Supersymmetry in Disorder and Chaos PDF Download

Author: Konstantin Efetov
Publisher: Cambridge University Press
ISBN: 9780521663823
Category : Mathematics
Languages : en
Pages : 470

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Book Description
This book provides a comprehensive treatment of the ideas and applications of supersymmetry.

Author: Igor V. Lerner
Publisher: Springer Science & Business Media
ISBN: 1461548756
Category : Science
Languages : en
Pages : 399

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Book Description
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: Fritz Haake
Publisher: Springer
ISBN: 3319975803
Category : Science
Languages : en
Pages : 659

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Book Description
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: Nina Hall
Publisher: W. W. Norton & Company
ISBN: 9780393312263
Category : Mathematics
Languages : en
Pages : 244

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Book Description
Chaos theory is giving scientists fresh insights into all sorts of unruly phenomena-from dripping faucets to swinging pendulums, from the vagaries of the weather to the movements of the planets, from heart rhythms to gold futures. In this collection of front-line reports, edited for the general reader, internationally recognized experts such as Ian Stewart, Robert M. May, and Benoit Mandelbrot draw on the latest research to trace the roots of chaos in modern science and mathematics.

Author: Giulio Casati
Publisher: IOS Press
ISBN: 9784274903663
Category : Optoelectronics
Languages : en
Pages : 554

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Author: Adam Nahum
Publisher: Springer
ISBN: 331906407X
Category : Science
Languages : en
Pages : 150

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Book Description
When close to a continuous phase transition, many physical systems can usefully be mapped to ensembles of fluctuating loops, which might represent for example polymer rings, or line defects in a lattice magnet, or worldlines of quantum particles. 'Loop models' provide a unifying geometric language for problems of this kind. This thesis aims to extend this language in two directions. The first part of the thesis tackles ensembles of loops in three dimensions, and relates them to the statistical properties of line defects in disordered media and to critical phenomena in two-dimensional quantum magnets. The second part concerns two-dimensional loop models that lie outside the standard paradigms: new types of critical point are found, and new results given for the universal properties of polymer collapse transitions in two dimensions. All of these problems are shown to be related to sigma models on complex or real projective space, CP^{n−1} or RP^{n−1} -- in some cases in a 'replica' limit -- and this thesis is also an in-depth investigation of critical behaviour in these field theories.

Author: P. Sebbah
Publisher: Springer Science & Business Media
ISBN: 9401009759
Category : Science
Languages : en
Pages : 452

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Book Description
Recent advances in wave propagation in random media are certainly consequences of new approaches to fundamental issues, as well as of a strong interest in potential applications. A collective effort has been made to present in this book the state of the art in fundamental concepts, as well as in biomedical imaging techniques. As an example, the recent introduction of wave chaos, and more specifically random matrix theory - an old tool from nuclear physics - to the study of multiple scattering, has pointed the way to a deeper understanding of wave coherence in complex media. At the same time, efficient new approaches for retrieving information from random media promise to allow wave imaging of small tumors in opaque tissues. Review chapters are written by experts in the field, with the aim of making the book accessible to the widest possible scientific audience: graduate students and research scientists in theoretical and applied physics, optics, acoustics, and biomedical physics.

Author: Frank Smith
Publisher: World Scientific
ISBN: 1786340240
Category : Mathematics
Languages : en
Pages : 205

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Book Description
This book is a guide to advanced techniques used widely in applied mathematical sciences research. Chapter by chapter, readers will be led from a foundation level understanding to advanced level understanding. This is the perfect text for graduate or PhD mathematical-science students looking for support in techniques such as practical analytical methods, finite elements and symmetry methods for differential equations.Advanced Techniques in Applied Mathematics is the first volume of the LTCC Advanced Mathematics Series. This series is the first to provide advanced introductions to mathematical science topics to advanced students of mathematics. Edited by the three joint heads of the London Taught Course Centre for PhD Students in the Mathematical Sciences (LTCC), each book supports readers in broadening their mathematical knowledge outside of their immediate research disciplines while also covering specialized key areas.

Author: David Neilson
Publisher: World Scientific
ISBN: 9814545236
Category :
Languages : en
Pages : 550

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Book Description
This inaugural volume in a new series on quantum many-body theory contains the papers presented at the Ninth International Conference on Recent Progress in Many-Body Theories. The conference focused on the development and refinement of many-body methods. A major aim was to foster the exchange of ideas among physicists working in such diverse areas as nuclear physics, quantum chemistry, complex systems, lattice Hamiltonians, quantum fluids and condensed matter physics. A special feature was a session devoted to theories for many-electron systems in low-dimensional quantum dots, wires and electrons.

Author: Gregory Schehr
Publisher: Oxford University Press
ISBN: 0198797311
Category : Mathematics
Languages : en
Pages : 641

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Book Description
This text covers in detail recent developments in the field of stochastic processes and Random Matrix Theory. Matrix models have been playing an important role in theoretical physics for a long time and are currently also a very active domain of research in mathematics.