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


Autoria(s): Bunder, J. E.; McKenzie, R. H.
Contribuinte(s)

G. Altarelli

W. Bartel

Data(s)

01/01/2001

Resumo

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.

Identificador

http://espace.library.uq.edu.au/view/UQ:59235

Idioma(s)

eng

Publicador

North-Holland

Palavras-Chave #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 #C1 #240201 Theoretical Physics #780102 Physical sciences
Tipo

Journal Article