Microlocal Analysis, Sharp Spectral Asymptotics and Applications II: Functional Methods and Eigenvalue Asymptotics, Ivrii Victor
Автор: Ivrii Victor Название: Microlocal Analysis, Sharp Spectral Asymptotics and Applications III: Magnetic Schrцdinger Operator 1 ISBN: 3030305392 ISBN-13(EAN): 9783030305390 Издательство: Springer Рейтинг: Цена: 158380.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: Smooth theory in dimensions 2 and 3.- Standard Theory.- 2D degenerating magnetic Schrцdinger operator.- 2D magnetic Schrцdinger near boundary.- Magnetic Schrцdinger operator: short loops.- Dirac operator with strong magnetic field.
Автор: Alice Guionnet Название: Asymptotics of Random Matrices and Related Models: The Uses of Dyson-Schwinger Equations ISBN: 1470450275 ISBN-13(EAN): 9781470450274 Издательство: Mare Nostrum (Eurospan) Рейтинг: Цена: 48490.00 T Наличие на складе: Невозможна поставка. Описание: Probability theory is based on the notion of independence. The celebrated law of large numbers and the central limit theorem describe the asymptotics of the sum of independent variables. However, there are many models of strongly correlated random variables: for instance, the eigenvalues of random matrices or the tiles in random tilings. Classical tools of probability theory are useless to study such models.These lecture notes describe a general strategy to study the fluctuations of strongly interacting random variables. This strategy is based on the asymptotic analysis of Dyson-Schwinger (or loop) equations: the author will show how these equations are derived, how to obtain the concentration of measure estimates required to study these equations asymptotically, and how to deduce from this analysis the global fluctuations of the model. The author will apply this strategy in different settings: eigenvalues of random matrices, matrix models with one or several cuts, random tilings, and several matrices models.
Автор: Ivrii Victor Название: Microlocal Analysis, Sharp Spectral Asymptotics and Applications V: Applications to Quantum Theory and Miscellaneous Problems ISBN: 3030305635 ISBN-13(EAN): 9783030305635 Издательство: Springer Рейтинг: Цена: 139750.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: No magnetic field case.- The case of external magnetic field.- The case of self-generated magnetic field, - The case of combined magnetic field.- Articles on asymptotics.- 100 years of Weyl's law
Автор: Victor Ivrii Название: Microlocal Analysis, Sharp Spectral Asymptotics and Applications II ISBN: 3030305406 ISBN-13(EAN): 9783030305406 Издательство: Springer Рейтинг: Цена: 79190.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: The prime goal of this monograph, which comprises a total of five volumes, is to derive sharp spectral asymptotics for broad classes of partial differential operators using techniques from semiclassical microlocal analysis, in particular, propagation of singularities, and to subsequently use the variational estimates in “small” domains to consider domains with singularities of different kinds. In turn, the general theory (results and methods developed) is applied to the Magnetic Schr?dinger operator, miscellaneous problems, and multiparticle quantum theory.In this volume the local spectral asymptotics of Volume I in the regular part of the domain are combined with variational estimates in the vicinity of singularities, and global asymptotics are derived in the general form. They are then applied to multiple cases and asymptotics with respect to a spectral parameter. Finally, cases in which only general methods but not the results can be applied (non-standard asymptotics) are studied.
Автор: Victor Ivrii Название: Microlocal Analysis, Sharp Spectral Asymptotics and Applications V ISBN: 3030305600 ISBN-13(EAN): 9783030305604 Издательство: Springer Рейтинг: Цена: 130430.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: The prime goal of this monograph, which comprises a total of five volumes, is to derive sharp spectral asymptotics for broad classes of partial differential operators using techniques from semiclassical microlocal analysis, in particular, propagation of singularities, and to subsequently use the variational estimates in “small” domains to consider domains with singularities of different kinds. In turn, the general theory (results and methods developed) is applied to the Magnetic Schr?dinger operator, miscellaneous problems, and multiparticle quantum theory.In this volume the methods developed in Volumes I, II, III and IV are applied to multiparticle quantum theory (asymptotics of the ground state energy and related problems), and to miscellaneous spectral problems.
