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Spectral Theory of Non-Commutative Harmonic Oscillators: An Introduction

2010-04-22 Mathematics
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Release : 2010-04-22
Genre : Mathematics
Kind : eBook
Book Rating : 212/5 ( reviews)

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Book Synopsis Spectral Theory of Non-Commutative Harmonic Oscillators: An Introduction by : Alberto Parmeggiani

Download or read book Spectral Theory of Non-Commutative Harmonic Oscillators: An Introduction written by Alberto Parmeggiani. This book was released on 2010-04-22. Available in PDF, EPUB and Kindle. Book excerpt: 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

2008
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Release : 2008
Genre :
Kind : eBook
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Book Synopsis Introduction to the Spectral Theory of Non-commutative Harmonic Oscillators by : Alberto Parmeggiani

Download or read book Introduction to the Spectral Theory of Non-commutative Harmonic Oscillators written by Alberto Parmeggiani. This book was released on 2008. Available in PDF, EPUB and Kindle. Book excerpt:

International Symposium on Mathematics, Quantum Theory, and Cryptography

2020-10-22 Technology & Engineering
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Release : 2020-10-22
Genre : Technology & Engineering
Kind : eBook
Book Rating : 91X/5 ( reviews)

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Book Synopsis International Symposium on Mathematics, Quantum Theory, and Cryptography by : Tsuyoshi Takagi

Download or read book International Symposium on Mathematics, Quantum Theory, and Cryptography written by Tsuyoshi Takagi. This book was released on 2020-10-22. Available in PDF, EPUB and Kindle. Book excerpt: 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

2013 Mathematics
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Release : 2013
Genre : Mathematics
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Book Rating : 01X/5 ( reviews)

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Book Synopsis Noncommutative Geometry and Physics 3 by : Giuseppe Dito

Download or read book Noncommutative Geometry and Physics 3 written by Giuseppe Dito. This book was released on 2013. Available in PDF, EPUB and Kindle. Book excerpt: 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

2010-10-19 Mathematics
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Release : 2010-10-19
Genre : Mathematics
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Book Rating : 138/5 ( reviews)

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Book Synopsis Casimir Force, Casimir Operators and the Riemann Hypothesis by : Gerrit Dijk

Download or read book Casimir Force, Casimir Operators and the Riemann Hypothesis written by Gerrit Dijk. This book was released on 2010-10-19. Available in PDF, EPUB and Kindle. Book excerpt: 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.

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