Overview

The motion of a particle in a random potential in two or more dimensions is chaotic, and the trajectories in deterministically chaotic systems are effectively random. It is therefore no surprise that there are links between the quantum properties of disordered systems and those of simple chaotic systems. The question is, how deep do the connec­ tions go? And to what extent do the mathematical techniques designed to understand one problem lead to new insights into the other? The canonical problem in the theory of disordered mesoscopic systems is that of a particle moving in a random array of scatterers. The aim is to calculate the statistical properties of, for example, the quantum energy levels, wavefunctions, and conductance fluctuations by averaging over different arrays; that is, by averaging over an ensemble of different realizations of the random potential. In some regimes, corresponding to energy scales that are large compared to the mean level spacing, this can be done using diagrammatic perturbation theory. In others, where the discreteness of the quantum spectrum becomes important, such an approach fails. A more powerful method, devel­ oped by Efetov, involves representing correlation functions in terms of a supersymmetric nonlinear sigma-model. This applies over a wider range of energy scales, covering both the perturbative and non-perturbative regimes. It was proved using this method that energy level correlations in disordered systems coincide with those of random matrix theory when the dimensionless conductance tends to infinity.

Full Product Details

Author:   Igor V. Lerner ,  Jonathan P. Keating ,  David E. Khmelnitskii
Publisher:   Springer-Verlag New York Inc.
Imprint:   Springer-Verlag New York Inc.
Edition:   Softcover reprint of the original 1st ed. 1999
Volume:   370
Dimensions:   Width: 17.80cm , Height: 2.20cm , Length: 25.40cm
Weight:   0.795kg
ISBN:  

9781461372127

ISBN 10:   1461372127
Pages:   404
Publication Date:   08 October 2012
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   Manufactured on demand  
We will order this item for you from a manufactured on demand supplier.

Table of Contents

Semiclassical Theory of Spectral Statistics and Riemann Zeros; J.P. Keating. Quantum Chaos: Lessons from Disordered Metals; A. Altland, et al. Supersymmetric Generalization of Dyson's Brownian Motion (Diffusion); T. Guhr. What Happens to the Integer Quantum Hall Effect in Three Dimensions? J.R. Chalker. Trace Formulas in Classical Dynamical Systems; P. Cvitanovic. Theory of Eigenfunction Scarring; L. Kaplan, E.J. Heller. Nonequilibrium Effects in the Tunneling Conductance Spectra of Small Metallic particles; O. Agam. Pair Correlations of Quantum Chaotic Maps from Supersymmetry; M.R. Zirnbauer. Semiclassical Quantization of Maps and Spectral Correlations; U. Smilansky. Wave Functions, Wigner Functions and Green Functions of Chaotic Systems; S. Fishman. Wave Functions in Chaotic Billiards: Supersymmetry Approach; K.B. Efetov. Correlations of Wave Functions in Disordered Systems; A.D. Mirlin. Spatial Correlations in Chaotic Eigenfunctions; M. Srednicki. Level Curvature Distribution Beyond Random matrix Theory; V.E. Kravtsov, et al. Almost-Hermitian Random Matrices: Applications to the Theory of Quantum Chaotic Scattering and Beyond; Y.V. Fyodorov. Topological Features of the Magnetic Response in Inhomogeneous Magnetic Fields; E. Akkermans. Trace Formulas in Classical Dynamical Systems; M. Wilkinson. From Classical to Quantum Kinetics; D.E. Khmelnitskii, B.A. Muzykantskii. Stochastic Scattering; H.A. Weidenmüller. H=xp and the Riemann Zeros; M.V. Berry, J.P. Keating.

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