Random Operators: Disorder Effects on Quantum Spectra and Dynamics, Michael Aizenman, Simone Warzel

Автор: Valter Moretti
Название: Spectral Theory and Quantum Mechanics
ISBN: 3319707051 ISBN-13(EAN): 9783319707051
Издательство: Springer
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Цена: 93160.00 T
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Описание: This mathematically rigorousm self-contained book explains the foundations of Quantum Mechanics and Quantum Theories in general. Includes a primer on general topology and abstract measure theory, along with material in the appendices on differential geometry.

Автор: Debra J. Searles; Ellak I.v. Nagy-Felsobuki
Название: Ab Initio Variational Calculations of Molecular Vibrational-Rotational Spectra
ISBN: 3540574654 ISBN-13(EAN): 9783540574651
Издательство: Springer
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Цена: 81050.00 T
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Описание: This monograph explores ab initio variational calculations of vibrational-rotational spectra in bent triatomic molecules. It provides a comprehensive derivation of the Eckart-Watson Hamiltonian in terms of an "f" co-ordinate system.

Автор: Lapidus Michel L., Frankenhuijsen Machiel van
Название: Fractal Geometry, Complex Dimensions and Zeta Functions / Geometry and Spectra of Fractal Strings
ISBN: 0387332855 ISBN-13(EAN): 9780387332857
Издательство: Springer
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Цена: 49330.00 T
Наличие на складе: Поставка под заказ.
Описание: Number theory, spectral geometry, and fractal geometry are interlinked in this in-depth study of the vibrations of fractal strings, that is, one-dimensional drums with fractal boundary.Key Features: - The Riemann hypothesis is given a natural geometric reformulation in the context of vibrating fractal strings- Complex dimensions of a fractal string, defined as the poles of an associated zeta function, are studied in detail, then used to understand the oscillations intrinsic to the corresponding fractal geometries and frequency spectra- Explicit formulas are extended to apply to the geometric, spectral, and dynamic zeta functions associated with a fractal- Examples of such formulas include Prime Orbit Theorem with error term for self-similar flows, and a tube formula- The method of diophantine approximation is used to study self-similar strings and flows- Analytical and geometric methods are used to obtain new results about the vertical distribution of zeros of number-theoretic and other zeta functionsThroughout new results are examined. The final chapter gives a new definition of fractality as the presence of nonreal complex dimensions with positive real parts.The significant studies and problems illuminated in this work may be used in a classroom setting at the graduate level. Fractal Geometry, Complex Dimensions and Zeta Functions will appeal to students and researchers in number theory, fractal geometry, dynamical systems, spectral geometry, and mathematical physics.

Автор: Leonid Pastur; Alexander Figotin
Название: Spectra of Random and Almost-Periodic Operators
ISBN: 364274348X ISBN-13(EAN): 9783642743481
Издательство: Springer
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Цена: 95770.00 T
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Описание: This is so not only because of the subject`s position at the in- tersection of operator spectral theory, probability theory and mathematical physics, but also because of its importance to theoretical physics, and par- ticularly to the theory of disordered condensed systems.

Автор: Takuya Kanazawa
Название: Dirac Spectra in Dense QCD
ISBN: 4431547061 ISBN-13(EAN): 9784431547068
Издательство: Springer
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Цена: 87060.00 T
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Описание: This book reviews dense quark matter in QCD with gauge group SU(2) using low-energy effective theoretical methods, and connections of statistical properties of the Dirac operator spectrum at high baryon chemical potential and a class of random matrix theories.

Автор: Valeri Ligatchev
Название: Mathematical & Physical Aspects of Experimental Investigations on Electron & Relaxation Time Spectra in Bulk & Nano-Structured Semiconductors & Insulators
ISBN: 1536125660 ISBN-13(EAN): 9781536125665
Издательство: Nova Science
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Цена: 257650.00 T
Наличие на складе: Невозможна поставка.
Описание: This book summarises important outcomes of a quarter century of developments in advanced mathematical approaches and their implementations for deconvolution. The analysis of electron and relaxation time spectra obtained from the results of appropriate physical experiments fulfilled on real samples of bulk amorphous/crystalline semiconductors and insulators as well as on nano-structured materials and devices are also discussed. The second chapter of this book depicts key features of many well-known traditional and some modern techniques for experimental investigations of electron density and time relaxation spectra in such semiconductors and insulators. as Additionally, there is an emphasis on archetypal problems related to the analysis and interpretation of the results of those experimental techniques. Some generic (though crucially important in the context of this book) physical and mathematical aspects of the polarisation and relaxation processes in solids, well-known one-dimensional direct and inverse integral transforms, linear integral equations of the first and second kinds, ill-posed mathematical problems and specific mathematical approaches to solution(s) of those are discussed in the third, fourth and fifth chapters, respectively. A majority of the aforementioned mathematical approaches are essentially based on the so-called regularisation concept, pioneered by famous Russian mathematicians (A N Tikhonov, M M Lavrentiev, V K Ivanov, V Ya Arsenin and their co-workers) in the second half of the twentieth century. Mathematical aspects of the regularisation concept are discussed (to some extent) in the fifth chapter of the book in comparison to the similar aspects of the traditional modelling approach with multiple references on appropriate original articles and books. Thanks to distinctive features of the regularisation concept, it endures a protracted history (which nowadays well exceeds 5 decades), becomes the dominant strategy for the solution of various inverse problems, and is widely used in many types of modern applications and computational packages. In particular, the regularisation algorithms are incorporated into Mathematica, Matlab, Python and Octave packages. This generic regularisation concept had been successfully implemented by the author of this book during the development and practical realisation (programming) of several essentially different regularisation algorithms (described in detail in the sixth chapter of the book) for unambiguous investigations and the analysis of results of appropriated physical experiments, fulfilled over a period from 1984 to 2009, both in Russia and in Singapore. Furthermore, actual results of such experimental investigations are discussed in the seventh chapter following closely appropriate original publications, and in comparison with their counterparts obtained by traditional (eg: modelling) approaches. As it is also demonstrated in the seventh chapter with the relevant examples and detailed discussion(s), the implementation of the aforementioned regularisation algorithms allows one to identify (and interpret thereafter) new important features of the intra-gap and near-band-gap electronic spectra of the amorphous and polycrystalline semiconductors and insulators. The relaxation time spectra of those materials, which are usually unattainable via the implementation of the modelling approach is also analysed. It is important that the regularisation concept (mathematically related to its alternative ones, e.g., the direct and inverse Radon integral transforms) has many other, very important implementations, e.g., in medical computerised tomography, security-related applications, archaeology, geophysics, etc. Similar to the abovementioned spectroscopic techniques, the X-ray-based computerised tomography eventually yields vital information on features of electron density distribution in a studied object, though the desired function in the latter case rather depends on spatial variables than on energetic ones. The mathematical essence of the Radon-transform-based computerised tomography is also summarised very briefly in one of the sections of this book. A comprehensive reference list of this book comprises many other key references (for those who are interested in the aforementioned topics discussed herein).

Автор: Daniel Lenz; Florian Sobieczky; Wolfgang Woess
Название: Random Walks, Boundaries and Spectra
ISBN: 3034803303 ISBN-13(EAN): 9783034803304
Издательство: Springer
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Цена: 121110.00 T
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Описание: These proceedings represent the current state of research on the topics `boundary theory` and `spectral and probability theory` of random walks on infinite graphs.