Multidimensional Periodic Schr dinger Operator

Author: Oktay Veliev
Publisher: Springer
ISBN: 3319166433
Format: PDF, Mobi
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The book describes the direct problems and the inverse problem of the multidimensional Schrödinger operator with a periodic potential. This concerns perturbation theory and constructive determination of the spectral invariants and finding the periodic potential from the given Bloch eigenvalues. The unique method of this book derives the asymptotic formulas for Bloch eigenvalues and Bloch functions for arbitrary dimension. Moreover, the measure of the iso-energetic surfaces in the high energy region is construct and estimated. It implies the validity of the Bethe-Sommerfeld conjecture for arbitrary dimensions and arbitrary lattices. Using the perturbation theory constructed in this book, the spectral invariants of the multidimensional operator from the given Bloch eigenvalues are determined. Some of these invariants are explicitly expressed by the Fourier coefficients of the potential. This way the possibility to determine the potential constructively by using Bloch eigenvalues as input data is given. In the end an algorithm for the unique determination of the potential is given.

Electronic States in Crystals of Finite Size

Author: Shang Yuan Ren
Publisher: Springer
ISBN: 9811047189
Format: PDF, Mobi
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This book presents an analytical theory of the electronic states in ideal low dimensional systems and finite crystals based on a differential equation theory approach. It provides precise and fundamental understandings on the electronic states in ideal low-dimensional systems and finite crystals, and offers new insights into some of the basic problems in low-dimensional systems, such as the surface states and quantum confinement effects, etc., some of which are quite different from what is traditionally believed in the solid state physics community. Many previous predictions have been confirmed in subsequent investigations by other authors on various relevant problems. In this new edition, the theory is further extended to one-dimensional photonic crystals and phononic crystals, and a general theoretical formalism for investigating the existence and properties of surface states/modes in semi-infinite one-dimensional crystals is developed. In addition, there are various revisions and improvements, including using the Kronig-Penney model to illustrate the analytical theory and make it easier to understand. This book is a valuable resource for solid-state physicists and material scientists.

Electroweak Processes in External Active Media

Author: Alexander Kuznetsov
Publisher: Springer
ISBN: 3642362265
Format: PDF, Docs
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Expanding on the concept of the authors’ previous book “Electroweak Processes in External Electromagnetic Fields,” this new book systematically describes the investigation methods for the effects of external active media, both strong electromagnetic fields and hot dense plasma, in quantum processes. Solving the solar neutrino puzzle in a unique experiment conducted with the help of the heavy-water detector at the Sudbery Neutrino Observatory, along with another neutrino experiments, brings to the fore electroweak physics in an active external medium. It is effectively demonstrated that processes of neutrino interactions with active media of astrophysical objects may lead, under some physical conditions, to such interesting effects as neutrino-driven shockwave revival in a supernova explosion, a “cherry stone shooting” mechanism for pulsar natal kick, and a neutrino pulsar. It is also shown how poor estimates of particle dispersion in external active media sometimes lead to confusion. The book will appeal to graduate and post-graduate students of theoretical physics with a prior understanding of Quantum Field Theory (QFT) and the Standard Model of Electroweak Interactions, as well as to specialists in QFT who want to know more about the problems of quantum phenomena in hot dense plasma and external electromagnetic fields.

The Method of Approximate Inverse Theory and Applications

Author: Thomas Schuster
Publisher: Springer
ISBN: 3540712275
Format: PDF
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This book is concerned with the method of approximate inverse which is a regularization technique for stably solving inverse problems in various settings. It demonstrates the performance and functionality of the method on several examples from medical imaging and non-destructive testing, such as computerized tomography, Doppler tomography, SONAR, X-ray diffractometry and thermoacoustic computerized tomography.

Nonlinear Dispersive Equations

Author: Jaime Angulo Pava
Publisher: American Mathematical Soc.
ISBN: 0821848976
Format: PDF, Docs
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This book provides a self-contained presentation of classical and new methods for studying wave phenomena that are related to the existence and stability of solitary and periodic travelling wave solutions for nonlinear dispersive evolution equations. Simplicity, concrete examples, and applications are emphasized throughout in order to make the material easily accessible. The list of classical nonlinear dispersive equations studied includes Korteweg-de Vries, Benjamin-Ono, and Schrodinger equations. Many special Jacobian elliptic functions play a role in these examples. The author brings the reader to the forefront of knowledge about some aspects of the theory and motivates future developments in this fascinating and rapidly growing field. The book can be used as an instructive study guide as well as a reference by students and mature scientists interested in nonlinear wave phenomena.

