The recursion equation for the resolvent

For more info about our services contact : help@bestpfe.com

Table of contents

Introduction
I The Anderson Localization Transition: introduction
I.1 Disorder and Localization
I.2 Characteristics of the transition and localized states
I.3 Anderson Localization in one and two dimensions and weak localization
I.4 Scaling theory and field theory formulation
I.5 Anderson transition on the Bethe Lattice: mean field
I.6 Anderson Localization and Random Matrix Theory
I.7 Brief review on numerical results
I.8 Experiments on Localization
I.9 Open problems
I.9.1 Interactions and Many Body Localization
I.9.2 The problem of the intermediate phase
II Overview on analytical techniques and known results
II.1 Definitions
II.2 Cavity equations
II.2.1 On the Bethe Lattice
II.3 Supersymmetric method
II.4 Dyson Brownian motion model
IIILocalization Transitions of Lévy Matrices
III.1 Introduction and motivations
III.2 The recursion equation for the resolvent
III.3 The density of states
III.4 Computation of the mobility edge
III.4.1 The mapping to directed polymers in random media
III.5 Numerical check of the phase diagram
III.6 The problem of the intermediate phase: previous results
III.7 The Supersymmetric method applied to Lévy Matrices
III.7.1 Equation on R() with the supersymmetric method
III.8 The Dyson Brownian motion argument
III.9 Numerical results for μ 2 (1, 2)
III.10 Numerical results for μ 2 (0, 1)
III.10.1 Numerical results for Q(G)
III.10.2 Wavefunction statistics and multifractal spectrum
III.11 Summary of the results
IV Critical properties of the Anderson model in high dimension
IV.1 Numerical results in d = 3, . . . , 6
IV.1.1 Transport properties
IV.1.2 Statistics of level spacings and of wave-functions coefficients .
IV.2 Strong Disorder RG
IV.3 Summary of the results
Conclusion and perspectives
A Transfer Matrix, conductance and localization length
A.1 Transfer Matrix and conductance
A.2 Transfer Matrix and localization length
B Critical wave functions: multifractality
C The IPR in terms of the Green function
D The DoS of Sparse RM model with the supersymmetric method
E Meaning of the order parameter function
F The generalized central limit theorem
G Computation of the mobility edge of Lévy Matrices
List of Figures
Bibliography