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Author: Tobias Brandes
Publisher: Springer Science & Business Media
ISBN: 9783540407850
Category : Science
Languages : en
Pages : 446
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Book Description
The phenomenon of localization of the electronic wave function in a random medium can be regarded as the key manifestation of quantum coherence in a condensed matter system. As one of the most remarkable phenomena in condensed matter physics discovered in the 20th century, the localization problem is an indispensable part of the theory of the quantum Hall effects and rivals superconductivity in its significance as a manifestation of quantum coherence at a macroscopic scale. The present volume, written by some of the leading experts in the field, is intended to highlight some of the recent progress in the field of localization, with particular emphasis on the effect of interactions on quantum coherence. The chapters are written in textbook style and should serve as a reliable and thorough introduction for advanced students or researchers already working in the field of mesoscopic physics.
Author: Tobias Brandes
Publisher: Springer Science & Business Media
ISBN: 9783540407850
Category : Science
Languages : en
Pages : 446
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Book Description
The phenomenon of localization of the electronic wave function in a random medium can be regarded as the key manifestation of quantum coherence in a condensed matter system. As one of the most remarkable phenomena in condensed matter physics discovered in the 20th century, the localization problem is an indispensable part of the theory of the quantum Hall effects and rivals superconductivity in its significance as a manifestation of quantum coherence at a macroscopic scale. The present volume, written by some of the leading experts in the field, is intended to highlight some of the recent progress in the field of localization, with particular emphasis on the effect of interactions on quantum coherence. The chapters are written in textbook style and should serve as a reliable and thorough introduction for advanced students or researchers already working in the field of mesoscopic physics.
Author: Tobias Brandes
Publisher: Springer
ISBN: 9783662143957
Category :
Languages : en
Pages : 328
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Book Description
Author: Y. Nagaoka
Publisher: Springer Science & Business Media
ISBN: 3642818412
Category : Science
Languages : en
Pages : 236
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Book Description
This volume contains the proceedings of the Fourth Taniguchi International Symposium on the Theory of Condensed Matter, which was held at Senkari Semi nar House of Kwansei Gakuin Universi~y in Sanda-shi, Japan, during the period of 3-8 November 1981. The topic of the symposium was "Anderson rocalization," one of the most fundamental problems in condensed-matter physics. Since Anderson's classic paper was published in 1958, much theoretical and experimental effort has been performed to study the problem of electron localization in a random potential. Quite recently, Abrahams, Anderson, Licciardello, and Ramakrishnan proposed a scaling theory of the Anderson lo calization which made it possible to perform microscopic investigations. Rapid progress has followed and we are now getting a coherent picture of the behavior of electrons in disordered systems. When we organized the symposium, we asked Dr. Anderson to participate in it and to give a review talk on theoretical aspects of the problem. Though he kindly accepted our invitation, he could not come due to a sudden illness. A review talk was given by Professor Thouless who kindly accepted our request to take the place of Dr. Anderson. Fortunately, Dr. Anderson has since re covered from his illness.
Author: Wolfgang Bührer
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Author: Hidetoshi Fukuyama
Publisher:
ISBN:
Category :
Languages : en
Pages : 56
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Book Description
Author: Richard Wielebinski
Publisher: Springer Science & Business Media
ISBN: 9783540241751
Category : Science
Languages : en
Pages : 306
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Book Description
While magnetic fields permeate the universe on all scales, the present book is dedicated to their investigation on the largest scales and affords a balanced account of both theoretical and observational aspects. Written as a set of advanced lectures and tutorial reviews that lead up to the forefront of research, this book offers both a modern source of reference for the experienced researchers as well as a high-level introductory text for postgraduate students and nonspecialist researchers working in related areas.
Author: Evdokiya Georgieva Kostadinova
Publisher: Springer
ISBN: 3030022129
Category : Science
Languages : en
Pages : 107
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Book Description
This book introduces the spectral approach to transport problems in infinite disordered systems characterized by Anderson-type Hamiltonians. The spectral approach determines (with probability one) the existence of extended states for nonzero disorder in infinite lattices of any dimension and geometry. Here, the author focuses on the critical 2D case, where previous numerical and experimental results have shown disagreement with theory. Not being based on scaling theory, the proposed method avoids issues related to boundary conditions and provides an alternative approach to transport problems where interaction with various types of disorder is considered. Beginning with a general overview of Anderson-type transport problems and their relevance to physical systems, it goes on to discuss in more detail the most relevant theoretical, numerical, and experimental developments in this field of research. The mathematical formulation of the innovative spectral approach is introduced together with a physical interpretation and discussion of its applicability to physical systems, followed by a numerical study of delocalization in the 2D disordered honeycomb, triangular, and square lattices. Transport in the 2D honeycomb lattice with substitutional disorder is investigated employing a spectral analysis of the quantum percolation problem. Next, the applicability of the method is extended to the classical regime, with an examination of diffusion of lattice waves in 2D disordered complex plasma crystals, along with discussion of proposed future developments in the study of complex transport problems using spectral theory.
Author: Elena Tarquini
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
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Book Description
In this thesis, we investigate the behavior of Anderson Localization in high dimension. In the first part we study Lévy Matrices (LMs), a Random Matrix model with long-range hopping presenting strong analogy with the problem of Anderson Localization on tree-like structure, representative of the limit of infinite dimensionality. We establish the equation determining the localization transition and obtain the phase diagram. We investigate then the unusual behavior of the delocalized phase. Using arguments based on supersymmetric field theory and Dyson Brownian motion we show that the eigenvalue statistics is the same one as of the Gaussian orthogonal ensemble in the whole delocalized phase and is Poisson-like in the localized phase. Our numerical analysis confirms this result, valid in the limit of infinitely large LMs, and provides information on the behavior of other observables like the wave-functions statistics. At the same time, numerical results also reveal that the characteristic scale governing finite size effects diverges much faster than a power law approaching the transition and is already very large far from it. This leads to a very wide crossover region in which the system looks as if it were in a mixed phase. In the second part we study numerically the behavior of the Anderson Model in dimension from 3 to 6 through exact diagonalization, Transfer Matrix method and an approximate Strong Disorder Renormalization Group technique. The results we find suggest that the upper critical dimension of Anderson Localization is infinite. Finally, we discuss the possible implications of this scenario on the anomalous behavior of the delocalized phase of models representative of the limit of infinite dimension, like Lévy Matrices and the Anderson model on tree-like structures.
Author: Eleftherios N. Economou
Publisher: Springer Science & Business Media
ISBN: 3540288414
Category : Science
Languages : en
Pages : 477
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Book Description
Of interest to advanced students, this book focuses on Green's functions for obtaining simple and general solutions to basic problems in quantum physics. It demonstrates the unifying formalism of Green's functions across many applications, including transport properties, carbon nanotubes, and photonics and photonic crystals.
Author: Mohd. Shafie Naimah
Publisher:
ISBN:
Category : Light
Languages : en
Pages : 90
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Book Description
