The Mathematics Of Superoscillations

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The Mathematics of Superoscillations

Author : Yakir Aharonov
Publisher :
ISBN 13 : 9781470437091
Total Pages : 107 pages
Book Rating : 4.4/5 (37 download)

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Book Synopsis The Mathematics of Superoscillations by : Yakir Aharonov

Download or read book The Mathematics of Superoscillations written by Yakir Aharonov and published by . This book was released on 2017 with total page 107 pages. Available in PDF, EPUB and Kindle. Book excerpt: "In the past 50 years, quantum physicists have discovered, and experimentally demonstrated, a phenomenon which they termed superoscillations. Aharonov and his collaborators showed that superoscillations naturally arise when dealing with weak values, a notion that provides a fundamentally different way to regard measurements in quantum physics. From a mathematical point of view, superoscillating functions are a superposition of small Fourier components with a bounded Fourier spectrum, which result, when appropriately summed, in a shift that can be arbitrarily large, and well outside the spectrum. Purpose of this work is twofold: on one hand we provide a self-contained survey of the existing literature, in order to offer a systematic mathematical approach to superoscillations; on the other hand, we obtain some new and unexpected results, by showing that superoscillating sequences can be seen of as solutions to a large class of convolution equations and can therefore be treated within the theory of Analytically Uniform spaces. In particular, we will also discuss the persistence of the superoscillatory behavior when superoscillating sequences are taken as initial values of the Schrödinger equation and other equations."--Page v.

The Mathematics of Superoscillations

Author : Yakir Aharonov
Publisher : American Mathematical Soc.
ISBN 13 : 1470423243
Total Pages : 120 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis The Mathematics of Superoscillations by : Yakir Aharonov

Download or read book The Mathematics of Superoscillations written by Yakir Aharonov and published by American Mathematical Soc.. This book was released on 2017-04-25 with total page 120 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the past 50 years, quantum physicists have discovered, and experimentally demonstrated, a phenomenon which they termed superoscillations. Aharonov and his collaborators showed that superoscillations naturally arise when dealing with weak values, a notion that provides a fundamentally different way to regard measurements in quantum physics. From a mathematical point of view, superoscillating functions are a superposition of small Fourier components with a bounded Fourier spectrum, which result, when appropriately summed, in a shift that can be arbitrarily large, and well outside the spectrum. The purpose of this work is twofold: on one hand the authors provide a self-contained survey of the existing literature, in order to offer a systematic mathematical approach to superoscillations; on the other hand, they obtain some new and unexpected results, by showing that superoscillating sequences can be seen of as solutions to a large class of convolution equations and can therefore be treated within the theory of analytically uniform spaces. In particular, the authors will also discuss the persistence of the superoscillatory behavior when superoscillating sequences are taken as initial values of the Schrödinger equation and other equations.

A Half-Century of Physical Asymptotics and Other Diversions

Author : Michael Berry
Publisher : World Scientific
ISBN 13 : 9813221224
Total Pages : 200 pages
Book Rating : 4.8/5 (132 download)

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Book Synopsis A Half-Century of Physical Asymptotics and Other Diversions by : Michael Berry

Download or read book A Half-Century of Physical Asymptotics and Other Diversions written by Michael Berry and published by World Scientific. This book was released on 2017-07-19 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt: Michael 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.

Recent Developments in Operator Theory, Mathematical Physics and Complex Analysis

Author : Daniel Alpay
Publisher : Springer Nature
ISBN 13 : 3031214609
Total Pages : 424 pages
Book Rating : 4.0/5 (312 download)

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Book Synopsis Recent Developments in Operator Theory, Mathematical Physics and Complex Analysis by : Daniel Alpay

Download or read book Recent Developments in Operator Theory, Mathematical Physics and Complex Analysis written by Daniel Alpay and published by Springer Nature. This book was released on 2023-04-11 with total page 424 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book features a collection of papers by plenary, semi-plenary and invited contributors at IWOTA2021, held at Chapman University in hybrid format in August 2021. The topics span areas of current research in operator theory, mathematical physics, and complex analysis.

Advanced Mathematical Methods

Author : Adam Ostaszewski
Publisher : Cambridge University Press
ISBN 13 : 9780521289641
Total Pages : 564 pages
Book Rating : 4.2/5 (896 download)

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Book Synopsis Advanced Mathematical Methods by : Adam Ostaszewski

Download or read book Advanced Mathematical Methods written by Adam Ostaszewski and published by Cambridge University Press. This book was released on 1990 with total page 564 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text is a self-contained second course on mathematical methods dealing with topics in linear algebra and multivariate calculus that can be applied to statistics.

