Constructive fractional-moment criteria for localization in random operators

Michael Aizenman; Jeffrey H. Schenker; Roland M. Friedrich; Dirk Hundertmark

doi:10.1016/S0378-4371(00)00012-1

Constructive fractional-moment criteria for localization in random operators

Michael Aizenman, Jeffrey H. Schenker, Roland M. Friedrich, Dirk Hundertmark

Research output: Contribution to journal › Article › peer-review

9 Scopus citations

Abstract

We present a family of finite-volume criteria which cover the regime of exponential decay for the fractional moments of Green functions of operators with random potentials. Such decay is a technically convenient characterization of localization for it is known to imply spectral localization, absence of level repulsion, dynamical localization and a related condition which plays a significant role in the quantization of the Hall conductance in two-dimensional Fermi gases. The constructive criteria also preclude fast power-law decay of the Green functions at mobility edges.

Original language	English (US)
Pages (from-to)	369-377
Number of pages	9
Journal	Physica A: Statistical Mechanics and its Applications
Volume	279
Issue number	1
DOIs	https://doi.org/10.1016/S0378-4371(00)00012-1
State	Published - May 1 2000

All Science Journal Classification (ASJC) codes

Statistical and Nonlinear Physics
Statistics and Probability

Access to Document

10.1016/S0378-4371(00)00012-1

Cite this

@article{94cb93f6318648f387616816379aefa8,

title = "Constructive fractional-moment criteria for localization in random operators",

abstract = "We present a family of finite-volume criteria which cover the regime of exponential decay for the fractional moments of Green functions of operators with random potentials. Such decay is a technically convenient characterization of localization for it is known to imply spectral localization, absence of level repulsion, dynamical localization and a related condition which plays a significant role in the quantization of the Hall conductance in two-dimensional Fermi gases. The constructive criteria also preclude fast power-law decay of the Green functions at mobility edges.",

author = "Michael Aizenman and Schenker, \{Jeffrey H.\} and Friedrich, \{Roland M.\} and Dirk Hundertmark",

year = "2000",

month = may,

day = "1",

doi = "10.1016/S0378-4371(00)00012-1",

language = "English (US)",

volume = "279",

pages = "369--377",

journal = "Physica A: Statistical Mechanics and its Applications",

issn = "0378-4371",

publisher = "Elsevier B.V.",

number = "1",

}

TY - JOUR

T1 - Constructive fractional-moment criteria for localization in random operators

AU - Aizenman, Michael

AU - Schenker, Jeffrey H.

AU - Friedrich, Roland M.

AU - Hundertmark, Dirk

PY - 2000/5/1

Y1 - 2000/5/1

N2 - We present a family of finite-volume criteria which cover the regime of exponential decay for the fractional moments of Green functions of operators with random potentials. Such decay is a technically convenient characterization of localization for it is known to imply spectral localization, absence of level repulsion, dynamical localization and a related condition which plays a significant role in the quantization of the Hall conductance in two-dimensional Fermi gases. The constructive criteria also preclude fast power-law decay of the Green functions at mobility edges.

AB - We present a family of finite-volume criteria which cover the regime of exponential decay for the fractional moments of Green functions of operators with random potentials. Such decay is a technically convenient characterization of localization for it is known to imply spectral localization, absence of level repulsion, dynamical localization and a related condition which plays a significant role in the quantization of the Hall conductance in two-dimensional Fermi gases. The constructive criteria also preclude fast power-law decay of the Green functions at mobility edges.

UR - https://www.scopus.com/pages/publications/0033727833

UR - https://www.scopus.com/inward/citedby.url?scp=0033727833&partnerID=8YFLogxK

U2 - 10.1016/S0378-4371(00)00012-1

DO - 10.1016/S0378-4371(00)00012-1

M3 - Article

AN - SCOPUS:0033727833

SN - 0378-4371

VL - 279

SP - 369

EP - 377

JO - Physica A: Statistical Mechanics and its Applications

JF - Physica A: Statistical Mechanics and its Applications

IS - 1

ER -

Constructive fractional-moment criteria for localization in random operators

Abstract

All Science Journal Classification (ASJC) codes

Access to Document

Other files and links

Fingerprint

Cite this