Автор: Johannes Sj?strand Название: Non-Self-Adjoint Differential Operators, Spectral Asymptotics and Random Perturbations ISBN: 303010818X ISBN-13(EAN): 9783030108182 Издательство: Springer Рейтинг: Цена: 102480.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: The asymptotic distribution of eigenvalues of self-adjoint differential operators in the high-energy limit, or the semi-classical limit, is a classical subject going back to H. Weyl of more than a century ago.In the last decades there has been a renewed interest in non-self-adjoint differential operators which have many subtle properties such as instability under small perturbations. Quite remarkably, when adding small random perturbations to such operators, the eigenvalues tend to distribute according to Weyl's law (quite differently from the distribution for the unperturbed operators in analytic cases). A first result in this direction was obtained by M. Hager in her thesis of 2005. Since then, further general results have been obtained, which are the main subject of the present book.Additional themes from the theory of non-self-adjoint operators are also treated. The methods are very much based on microlocal analysis and especially on pseudodifferential operators. The reader will find a broad field with plenty of open problems.
Автор: Berry Michael Victor Название: Half-century Of Physical Asymptotics And Other Diversions, A: Selected Works By Michael Berry ISBN: 9813221208 ISBN-13(EAN): 9789813221208 Издательство: World Scientific Publishing Рейтинг: Цена: 65470.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: 'Comments made on the philosophy and conduct of science are valuable and have been influenced strongly by academic contacts at the University of Bristol, and indeed worldwide ... The variety of papers and their intended readerships make much of this volume appropriate and enjoyable for general readers, as well as for specialists.'Contemporary PhysicsMichael Berry is a theoretical physicist who has contributed to a wide variety of areas in quantum mechanics, optics and related mathematics, linked by the geometrical aspects of waves, especially phase. This collection of his selected published and unpublished papers, reviews, tributes to other scientists, speeches and other works ranges from the technical to the popular. It is organized by the themes of his significant scientific contributions. Detailed introductions emphasize the rich connections between the different themes. An essential read for physicists, mathematicians, students and philosophers of science.
Автор: Berry Michael Victor Название: Half-century Of Physical Asymptotics And Other Diversions, A: Selected Works By Michael Berry ISBN: 9813221194 ISBN-13(EAN): 9789813221192 Издательство: World Scientific Publishing Рейтинг: Цена: 242880.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: 'Comments made on the philosophy and conduct of science are valuable and have been influenced strongly by academic contacts at the University of Bristol, and indeed worldwide ... The variety of papers and their intended readerships make much of this volume appropriate and enjoyable for general readers, as well as for specialists.'Contemporary PhysicsMichael Berry is a theoretical physicist who has contributed to a wide variety of areas in quantum mechanics, optics and related mathematics, linked by the geometrical aspects of waves, especially phase. This collection of his selected published and unpublished papers, reviews, tributes to other scientists, speeches and other works ranges from the technical to the popular. It is organized by the themes of his significant scientific contributions. Detailed introductions emphasize the rich connections between the different themes. An essential read for physicists, mathematicians, students and philosophers of science.
Автор: Ivrii Victor Название: Microlocal Analysis, Sharp Spectral Asymptotics and Applications IV: Magnetic Schrцdinger Operator 2 ISBN: 3030305473 ISBN-13(EAN): 9783030305475 Издательство: Springer Рейтинг: Цена: 139750.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: Non-smooth theory and higher dimensions.- Irregular coefficients in dimensions 2, 3.- Full-rank case.- Non-full-rank case.- 4D-Schrцdinger with degenerating magnetic field.- 4D-Schrцdinger Operator with the strong magnetic field.- Eigenvalue asymptotics for Schrцdinger and dirac operators with the strong magnetic field.- Eigenvalue asymptotics: 2D case.- Eigenvalue asymptotics: 3D case.
Автор: Victor Ivrii Название: Microlocal Analysis, Sharp Spectral Asymptotics and Applications IV ISBN: 3030305449 ISBN-13(EAN): 9783030305444 Издательство: Springer Рейтинг: Цена: 130430.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: The prime goal of this monograph, which comprises a total of five volumes, is to derive sharp spectral asymptotics for broad classes of partial differential operators using techniques from semiclassical microlocal analysis, in particular, propagation of singularities, and to subsequently use the variational estimates in “small” domains to consider domains with singularities of different kinds. In turn, the general theory (results and methods developed) is applied to the Magnetic Schr?dinger operator, miscellaneous problems, and multiparticle quantum theory.In this volume the methods developed in Volumes I, II and III are applied to the Schr?dinger and Dirac operators in non-smooth settings and in higher dimensions.
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