A general description of quantum dynamical spreading over an orthonormal basis and applicationsto Schrödinger operators

David Damanik; Serguei Tcheremchantsev

doi:10.3934/dcds.2010.28.1381

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2010, Volume 28, Issue 4: 1381-1412. Doi: 10.3934/dcds.2010.28.1381

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A general description of quantum dynamical spreading over an orthonormal basis and applications to Schrödinger operators

David Damanik^1, and
Serguei Tcheremchantsev^2,

1.
Department of Mathematics, Rice University, Houston, TX 77005
2.
UMR 6628–MAPMO, Université d’Orléans, B.P. 6759, F-45067 Orléans Cedex

Received: September 30, 2009

Revised: January 31, 2010

Published: November 2010

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Abstract

We discuss the long-time behavior of solutions to the Schrödinger 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.

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Mathematics Subject Classification: Primary: 81Q10; Secondary: 47B36, 47N50.

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