Result: Quantum Diffusion and Eigenfunction Delocalization in a Random Band Matrix Model
Title:
Quantum Diffusion and Eigenfunction Delocalization in a Random Band Matrix Model
Authors:
Source:
Communications in mathematical physics. 303(2):509-554
Publisher Information:
Heidelberg: Springer, 2011.
Publication Year:
2011
Physical Description:
print, 48 ref
Original Material:
INIST-CNRS
Subject Terms:
Mathematics, Mathématiques, Theoretical physics, Physique théorique, Sciences exactes et technologie, Exact sciences and technology, Sciences et techniques communes, Sciences and techniques of general use, Mathematiques, Mathematics, Algèbre, Algebra, Algèbre linéaire et multilinéaire, matrices, Linear and multilinear algebra, matrix theory, Analyse numérique. Calcul scientifique, Numerical analysis. Scientific computation, Analyse numérique, Numerical analysis, Algèbre linéaire numérique, Numerical linear algebra, Equations algébriques et transcendantes non linéaires, Nonlinear algebraic and transcendental equations, Physique, Physics, Generalites, General, Méthodes mathématiques en physique, Mathematical methods in physics, Divers, Other topics in mathematical methods in physics, Fonction propre, Eigenfunctions, Hamiltonien, Hamiltonians, Localisation, Localization, Localización, Matrice bande, Band matrix, Matriz banda, Matrice symétrique, Symmetric matrix, Matriz simétrica, Physique mathématique, Mathematical physics, Variable aléatoire, Random variable, Variable aléatoria, Vecteur propre, Eigenvectors, 15A52, 65F15, 65H17
Document Type:
Academic journal
Article
File Description:
text
Language:
English
Author Affiliations:
Institute of Mathematics, University of Munich, Theresienstr. 39, 80333 Munich, Germany
Department of Mathematics, Harvard University, Cambridge, MA 02138, United States
Department of Mathematics, Harvard University, Cambridge, MA 02138, United States
ISSN:
0010-3616
Rights:
Copyright 2014 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.24069804
Database:
PASCAL Archive
Further Information
We consider Hermitian and symmetric random band matrices H in d ≥ 1 dimensions. The matrix elements Hxy, indexed by x, y E A C ℤd, are independent, uniformly distributed random variables if |x-y| is less than the band width W, and zero otherwise. We prove that the time evolution of a quantum particle subject to the Hamiltonian H is diffusive on time scales t ≪ Wd/3. We also show that the localization length of the eigenvectors of H is larger than a factor Wd/6 times the band width. All results are uniform in the size |Λ| of the matrix.