Supersymmetry In Disorder And Chaos

Author : Konstantin Efetov
Publisher : Cambridge University Press
ISBN 13 : 9780521663823
Total Pages : 470 pages
Book Rating : 4.22/5 ( download)

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Download or read book Supersymmetry in Disorder and Chaos written by Konstantin Efetov and published by Cambridge University Press. This book was released on 1999-09-13 with total page 470 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a comprehensive treatment of the ideas and applications of supersymmetry.

Author : Igor V. Lerner
Publisher : Springer Science & Business Media
ISBN 13 : 1461548756
Total Pages : 399 pages
Book Rating : 4.51/5 ( download)

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Download or read book Supersymmetry and Trace Formulae written by Igor V. Lerner and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 399 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Giulio Casati
Publisher : IOS Press
ISBN 13 : 9784274903663
Total Pages : 554 pages
Book Rating : 4.64/5 ( download)

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Download or read book New Directions in Quantum Chaos written by Giulio Casati and published by IOS Press. This book was released on 2000 with total page 554 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Fritz Haake
Publisher : Springer
ISBN 13 : 3319975803
Total Pages : 659 pages
Book Rating : 4.01/5 ( download)

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Download or read book Quantum Signatures of Chaos written by Fritz Haake and published by Springer. This book was released on 2019-02-18 with total page 659 pages. Available in PDF, EPUB and Kindle. Book excerpt: This classic text provides an excellent introduction to a new and rapidly developing field of research. Now well established as a textbook in this rapidly developing field of research, the new edition is much enlarged and covers a host of new results.

Author : Édouard Brezin
Publisher : Springer Science & Business Media
ISBN 13 : 9781402045295
Total Pages : 532 pages
Book Rating : 4.98/5 ( download)

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Download or read book Applications of Random Matrices in Physics written by Édouard Brezin and published by Springer Science & Business Media. This book was released on 2006-03-03 with total page 532 pages. Available in PDF, EPUB and Kindle. Book excerpt: Proceedings of the NATO Advanced Study Institute on Applications of Random Matrices in Physics, Les Houches, France, 6-25 June 2004

Author : Adam Smith
Publisher : Springer
ISBN 13 : 3030208516
Total Pages : 143 pages
Book Rating : 4.16/5 ( download)

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Download or read book Disorder-Free Localization written by Adam Smith and published by Springer. This book was released on 2019-07-01 with total page 143 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis is a contribution at the intersection of a number of active fields in theoretical and experimental condensed matter, particularly those concerned with disordered systems, integrable models, lattice gauge theories, and non-equilibrium quantum dynamics. It contributes an important new facet to our understanding of relaxation in isolated quantum systems by conclusively demonstrating localization without disorder for the first time, answering a long-standing question in this field. This is achieved by introducing a family of models – intimately related to paradigmatic condensed matter models – and studying their non-equilibrium dynamics through a combination of exact analytical mappings and an array of numerical techniques. This thesis also makes contributions relevant to the theory of quantum chaotic behaviour by calculating novel, and often intractable, entanglement measures and out-of-time-ordered correlators. A concrete and feasible proposal is also made for the experimental realization and dynamical study of the family of models, based on currently available technologies.

Author : Giulio Casati
Publisher : Cambridge University Press
ISBN 13 : 052143291X
Total Pages : 703 pages
Book Rating : 4.17/5 ( download)

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Download or read book Quantum Chaos written by Giulio Casati and published by Cambridge University Press. This book was released on 1995-04-27 with total page 703 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a comprehensive overview of our understanding of chaotic behaviour in quantum systems.

Author : Vladimir M. Akulin
Publisher : Springer Science & Business Media
ISBN 13 : 940077205X
Total Pages : 683 pages
Book Rating : 4.52/5 ( download)

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Download or read book Dynamics of Complex Quantum Systems written by Vladimir M. Akulin and published by Springer Science & Business Media. This book was released on 2013-12-30 with total page 683 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gathers together a range of similar problems that can be encountered in different fields of modern quantum physics and that have common features with regard to multilevel quantum systems. The main motivation was to examine from a uniform standpoint various models and approaches that have been developed in atomic, molecular, condensed matter, chemical, laser and nuclear physics in various contexts. The book should help senior-level undergraduate, graduate students and researchers putting particular problems in these fields into a broader scientific context and thereby taking advantage of well-established techniques used in adjacent fields. This second edition has been expanded to include substantial new material (e.g. new sections on Dynamic Localization and on Euclidean Random Matrices and new chapters on Entanglement, Open Quantum Systems, and Coherence Protection). It is based on the author’s lectures at the Moscow Institute of Physics and Technology, at the CNRS Aimé Cotton Laboratory, and on other courses he has given over the last two decades.

Author : Vladimir M. Akulin
Publisher : Springer Science & Business Media
ISBN 13 : 3540292713
Total Pages : 477 pages
Book Rating : 4.15/5 ( download)

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Download or read book Coherent Dynamics of Complex Quantum Systems written by Vladimir M. Akulin and published by Springer Science & Business Media. This book was released on 2005-12-21 with total page 477 pages. Available in PDF, EPUB and Kindle. Book excerpt: Coherent Dynamics of Complex Quantum Systems is aimed at senior-level undergraduate students in the areas of atomic, molecular, and laser physics, physical chemistry, quantum optics and quantum informatics. It should help them put particular problems in these fields into a broader scientific context and thereby take advantage of the well-elaborated technique of the adjacent fields.

Author : Franz Wegner
Publisher : Springer
ISBN 13 : 3662491702
Total Pages : 374 pages
Book Rating : 4.06/5 ( download)

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Download or read book Supermathematics and its Applications in Statistical Physics written by Franz Wegner and published by Springer. This book was released on 2016-03-25 with total page 374 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text presents the mathematical concepts of Grassmann variables and the method of supersymmetry to a broad audience of physicists interested in applying these tools to disordered and critical systems, as well as related topics in statistical physics. Based on many courses and seminars held by the author, one of the pioneers in this field, the reader is given a systematic and tutorial introduction to the subject matter. The algebra and analysis of Grassmann variables is presented in part I. The mathematics of these variables is applied to a random matrix model, path integrals for fermions, dimer models and the Ising model in two dimensions. Supermathematics - the use of commuting and anticommuting variables on an equal footing - is the subject of part II. The properties of supervectors and supermatrices, which contain both commuting and Grassmann components, are treated in great detail, including the derivation of integral theorems. In part III, supersymmetric physical models are considered. While supersymmetry was first introduced in elementary particle physics as exact symmetry between bosons and fermions, the formal introduction of anticommuting spacetime components, can be extended to problems of statistical physics, and, since it connects states with equal energies, has also found its way into quantum mechanics. Several models are considered in the applications, after which the representation of the random matrix model by the nonlinear sigma-model, the determination of the density of states and the level correlation are derived. Eventually, the mobility edge behavior is discussed and a short account of the ten symmetry classes of disorder, two-dimensional disordered models, and superbosonization is given.