Trace Ideals and Their Applications

Author: Barry Simon
Publisher: American Mathematical Soc.
ISBN: 0821849883
Format: PDF, Mobi
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From a review of the first edition: Beautifully written and well organized ... indispensable for those interested in certain areas of mathematical physics ... for the expert and beginner alike. The author deserves to be congratulated both for his work in unifying a subject and for showing workers in the field new directions for future development. --Zentralblatt MATH This is a second edition of a well-known book on the theory of trace ideals in the algebra of operators in a Hilbert space. Because of the theory's many different applications, the book was widely used and much in demand. For this second edition, the author has added four chapters on the closely related theory of rank one perturbations of self-adjoint operators. He has also included a comprehensive index and an addendum describing some developments since the original notes were published. This book continues to be a vital source of information for those interested in the theory of trace ideals and in its applications to various areas of mathematical physics.

Physics of Ferroelectrics

Author: Karin M. Rabe
Publisher: Springer Science & Business Media
ISBN: 3540345914
Format: PDF
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The past two decades have witnessed revolutionary breakthroughs in the understanding of ferroelectric materials, both from the perspective of theory and experiment. This book addresses the paradigmatic shifts in understanding brought about by these breakthroughs, including the consideration of novel fabrication methods and nanoscale applications of these materials, and new theoretical methods such as the effective Hamiltonian approach and density functional theory.

Introduction to Quantum Graphs

Author: Gregory Berkolaiko
Publisher: American Mathematical Soc.
ISBN: 0821892118
Format: PDF, ePub, Mobi
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A ``quantum graph'' is a graph considered as a one-dimensional complex and equipped with a differential operator (``Hamiltonian''). Quantum graphs arise naturally as simplified models in mathematics, physics, chemistry, and engineering when one considers propagation of waves of various nature through a quasi-one-dimensional (e.g., ``meso-'' or ``nano-scale'') system that looks like a thin neighborhood of a graph. Works that currently would be classified as discussing quantum graphs have been appearing since at least the 1930s, and since then, quantum graphs techniques have been applied successfully in various areas of mathematical physics, mathematics in general and its applications. One can mention, for instance, dynamical systems theory, control theory, quantum chaos, Anderson localization, microelectronics, photonic crystals, physical chemistry, nano-sciences, superconductivity theory, etc. Quantum graphs present many non-trivial mathematical challenges, which makes them dear to a mathematician's heart. Work on quantum graphs has brought together tools and intuition coming from graph theory, combinatorics, mathematical physics, PDEs, and spectral theory. This book provides a comprehensive introduction to the topic, collecting the main notions and techniques. It also contains a survey of the current state of the quantum graph research and applications.

Transport of Energetic Electrons in Solids

Author: Maurizio Dapor
Publisher: Springer
ISBN: 3319474928
Format: PDF, ePub, Mobi
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This new edition describes all the mechanisms of elastic and inelastic scattering of electrons with the atoms of the target as simple as possible. The use of techniques of quantum mechanics is described in detail for the investigation of interaction processes of electrons with matter. It presents the strategies of the Monte Carlo method, as well as numerous comparisons among the results of the simulations and the experimental data available in the literature. New in this edition is the description of the Mermin theory, a comparison between Mermin theory and Drude theory, a discussion about the dispersion laws, and details about the calculation of the phase shifts that are used in the relativistic partial wave expansion method. The role of secondary electrons in proton cancer therapy is discussed in the chapter devoted to applications. In this context, Monte Carlo results about the radial distribution of the energy deposited in PMMA by secondary electrons generated by energetic proton beams are presented.

Nonlinear and Complex Dynamics

Author: José António Tenreiro Machado
Publisher: Springer Science & Business Media
ISBN: 9781461402312
Format: PDF, ePub, Docs
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Nonlinear Dynamics of Complex Systems describes chaos, fractal and stochasticities within celestial mechanics, financial systems and biochemical systems. Part I discusses methods and applications in celestial systems and new results in such areas as low energy impact dynamics, low-thrust planar trajectories to the moon and earth-to-halo transfers in the sun, earth and moon. Part II presents the dynamics of complex systems including bio-systems, neural systems, chemical systems and hydro-dynamical systems. Finally, Part III covers economic and financial systems including market uncertainty, inflation, economic activity and foreign competition and the role of nonlinear dynamics in each.