A GENERAL DESCRIPTION OF QUANTUM DYNAMICAL SPREADING OVER AN ORTHONORMAL BASIS AND APPLICATIONS TO SCHRODINGER OPERATORS

被引：17

作者：

Damanik, David ^{[1
]}

Tcheremchantsev, Serguei ^{[2
]}

机构：

[1] Rice Univ, Dept Math, Houston, TX 77005 USA

[2] Univ Orleans, MAPMO, UMR 6628, F-45067 Orleans, France

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS | 2010年 / 28卷 / 04期

关键词：

Quantum dynamics; Schrodinger equation; Schrodinger operators; ABSOLUTELY CONTINUOUS-SPECTRUM; SINGULAR CONTINUOUS-SPECTRUM; DIMENSIONAL QUASI-CRYSTALS; UPPER-BOUNDS; JACOBI MATRICES; SPARSE POTENTIALS; MATHIEU OPERATOR; LOCALIZATION; CONTINUITY; TRANSPORT;

D O I：

10.3934/dcds.2010.28.1381

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We discuss the long-time behavior of solutions to the Schrodinger equation in some separable Hilbert space, with particular emphasis on the spreading over some orthonormal basis. Various ways of studying wavepacket spreading from this perspective are described and their inter-relations investigated. We also state and discuss known results for concrete quantum systems relative to this general framework.

引用

页码：1381 / 1412

页数：32

共 42 条

[1]

Avila A., ARXIV08102965

[2]

AVILA A, J EUR MATH IN PRESS

[3] Absolute continuity of the integrated density of states for the almost Mathieu operator with non-critical coupling [J].