Derivation of the probability distribution function for the local density of states of a disordered quantum wire via the replica trick and supersymmetry

Bunder, J. E. and McKenzie, R. H. (2001) Derivation of the probability distribution function for the local density of states of a disordered quantum wire via the replica trick and supersymmetry. Nuclear Physics B, 592 3: 445-478. doi:10.1016/S0550-3213(00)00596-4


Author Bunder, J. E.
McKenzie, R. H.
Title Derivation of the probability distribution function for the local density of states of a disordered quantum wire via the replica trick and supersymmetry
Journal name Nuclear Physics B   Check publisher's open access policy
ISSN 0550-3213
Publication date 2001-01-01
Sub-type Article (original research)
DOI 10.1016/S0550-3213(00)00596-4
Open Access Status DOI
Volume 592
Issue 3
Start page 445
End page 478
Total pages 34
Editor G. Altarelli
W. Bartel
Place of publication Amsterdam
Publisher North-Holland
Language eng
Subject C1
240201 Theoretical Physics
780102 Physical sciences
Abstract We consider the statistical properties of the local density of states of a one-dimensional Dirac equation in the presence of various types of disorder with Gaussian white-noise distribution. It is shown how either the replica trick or supersymmetry can be used to calculate exactly all the moments of the local density of states.' Careful attention is paid to how the results change if the local density of states is averaged over atomic length scales. For both the replica trick and supersymmetry the problem is reduced to finding the ground state of a zero-dimensional Hamiltonian which is written solely in terms of a pair of coupled spins which are elements of u(1, 1). This ground state is explicitly found for the particular case of the Dirac equation corresponding to an infinite metallic quantum wire with a single conduction channel. The calculated moments of the local density of states agree with those found previously by Al'tshuler and Prigodin [Sov. Phys. JETP 68 (1989) 198] using a technique based on recursion relations for Feynman diagrams. (C) 2001 Elsevier Science B.V. All rights reserved.
Keyword Physics, Particles & Fields
Disordered Systems
Replica Trick
Supersymmetry
Path Integral
Localization
Mesoscopics
Lowest Landau-level
Strong Magnetic-field
Random-matrix Theory
Xy Spin Chains
Statistical Properties
Electron Localization
Phase-transitions
Of-states
Systems
Particles
Q-Index Code C1

Document type: Journal Article
Sub-type: Article (original research)
Collections: Centre for Organic Photonics and Electronics
School of Physical Sciences Publications
 
Versions
Version Filter Type
Citation counts: TR Web of Science Citation Count  Cited 6 times in Thomson Reuters Web of Science Article | Citations
Scopus Citation Count Cited 6 times in Scopus Article | Citations
Google Scholar Search Google Scholar
Created: Wed, 15 Aug 2007, 01:40:07 EST