Quantum Theory: A Two-Time Success Story

Author : Daniele C. Struppa
Publisher : Springer Science & Business Media
ISBN 13 : 8847052173
Total Pages : 402 pages
Book Rating : 4.8/5 (47 download)

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Book Synopsis Quantum Theory: A Two-Time Success Story by : Daniele C. Struppa

Download or read book Quantum Theory: A Two-Time Success Story written by Daniele C. Struppa and published by Springer Science & Business Media. This book was released on 2013-09-12 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: Yakir Aharonov is one of the leading figures in the foundations of quantum physics. His contributions range from the celebrated Aharonov-Bohm effect (1959), to the more recent theory of weak measurements (whose experimental confirmations were recently ranked as the two most important results of physics in 2011). This volume will contain 27 original articles, contributed by the most important names in quantum physics, in honor of Aharonov's 80-th birthday. Sections include "Quantum mechanics and reality," with contributions from Nobel Laureates David Gross and Sir Anthony Leggett and Yakir Aharonov, S. Popescu and J. Tollaksen; "Building blocks of Nature" with contributions from Francois Englert (co-proposer of the scalar boson along with Peter Higgs); "Time and Cosmology" with contributions from Leonard Susskind, P.C.W. Davies and James Hartle; "Universe as a Wavefunction," with contributions from Phil Pearle, Sean Carroll and David Albert; "Nonlocality," with contributions from Nicolas Gisin, Daniel Rohrlich, Ray Chiao and Lev Vaidman; and finishing with multiple sections on weak values with contributions from A. Jordan, A. Botero, A.D. Parks, L. Johansen, F. Colombo, I. Sabadini, D.C. Struppa, M.V. Berry, B. Reznik, N. Turok, G.A.D. Briggs, Y. Gefen, P. Kwiat, and A. Pines, among others.

Noncommutative Analysis, Operator Theory and Applications

Author : Daniel Alpay
Publisher : Birkhäuser
ISBN 13 : 3319291165
Total Pages : 285 pages
Book Rating : 4.3/5 (192 download)

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Book Synopsis Noncommutative Analysis, Operator Theory and Applications by : Daniel Alpay

Download or read book Noncommutative Analysis, Operator Theory and Applications written by Daniel Alpay and published by Birkhäuser. This book was released on 2016-06-30 with total page 285 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book illustrates several aspects of the current research activity in operator theory, operator algebras and applications in various areas of mathematics and mathematical physics. It is addressed to specialists but also to graduate students in several fields including global analysis, Schur analysis, complex analysis, C*-algebras, noncommutative geometry, operator algebras, operator theory and their applications. Contributors: F. Arici, S. Bernstein, V. Bolotnikov, J. Bourgain, P. Cerejeiras, F. Cipriani, F. Colombo, F. D'Andrea, G. Dell'Antonio, M. Elin, U. Franz, D. Guido, T. Isola, A. Kula, L.E. Labuschagne, G. Landi, W.A. Majewski, I. Sabadini, J.-L. Sauvageot, D. Shoikhet, A. Skalski, H. de Snoo, D. C. Struppa, N. Vieira, D.V. Voiculescu, and H. Woracek.

Theoretical Physics, Wavelets, Analysis, Genomics

Author : Patrick Flandrin
Publisher : Springer Nature
ISBN 13 : 3030458474
Total Pages : 650 pages
Book Rating : 4.0/5 (34 download)

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Book Synopsis Theoretical Physics, Wavelets, Analysis, Genomics by : Patrick Flandrin

Download or read book Theoretical Physics, Wavelets, Analysis, Genomics written by Patrick Flandrin and published by Springer Nature. This book was released on 2023-05-31 with total page 650 pages. Available in PDF, EPUB and Kindle. Book excerpt: Over the course of a scientific career spanning more than fifty years, Alex Grossmann (1930-2019) made many important contributions to a wide range of areas including, among others, mathematics, numerical analysis, physics, genetics, and biology. His lasting influence can be seen not only in his research and numerous publications, but also through the relationships he cultivated with his collaborators and students. This edited volume features chapters written by some of these colleagues, as well as researchers whom Grossmann’s work and way of thinking has impacted in a decisive way. Reflecting the diversity of his interests and their interdisciplinary nature, these chapters explore a variety of current topics in quantum mechanics, elementary particles, and theoretical physics; wavelets and mathematical analysis; and genomics and biology. A scientific biography of Grossmann, along with a more personal biography written by his son, serve as an introduction. Also included are the introduction to his PhD thesis and an unpublished paper coauthored by him. Researchers working in any of the fields listed above will find this volume to be an insightful and informative work.

