Strong resonant tunneling, level repulsion and spectral type for one-dimensional adiabatic quasi-periodic Schrodinger operators

被引：10

作者：

Fedotov, A

Klopp, FR

机构：

[1] St Petersburg State Univ, Dept Math Phys, St Petersburg 198904, Russia

[2] Univ Paris 13, CNRS, LAGA, UMR 7539, F-93430 Villetaneuse, France

来源：

ANNALES SCIENTIFIQUES DE L ECOLE NORMALE SUPERIEURE | 2005年 / 38卷 / 06期

关键词：

D O I：

10.1016/j.ansens.2005.10.002

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we consider one-dimensional adiabatic quasi-periodic Schrodinger operators in the regime of strong resonant tunneling. We show the emergence of a level repulsion phenomenon which is seen to be very naturally related to the local spectral type of the operator: the more singular the spectrum, the weaker the repulsion. (c) 2005 Elsevier SAS.

引用

页码：889 / 950

页数：62

共 50 条

[1] Level repulsion and spectral type for one-dimensional adiabatic quasi-periodic Schrodinger operators
Fedotov, Alexander
Klopp, Frederic
[J]. MATHEMATICAL PHYSICS OF QUANTUM MECHANICS: SELECTED AND REFEREED LECTURES FROM QMATH9, 2006, 690 : 383 - +
[2] One-dimensional quasi-periodic Schrodinger operators - Dynamical systems and spectral theory
Eliasson, LH
[J]. EUROPEAN CONGRESS OF MATHEMATICS, VOL I, 1998, 168 : 178 - 190
[3] On the absolutely continuous spectrum of one-dimensional quasi-periodic Schrodinger operators in the adiabatic limit
Fedotov, A
Klopp, F
[J]. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2005, 357 (11) : 4481 - 4516
[4] LOCALIZATION FOR A CLASS OF ONE-DIMENSIONAL QUASI-PERIODIC SCHRODINGER-OPERATORS
FROHLICH, J
SPENCER, T
WITTWER, P
[J]. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1990, 132 (01) : 5 - 25
[5] Discrete one-dimensional quasi-periodic Schrodinger operators with pure point spectrum
Eliasson, LH
[J]. ACTA MATHEMATICA, 1997, 179 (02) : 153 - 196
[6] Reducibility of one-dimensional quasi-periodic Schrodinger equations
Geng, Jiansheng
Zhao, Zhiyan
[J]. JOURNAL DE MATHEMATIQUES PURES ET APPLIQUEES, 2015, 104 (03): : 436 - 453
[7] On the density of states of the one dimensional quasi-periodic Schrodinger operators
Amor, Sana Hadj
[J]. COMPTES RENDUS MATHEMATIQUE, 2006, 343 (06) : 423 - 426
[8] Dynamics and spectral theory of quasi-periodic Schrodinger-type operators
Marx, C. A.
Jitomirskaya, S.
[J]. ERGODIC THEORY AND DYNAMICAL SYSTEMS, 2017, 37 : 2353 - 2393
[9] Ballistic transport in one-dimensional quasi-periodic continuous Schrodinger equation
Zhao, Zhiyan
[J]. JOURNAL OF DIFFERENTIAL EQUATIONS, 2017, 262 (09) : 4523 - 4566
[10] Ballistic Motion in One-Dimensional Quasi-Periodic Discrete Schrodinger Equation
Zhao, Zhiyan
[J]. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2016, 347 (02) : 511 - 549

← 1 2 3 4 5 →