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Nato Science Series B:

Supersymmetry and Trace Formulae

Chaos and Disorder

Editors: Lerner, Igor V., Keating, Jonathan P., Khmelnitskii, David E. (Eds.)

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About this book

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.

Table of contents (20 chapters)

Table of contents (20 chapters)

Buy this book

eBook $109.00
price for USA in USD (gross)
  • ISBN 978-1-4615-4875-1
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $219.99
price for USA in USD
  • ISBN 978-0-306-45933-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $149.99
price for USA in USD
  • ISBN 978-1-4613-7212-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Supersymmetry and Trace Formulae
Book Subtitle
Chaos and Disorder
Editors
  • Igor V. Lerner
  • Jonathan P. Keating
  • David E. Khmelnitskii
Series Title
Nato Science Series B:
Series Volume
370
Copyright
1999
Publisher
Springer US
Copyright Holder
Springer Science+Business Media New York
eBook ISBN
978-1-4615-4875-1
DOI
10.1007/978-1-4615-4875-1
Hardcover ISBN
978-0-306-45933-7
Softcover ISBN
978-1-4613-7212-7
Series ISSN
0258-1221
Edition Number
1
Number of Pages
IX, 404
Topics