The spectrum minimum for random Schroedinger operators with indefinite sign potentials

doi:10.1063/1.2162825

Title: The spectrum minimum for random Schroedinger operators with indefinite sign potentials

Full Record
Other Related Research

Abstract

This paper sets out to study the spectral minimum for an operator belonging to the family of random Schroedinger operators of the form H{sub {lambda}}{sub ,{omega}}=-{delta}+W{sub per}+{lambda}V{sub {omega}}, where we suppose that V{sub {omega}} is of Anderson type and the single site is assumed to be with an indefinite sign. Under some assumptions we prove that there exists {lambda}{sub 0}>0 such that for any {lambda} set-membership sign [0,{lambda}{sub 0}], the minimum of the spectrum of H{sub {lambda}}{sub ,{omega}} is obtained by a given realization of the random variables.

Authors:

Najar, Hatem ^[1]

Departement de Mathematiques Physiques, I.P.E.I. Monastir, 5000 Monastir (Tunisia)

Publication Date:: Sun Jan 15 00:00:00 EST 2006

OSTI Identifier:: 20768718

Resource Type:: Journal Article

Resource Relation:: Journal Name: Journal of Mathematical Physics; Journal Volume: 47; Journal Issue: 1; Other Information: DOI: 10.1063/1.2162825; (c) 2006 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA)

Country of Publication:: United States

Language:: English

Subject:: 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; POTENTIALS; QUANTUM OPERATORS; RANDOMNESS; SCHROEDINGER EQUATION; SPECTRA

Citation Formats


                    Najar, Hatem. The spectrum minimum for random Schroedinger operators with indefinite sign potentials.  United States: N. p., 2006. 
        Web.  doi:10.1063/1.2162825.

Copy to clipboard


                    Najar, Hatem. The spectrum minimum for random Schroedinger operators with indefinite sign potentials.  United States.  doi:10.1063/1.2162825.

Copy to clipboard


                    Najar, Hatem. Sun .  
        "The spectrum minimum for random Schroedinger operators with indefinite sign potentials".  United States.  
        doi:10.1063/1.2162825.

Copy to clipboard


                    
@article{osti_20768718,

  title        = {The spectrum minimum for random Schroedinger operators with indefinite sign potentials},

  author       = {Najar, Hatem},

  abstractNote = {This paper sets out to study the spectral minimum for an operator belonging to the family of random Schroedinger operators of the form H{sub {lambda}}{sub ,{omega}}=-{delta}+W{sub per}+{lambda}V{sub {omega}}, where we suppose that V{sub {omega}} is of Anderson type and the single site is assumed to be with an indefinite sign. Under some assumptions we prove that there exists {lambda}{sub 0}>0 such that for any {lambda} set-membership sign [0,{lambda}{sub 0}], the minimum of the spectrum of H{sub {lambda}}{sub ,{omega}} is obtained by a given realization of the random variables.},

  doi          = {10.1063/1.2162825},

  journal      = {Journal of Mathematical Physics},

  number       = 1,

  volume       = 47,

  place        = {United States},

  year         = {Sun Jan 15 00:00:00 EST 2006},

  month        = {Sun Jan 15 00:00:00 EST 2006}

}

Copy to clipboard

Journal Article:

DOI: 10.1063/1.2162825

Other availability

Find in Google Scholar

Search WorldCat to find libraries that may hold this journal

Save / Share:

Export Metadata

Save to My Library

Similar records in OSTI.GOV collections:

The resonance spectrum of Schroedinger operators with rapidly decaying potentials

Journal Article Stepin, Stanislav A ; Tarasov, Aleksei G - Sbornik. Mathematics

Resonances of the one-dimensional Schroedinger operator are investigated, that is, the poles of the analytic extension of the corresponding scattering matrix. For a certain class of superexponentially decreasing potentials, including the Gaussian potential, the Born approximation is substantiated for the problem of localizing the poles of the scattering matrix. This makes it possible to find an asymptotic law (a quantization rule) for the distribution of these poles. For the first time, using the method developed in the paper, asymptotic formulae for resonances are obtained in the case of potentials with noncompact support. Bibliography: 15 titles.
DOI: 10.1070/SM2009V200N12ABEH004062; COUNTRY OF INPUT: INTERNATIONAL ATOMIC ENERGY AGENCY (IAEA)
Basic properties of the current-current correlation measure for random Schroedinger operators

Journal Article Hislop, Peter D. ; Lenoble, Olivier ; Mathematics Department, University of California, Irvine, California 92697-3875 - Journal of Mathematical Physics

The current-current correlation measure plays a crucial role in the theory of conductivity for disordered systems. We prove a Pastur-Shubin-type formula for the current-current correlation measure expressing it as a thermodynamic limit for random Schroedinger operators on the lattice and the continuum. We prove that the limit is independent of the self-adjoint boundary conditions and independent of a large family of expanding regions. We relate this finite-volume definition to the definition obtained by using the infinite-volume operators and the trace-per-unit volume.
DOI: 10.1063/1.2378618
Inverse spectral results for Schroedinger operators on the unit interval with partial information given on the potentials

Journal Article Amour, L. ; Raoux, T. ; Faupin, J. - Journal of Mathematical Physics

We pursue the analysis of the Schroedinger operator on the unit interval in inverse spectral theory initiated in the work of Amour and Raoux [''Inverse spectral results for Schroedinger operators on the unit interval with potentials in Lp spaces,'' Inverse Probl. 23, 2367 (2007)]. While the potentials in the work of Amour and Raoux belong to L{sup 1} with their difference in L{sup p}(1{<=}p<{infinity}), we consider here potentials in W{sup k,1} spaces having their difference in W{sup k,p}, where 1{<=}p{<=}+{infinity}, k(set-membership sign)(0,1,2). It is proved that two potentials in W{sup k,1}([0,1]) being equal on [a,1] are also equal on [0,1]more »« less
DOI: 10.1063/1.3087426
Schroedinger operators with singular potentials and magnetic fields

Journal Article Kolokoltsov, V N - Sbornik. Mathematics

A formal Schroedinger operator of the form H=(-i {partial_derivative}/{partial_derivative}x +A(x)){sup 2} + V(x), in R{sup d} is considered, where A is a bounded measurable vector-valued function and both V(x) and divA are measures satisfying certain additional conditions. It is shown that one can give meaning to such an operator as a lower bounded self-adjoint operator in L{sup 2}(R{sup d}). The corresponding heat kernel is constructed and its small-time asymptotics are obtained. A rigorous Feynman path integral representation for the solutions of the heat and Schroedinger's equations with generator H is given.
DOI: 10.1070/SM2003V194N06ABEH000744; COUNTRY OF INPUT: INTERNATIONAL ATOMIC ENERGY AGENCY (IAEA)
Wave operator bounds for one-dimensional Schroedinger operators with singular potentials and applications

Journal Article Duchene, Vincent ; Marzuola, Jeremy L. ; Weinstein, Michael I. - Journal of Mathematical Physics

Boundedness of wave operators for Schroedinger operators in one space dimension for a class of singular potentials, admitting finitely many Dirac delta distributions, is proved. Applications are presented to, for example, dispersive estimates and commutator bounds.
DOI: 10.1063/1.3525977

Similar Records