Integrated Density Of States For Random Schrodinger Operators On Manifolds
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Existence and Regularity Properties of the Integrated Density of States of Random Schrödinger Operators
Author | : Ivan Veselic |
Publisher | : Springer Science & Business Media |
Total Pages | : 151 |
Release | : 2008-01-02 |
Genre | : Mathematics |
ISBN | : 3540726896 |
This book describes in detail a quantity encoding spectral feature of random operators: the integrated density of states or spectral distribution function. It presents various approaches to the construction of the integrated density of states and the proof of its regularity properties. The book also includes references to and a discussion of other properties of the IDS as well as a variety of models beyond those treated in detail here.
Smoothness of the Integrated Density of States for Random Schrodinger Operators on Multidimensional Strips
Author | : Clemens H. Glaffig |
Publisher | : |
Total Pages | : 150 |
Release | : 1988 |
Genre | : Electronic dissertations |
ISBN | : |
Spectral Theory of Schrodinger Operators
Author | : Rafael del Río |
Publisher | : American Mathematical Soc. |
Total Pages | : 264 |
Release | : 2004 |
Genre | : Mathematics |
ISBN | : 0821832972 |
This volume gathers the articles based on a series of lectures from a workshop held at the Institute of Applied Mathematics of the National University of Mexico. The aim of the book is to present to a non-specialized audience the basic tools needed to understand and appreciate new trends of research on Schrodinger operator theory. Topics discussed include various aspects of the spectral theory of differential operators, the theory of self-adjoint operators, finite rank perturbations, spectral properties of random Schrodinger operators, and scattering theory for Schrodinger operators. The material is suitable for graduate students and research mathematicians interested in differential operators, in particular, spectral theory of Schrodinger operators.
Spectral Analysis of Quantum Hamiltonians
Author | : Rafael Benguria |
Publisher | : Springer Science & Business Media |
Total Pages | : 341 |
Release | : 2012-06-30 |
Genre | : Mathematics |
ISBN | : 3034804148 |
This volume contains surveys as well as research articles broadly centered on spectral analysis. Topics range from spectral continuity for magnetic and pseudodifferential operators to localization in random media, from the stability of matter to properties of Aharonov-Bohm and Quantum Hall Hamiltonians, from waveguides and resonances to supersymmetric models and dissipative fermion systems. This is the first of a series of volumes reporting every two years on recent progress in spectral theory.
Analysis and Geometry on Graphs and Manifolds
Author | : Matthias Keller |
Publisher | : Cambridge University Press |
Total Pages | : 493 |
Release | : 2020-08-20 |
Genre | : Mathematics |
ISBN | : 1108587380 |
This book addresses the interplay between several rapidly expanding areas of mathematics. Suitable for graduate students as well as researchers, it provides surveys of topics linking geometry, spectral theory and stochastics.
Modern Approaches to Discrete Curvature
Author | : Laurent Najman |
Publisher | : Springer |
Total Pages | : 378 |
Release | : 2017-10-04 |
Genre | : Mathematics |
ISBN | : 3319580027 |
This book provides a valuable glimpse into discrete curvature, a rich new field of research which blends discrete mathematics, differential geometry, probability and computer graphics. It includes a vast collection of ideas and tools which will offer something new to all interested readers. Discrete geometry has arisen as much as a theoretical development as in response to unforeseen challenges coming from applications. Discrete and continuous geometries have turned out to be intimately connected. Discrete curvature is the key concept connecting them through many bridges in numerous fields: metric spaces, Riemannian and Euclidean geometries, geometric measure theory, topology, partial differential equations, calculus of variations, gradient flows, asymptotic analysis, probability, harmonic analysis, graph theory, etc. In spite of its crucial importance both in theoretical mathematics and in applications, up to now, almost no books have provided a coherent outlook on this emerging field.