Result: Tunneling for a Class of Difference Operators
Title:
Tunneling for a Class of Difference Operators
Authors:
Source:
Annales Henri Poincaré. 13(5):1231-1269
Publisher Information:
Heidelberg: Springer, 2012.
Publication Year:
2012
Physical Description:
print, 15 ref
Original Material:
INIST-CNRS
Subject Terms:
Mathematics, Mathématiques, Physics, Physique, Theoretical physics, Physique théorique, Sciences exactes et technologie, Exact sciences and technology, Sciences et techniques communes, Sciences and techniques of general use, Mathematiques, Mathematics, Analyse mathématique, Mathematical analysis, Equations aux dérivées partielles, Partial differential equations, Physique, Physics, Generalites, General, Méthodes mathématiques en physique, Mathematical methods in physics, Divers, Other topics in mathematical methods in physics, Opérateur Schrödinger, Schrödinger operator, Operador Schrodinger, Physique mathématique, Mathematical physics, Problème valeur propre, Eigenvalue problem, Problema valor propio, Puits potentiel, Potential well, Pozo potencial, 35J10, Analyse matricielle, Matrix analysis, Matrice similitude, Opérateur différence, Perturbation faible, Small perturbation, Petite perturbation
Document Type:
Academic journal
Article
File Description:
text
Language:
English
Author Affiliations:
Universität Potsdam, Institut für Mathematik, Am Neuen Palais 10, 14469 Potsdam, Germany
ISSN:
1424-0637
Rights:
Copyright 2015 INIST-CNRS
CC BY 4.0
Sauf mention contraire ci-dessus, le contenu de cette notice bibliographique peut être utilisé dans le cadre d’une licence CC BY 4.0 Inist-CNRS / Unless otherwise stated above, the content of this bibliographic record may be used under a CC BY 4.0 licence by Inist-CNRS / A menos que se haya señalado antes, el contenido de este registro bibliográfico puede ser utilizado al amparo de una licencia CC BY 4.0 Inist-CNRS
CC BY 4.0
Sauf mention contraire ci-dessus, le contenu de cette notice bibliographique peut être utilisé dans le cadre d’une licence CC BY 4.0 Inist-CNRS / Unless otherwise stated above, the content of this bibliographic record may be used under a CC BY 4.0 licence by Inist-CNRS / A menos que se haya señalado antes, el contenido de este registro bibliográfico puede ser utilizado al amparo de una licencia CC BY 4.0 Inist-CNRS
Notes:
Mathematics
Theoretical physics
Theoretical physics
Accession Number:
edscal.26007576
Database:
PASCAL Archive
Further Information
We analyze a general class of difference operators Hε = Tε + Vε on ℓ2 ((εℤ)d) where Vε is a multi-well potential and ε is a small parameter. We decouple the wells by introducing certain Dirichlet operators on regions containing only one potential well, and we shall treat the eigenvalue problem for Hε as a small perturbation of these comparison problems. We describe tunneling by a certain interaction matrix, similar to the analysis for the Schrödinger operator [see Helffer and Sjöstrand in Commun Partial Differ Equ 9:337-408, 1984], and estimate the remainder, which is exponentially small and roughly quadratic compared with the interaction matrix.