Articles liés à Supersymmetry and Trace Formulae: Chaos and Disorder
Synopsis
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.
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Supersymmetry and Trace Formulae
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Springer US Apr 1999, 1999
ISBN 10 : 0306459337
ISBN 13 : 9780306459337
Neuf
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Vendeur : BuchWeltWeit Ludwig Meier e.K., Bergisch Gladbach, Allemagne
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Buch. Etat : Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -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. 420 pp. Englisch. N° de réf. du vendeur 9780306459337
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Supersymmetry and Trace Formulae
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Gebunden. Etat : New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. Proceedings of a NATO ASI held in Cambridge, United Kingdom, September 8--20, 1997 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. N° de réf. du vendeur 5902834
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Supersymmetry and Trace Formulae: Chaos and Disorder (NATO Science Series B:, 370)
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Supersymmetry and Trace Formulae | Chaos and Disorder
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Buch. Etat : Neu. Supersymmetry and Trace Formulae | Chaos and Disorder | Igor V. Lerner (u. a.) | Buch | ix | Englisch | 1999 | Springer | EAN 9780306459337 | Verantwortliche Person für die EU: Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg, juergen[dot]hartmann[at]springer[dot]com | Anbieter: preigu Print on Demand. N° de réf. du vendeur 101980415
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Supersymmetry and Trace Formulae
Edité par
Springer US, Springer Apr 1999, 1999
ISBN 10 : 0306459337
ISBN 13 : 9780306459337
Neuf
Couverture rigide
Vendeur : buchversandmimpf2000, Emtmannsberg, BAYE, Allemagne
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Buch. Etat : Neu. This item is printed on demand - Print on Demand Titel. Neuware -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.Springer-Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 420 pp. Englisch. N° de réf. du vendeur 9780306459337
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Supersymmetry and Trace Formulae
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Supersymmetry and Trace Formulae : Chaos and Disorder
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Buch. Etat : Neu. nach der Bestellung gedruckt Neuware - Printed after ordering - 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. N° de réf. du vendeur 9780306459337
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SUPERSYMMETRY AND TRACE FORMULAE (HB 1999)
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