GENERIC QUASILOCALIZED AND QUASIBALLISTIC DISCRETE SCHRODINGER OPERATORS

被引：9

作者：

Carvalho, Silas L. ^{[1
]}

de Oliveira, Cesar R. ^{[2
]}

机构：

[1] Univ Fed Minas Gerais, Dept Matemat, BR-30161970 Belo Horizonte, MG, Brazil

[2] Univ Fed Sao Carlos, Dept Matemat, BR-13560970 Sao Carlos, SP, Brazil

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2016年 / 144卷 / 01期

关键词：

SINGULAR CONTINUOUS-SPECTRUM; TRANSFER-MATRICES; TRANSPORT;

D O I：

10.1090/proc/12697

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We derive sufficient conditions for the presence of generic sets of discrete Schrodinger operators on l(2)(Z(d)), d >= 1, with both quasilocalized and quasiballistic dynamics, and apply them to three operator spaces, that is, with uniformly bounded, analytic quasiperiodic and unbounded potentials. It is concluded, for these spaces, that the dynamics is typically (from the topological viewpoint) nontrivial, whereas quantum intermittency is exceptional.

引用

页码：129 / 141

页数：13

共 11 条

[1] Positivity and continuity of the Lyapounov exponent for shifts on Td with arbitrary frequency vector and real analytic potential
Bourgain, J
[J]. JOURNAL D ANALYSE MATHEMATIQUE, 2005, 96 (1): : 313 - 355
[2] Power-law bounds on transfer matrices and quantum dynamics in one dimension-II
Damanik, D
Süto, A
Tcheremchantsev, S
[J]. JOURNAL OF FUNCTIONAL ANALYSIS, 2004, 216 (02) : 362 - 387
[3] de Oliveira CR, 2009, PROG MATH PHYS, V54, P5
[4] Operators with singular continuous spectrum .4. Hausdorff dimensions, rank one perturbations, and localization
delRio, R
Jitomirskaya, S
Last, Y
Simon, B
[J]. JOURNAL D ANALYSE MATHEMATIQUE, 1996, 69 : 153 - 200
[5] Transfer matrices and transport for Schrodinger operators
Germinet, F
Kiselev, A
Tcheremchantsev, S
[J]. ANNALES DE L INSTITUT FOURIER, 2004, 54 (03) : 787 - +
[6] A characterization of the Anderson metal-insulator transport transition
Germinet, F
Klein, A
[J]. DUKE MATHEMATICAL JOURNAL, 2004, 124 (02) : 309 - 350
[7] Germinet Francois, 2003, SEM EQ DER PART 2002
[8] MULTIFRACTAL ENERGY-SPECTRA AND THEIR DYNAMICAL IMPLICATIONS
GUARNERI, I
MANTICA, G
[J]. PHYSICAL REVIEW LETTERS, 1994, 73 (25) : 3379 - 3382
[9] Mantica G., 1997, PHYSICA D, V103, P476
[10] OPERATORS WITH SINGULAR CONTINUOUS-SPECTRUM .1. GENERAL OPERATORS
SIMON, B
[J]. ANNALS OF MATHEMATICS, 1995, 141 (01) : 131 - 145

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