Spectral Theory of Non-Commutative Harmonic Oscillators: An Introduction PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Spectral Theory of Non-Commutative Harmonic Oscillators: An Introduction PDF full book. Access full book title Spectral Theory of Non-Commutative Harmonic Oscillators: An Introduction by Alberto Parmeggiani. Download full books in PDF and EPUB format.
Author: Alberto Parmeggiani
Publisher: Springer Science & Business Media
ISBN: 3642119212
Category : Mathematics
Languages : en
Pages : 260
Get Book Here
Book Description
This volume describes the spectral theory of the Weyl quantization of systems of polynomials in phase-space variables, modelled after the harmonic oscillator. The main technique used is pseudodifferential calculus, including global and semiclassical variants. The main results concern the meromorphic continuation of the spectral zeta function associated with the spectrum, and the localization (and the multiplicity) of the eigenvalues of such systems, described in terms of “classical” invariants (such as the periods of the periodic trajectories of the bicharacteristic flow associated with the eiganvalues of the symbol). The book utilizes techniques that are very powerful and flexible and presents an approach that could also be used for a variety of other problems. It also features expositions on different results throughout the literature.
Author: Alberto Parmeggiani
Publisher: Springer Science & Business Media
ISBN: 3642119212
Category : Mathematics
Languages : en
Pages : 260
Get Book Here
Book Description
This volume describes the spectral theory of the Weyl quantization of systems of polynomials in phase-space variables, modelled after the harmonic oscillator. The main technique used is pseudodifferential calculus, including global and semiclassical variants. The main results concern the meromorphic continuation of the spectral zeta function associated with the spectrum, and the localization (and the multiplicity) of the eigenvalues of such systems, described in terms of “classical” invariants (such as the periods of the periodic trajectories of the bicharacteristic flow associated with the eiganvalues of the symbol). The book utilizes techniques that are very powerful and flexible and presents an approach that could also be used for a variety of other problems. It also features expositions on different results throughout the literature.
Author: Alberto Parmeggiani
Publisher:
ISBN:
Category :
Languages : en
Pages : 233
Get Book Here
Book Description
Author: Tsuyoshi Takagi
Publisher: Springer Nature
ISBN: 981155191X
Category : Technology & Engineering
Languages : en
Pages : 275
Get Book Here
Book Description
This open access book presents selected papers from International Symposium on Mathematics, Quantum Theory, and Cryptography (MQC), which was held on September 25-27, 2019 in Fukuoka, Japan. The international symposium MQC addresses the mathematics and quantum theory underlying secure modeling of the post quantum cryptography including e.g. mathematical study of the light-matter interaction models as well as quantum computing. The security of the most widely used RSA cryptosystem is based on the difficulty of factoring large integers. However, in 1994 Shor proposed a quantum polynomial time algorithm for factoring integers, and the RSA cryptosystem is no longer secure in the quantum computing model. This vulnerability has prompted research into post-quantum cryptography using alternative mathematical problems that are secure in the era of quantum computers. In this regard, the National Institute of Standards and Technology (NIST) began to standardize post-quantum cryptography in 2016. This book is suitable for postgraduate students in mathematics and computer science, as well as for experts in industry working on post-quantum cryptography.
Author: Giuseppe Dito
Publisher: World Scientific
ISBN: 981442501X
Category : Mathematics
Languages : en
Pages : 537
Get Book Here
Book Description
Noncommutative differential geometry has many actual and potential applications to several domains in physics ranging from solid state to quantization of gravity. The strategy is to formulate usual differential geometry in a somewhat unusual manner, using in particular operator algebras and related concepts, so as to be able to plug in noncommutativity in a natural way. Algebraic tools such as K-theory and cyclic cohomology and homology play an important role in this field.
Author: Tsuyoshi Takagi
Publisher: Springer
ISBN: 9811050651
Category : Computers
Languages : en
Pages : 363
Get Book Here
Book Description
This book presents the mathematical background underlying security modeling in the context of next-generation cryptography. By introducing new mathematical results in order to strengthen information security, while simultaneously presenting fresh insights and developing the respective areas of mathematics, it is the first-ever book to focus on areas that have not yet been fully exploited for cryptographic applications such as representation theory and mathematical physics, among others. Recent advances in cryptanalysis, brought about in particular by quantum computation and physical attacks on cryptographic devices, such as side-channel analysis or power analysis, have revealed the growing security risks for state-of-the-art cryptographic schemes. To address these risks, high-performance, next-generation cryptosystems must be studied, which requires the further development of the mathematical background of modern cryptography. More specifically, in order to avoid the security risks posed by adversaries with advanced attack capabilities, cryptosystems must be upgraded, which in turn relies on a wide range of mathematical theories. This book is suitable for use in an advanced graduate course in mathematical cryptography, while also offering a valuable reference guide for experts.
Author: Simone Malacrida
Publisher: Simone Malacrida
ISBN:
Category : Mathematics
Languages : en
Pages : 52
Get Book Here
Book Description
The following topics are presented in this book: basic concepts of operator functional analysis spectral theorem and spectral measurements Stone's theorem and physical applications
Author: K. B. Laursen
Publisher: Oxford University Press
ISBN: 9780198523819
Category : Mathematics
Languages : en
Pages : 610
Get Book Here
Book Description
Modern local spectral theory is built on the classical spectral theorem, a fundamental result in single-operator theory and Hilbert spaces. This book provides an in-depth introduction to the natural expansion of this fascinating topic of Banach space operator theory. It gives complete coverage of the field, including the fundamental recent work by Albrecht and Eschmeier which provides the full duality theory for Banach space operators. One of its highlights are the many characterizations of decomposable operators, and of other related, important classes of operators, including identifications of distinguished parts, and results on permanence properties of spectra with respect to several types of similarity. Written in a careful and detailed style, it contains numerous examples, many simplified proofs of classical results, extensive references, and open problems, suitable for continued research.
Author: Paul Frank Baum
Publisher: Springer
ISBN: 3642157084
Category : Mathematics
Languages : en
Pages : 322
Get Book Here
Book Description
This volume is an introductory textbook to K-theory, both algebraic and topological, and to various current research topics within the field, including Kasparov's bivariant K-theory, the Baum-Connes conjecture, the comparison between algebraic and topological K-theory of topological algebras, the K-theory of schemes, and the theory of dg-categories.
Author: Bei Hu
Publisher: Springer
ISBN: 364218460X
Category : Mathematics
Languages : en
Pages : 137
Get Book Here
Book Description
There is an enormous amount of work in the literature about the blow-up behavior of evolution equations. It is our intention to introduce the theory by emphasizing the methods while seeking to avoid massive technical computations. To reach this goal, we use the simplest equation to illustrate the methods; these methods very often apply to more general equations.
Author: Thomas Duquesne
Publisher: Springer Science & Business Media
ISBN: 3642140068
Category : Mathematics
Languages : en
Pages : 216
Get Book Here
Book Description
Focusing on the breadth of the topic, this volume explores Lévy processes and applications, and presents the state-of-the-art in this evolving area of study. These expository articles help to disseminate important theoretical and applied research to those studying the field.
