Polynomials on the Unit Circle, Part 2. American Mathematical Society, Providence (2005)

Simon, B.: Aizenman’s theorem for orthogonal polynomials on the unit circle. Constr. Approx. 23, 229–240 (2006)

Simon, B.: CMV matrices: five years after. J. Comput. Appl. Math. 208, 120–154 (2007)

Simon, B.: Absence of ballistic motion. Commun. Math. Phys. 134, 209–212 (1990)

Simon, B., Wolff, T.: Singular continuous spectrum under rank one perturbations and localization for random Hamiltonians. Commun. Pure Appl. Math. 39, 75–90 (1986)

Stoiciu, M.; Poisson statistics for eigenvalues: from random Schrödinger operators to random CMV matrices. In: CRM Proceedings and Lecture Notes, vol. 42, pp. 465–475 (2007)

Stollmann, P.: Caught by Disorder, Bound States in Random Media, Progress in Mathematical Physics, vol. 20. Birkhäuser, Boston (2001)

Yajima, K.: Scattering theory for Schrödinger equations with potential periodic in time. J. Math. Soc. Jpn. 29, 729–743 (1977)