Spectral Theory Of Non Commutative Harmonic Oscillators An Introduction
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Spectral Theory Of Non Commutative Harmonic Oscillators An Introduction
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Author : Alberto Parmeggiani
language : en
Publisher: Springer
Release Date : 2010-07-23
Spectral Theory Of Non Commutative Harmonic Oscillators An Introduction written by Alberto Parmeggiani and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-07-23 with Mathematics categories.
This book grew out of a series of lectures given at the Mathematics Department of Kyushu University in the Fall 2006, within the support of the 21st Century COE Program (2003–2007) “Development of Dynamical Mathematics with High Fu- tionality” (Program Leader: prof. Mitsuhiro Nakao). It was initially published as the Kyushu University COE Lecture Note n- ber 8 (COE Lecture Note, 8. Kyushu University, The 21st Century COE Program “DMHF”, Fukuoka, 2008. vi+234 pp.), and in the present form is an extended v- sion of it (in particular, I have added a section dedicated to the Maslov index). The book is intended as a rapid (though not so straightforward) pseudodiff- ential introduction to the spectral theory of certain systems, mainly of the form a +a where the entries of a are homogeneous polynomials of degree 2 in the 2 0 2 n n (x,?)-variables, (x,?)? R×R,and a is a constant matrix, the so-called non- 0 commutative harmonic oscillators, with particular emphasis on a class of systems introduced by M. Wakayama and myself about ten years ago. The class of n- commutative harmonic oscillators is very rich, and many problems are still open, and worth of being pursued.
Spectral Theory Of Non Commutative Harmonic Oscillators An Introduction
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Author : Alberto Parmeggiani
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-04-22
Spectral Theory Of Non Commutative Harmonic Oscillators An Introduction written by Alberto Parmeggiani and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-04-22 with Mathematics categories.
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.
Introduction To The Spectral Theory Of Non Commutative Harmonic Oscillators
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Author : Alberto Parmeggiani
language : en
Publisher:
Release Date : 2008
Introduction To The Spectral Theory Of Non Commutative Harmonic Oscillators written by Alberto Parmeggiani and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with categories.
International Symposium On Mathematics Quantum Theory And Cryptography
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Author : Tsuyoshi Takagi
language : en
Publisher: Springer Nature
Release Date : 2020-10-22
International Symposium On Mathematics Quantum Theory And Cryptography written by Tsuyoshi Takagi and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-10-22 with Technology & Engineering categories.
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.
Noncommutative Geometry And Physics 3
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Author : Giuseppe Dito
language : en
Publisher: World Scientific
Release Date : 2013
Noncommutative Geometry And Physics 3 written by Giuseppe Dito and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013 with Mathematics categories.
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.
Casimir Force Casimir Operators And The Riemann Hypothesis
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Author : Gerrit Dijk
language : en
Publisher: Walter de Gruyter
Release Date : 2010-10-19
Casimir Force Casimir Operators And The Riemann Hypothesis written by Gerrit Dijk and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-10-19 with Mathematics categories.
This volume contains the proceedings of the conference "Casimir Force, Casimir Operators and the Riemann Hypothesis – Mathematics for Innovation in Industry and Science" held in November 2009 in Fukuoka (Japan). The motive for the conference was the celebration of the 100th birthday of Casimir and the 150th birthday of the Riemann hypothesis. The conference focused on the following topics: Casimir operators in harmonic analysis and representation theory Number theory, in particular zeta functions and cryptography Casimir force in physics and its relation with nano-science Mathematical biology Importance of mathematics for innovation in industry The latter topic was inspired both by the call for innovation in industry worldwide and by the fact that Casimir, who was the director of Philips research for a long time in his career, had an outspoken opinion on the importance of fundamental science for industry. These proceedings are of interest both to research mathematicians and to those interested in the role science, and in particular mathematics, can play in innovation in industry.
Geometric Analysis Of Pdes And Several Complex Variables
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Author : Shiferaw Berhanu
language : en
Publisher: Springer Nature
Release Date : 2024-10-26
Geometric Analysis Of Pdes And Several Complex Variables written by Shiferaw Berhanu and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-10-26 with Mathematics categories.
This volume convenes selected, peer-reviewed papers presented at the international workshop dedicated to Dr. Jorge Hounie on the occasion of his 75th birthday, held in Serra Negra, Brazil, from July 31 to August 4, 2023. The papers in this volume cover areas that include several complex variables, Cauchy-Riemann geometry, and partial differential equations. An Emeritus at the Federal University of São Carlos (UFScar), Brazil, Dr. Hounie has made significant contributions to partial differential equations, complex variables, harmonic analysis, and involutive structures. He has also been a kind and great mentor to numerous graduate students and postdocs who have gone on to pursue successful academic careers. Born in Bahia Blanca, Argentina, he completed his PhD studies at Rutgers University in 1974 and joined UFSCar as a Full Professor in 1995. He is a Full Member of the Brazilian Academy of Sciences. Within this book, readers will encounter a collection of cutting-edge research papers reflecting Dr. Hounie's research interests, valuable for both experienced researchers and graduate students alike.
Mathematical Modelling For Next Generation Cryptography
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Author : Tsuyoshi Takagi
language : en
Publisher: Springer
Release Date : 2017-07-25
Mathematical Modelling For Next Generation Cryptography written by Tsuyoshi Takagi and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-07-25 with Computers categories.
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.
Topics In Algebraic And Topological K Theory
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Author : Paul Frank Baum
language : en
Publisher: Springer
Release Date : 2010-10-28
Topics In Algebraic And Topological K Theory written by Paul Frank Baum and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-10-28 with Mathematics categories.
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.
Blow Up Theories For Semilinear Parabolic Equations
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Author : Bei Hu
language : en
Publisher: Springer
Release Date : 2011-03-17
Blow Up Theories For Semilinear Parabolic Equations written by Bei Hu and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-03-17 with Mathematics categories.
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.