New Insights on Oscillators and Their Applications to Engineering and Science

Author : Jose M. Balthazar
Publisher : BoD – Books on Demand
ISBN 13 : 1803561912
Total Pages : 198 pages
Book Rating : 4.8/5 (35 download)

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Book Synopsis New Insights on Oscillators and Their Applications to Engineering and Science by : Jose M. Balthazar

Download or read book New Insights on Oscillators and Their Applications to Engineering and Science written by Jose M. Balthazar and published by BoD – Books on Demand. This book was released on 2024-03-20 with total page 198 pages. Available in PDF, EPUB and Kindle. Book excerpt: Over the years, the construction of models has played an important part in the discovery and dissemination of knowledge. The study of problems involving the coupling of several systems has been widely explored, essentially in the function of the change of constructive characteristics of machines and structures. Accordingly, vibrating (oscillatory) processes can be divided into the following types: free, forced, parametric, and self-excited oscillations. Furthermore, two or more oscillations can interact in the same oscillatory system. This book provides a comprehensive overview of oscillators and their applications. It includes eight chapters organized into three sections “MEMS and NEMS”, “Vibrations” and “Modeling”.

Entire Solutions for Bistable Lattice Differential Equations with Obstacles

Author : Aaron Hoffman
Publisher : American Mathematical Soc.
ISBN 13 : 1470422018
Total Pages : 132 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Entire Solutions for Bistable Lattice Differential Equations with Obstacles by : Aaron Hoffman

Download or read book Entire Solutions for Bistable Lattice Differential Equations with Obstacles written by Aaron Hoffman and published by American Mathematical Soc.. This book was released on 2018-01-16 with total page 132 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors consider scalar lattice differential equations posed on square lattices in two space dimensions. Under certain natural conditions they show that wave-like solutions exist when obstacles (characterized by “holes”) are present in the lattice. Their work generalizes to the discrete spatial setting the results obtained in Berestycki, Hamel, and Matuno (2009) for the propagation of waves around obstacles in continuous spatial domains. The analysis hinges upon the development of sub and super-solutions for a class of discrete bistable reaction-diffusion problems and on a generalization of a classical result due to Aronson and Weinberger that concerns the spreading of localized disturbances.

Knot Invariants and Higher Representation Theory

Author : Ben Webster
Publisher : American Mathematical Soc.
ISBN 13 : 1470426501
Total Pages : 154 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Knot Invariants and Higher Representation Theory by : Ben Webster

Download or read book Knot Invariants and Higher Representation Theory written by Ben Webster and published by American Mathematical Soc.. This book was released on 2018-01-16 with total page 154 pages. Available in PDF, EPUB and Kindle. Book excerpt: The author constructs knot invariants categorifying the quantum knot variants for all representations of quantum groups. He shows that these invariants coincide with previous invariants defined by Khovanov for sl and sl and by Mazorchuk-Stroppel and Sussan for sl . The author's technique is to study 2-representations of 2-quantum groups (in the sense of Rouquier and Khovanov-Lauda) categorifying tensor products of irreducible representations. These are the representation categories of certain finite dimensional algebras with an explicit diagrammatic presentation, generalizing the cyclotomic quotient of the KLR algebra. When the Lie algebra under consideration is sl , the author shows that these categories agree with certain subcategories of parabolic category for gl .

The Best Writing on Mathematics 2015

Author : Mircea Pitici
Publisher : Princeton University Press
ISBN 13 : 1400873371
Total Pages : 408 pages
Book Rating : 4.4/5 (8 download)

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Book Synopsis The Best Writing on Mathematics 2015 by : Mircea Pitici

Download or read book The Best Writing on Mathematics 2015 written by Mircea Pitici and published by Princeton University Press. This book was released on 2016-01-12 with total page 408 pages. Available in PDF, EPUB and Kindle. Book excerpt: The year's finest writing on mathematics from around the world This annual anthology brings together the year's finest mathematics writing from around the world. Featuring promising new voices alongside some of the foremost names in the field, The Best Writing on Mathematics 2015 makes available to a wide audience many articles not easily found anywhere else—and you don’t need to be a mathematician to enjoy them. These writings offer surprising insights into the nature, meaning, and practice of mathematics today. They delve into the history, philosophy, teaching, and everyday occurrences of math, and take readers behind the scenes of today’s hottest mathematical debates. Here David Hand explains why we should actually expect unlikely coincidences to happen; Arthur Benjamin and Ethan Brown unveil techniques for improvising custom-made magic number squares; Dana Mackenzie describes how mathematicians are making essential contributions to the development of synthetic biology; Steven Strogatz tells us why it’s worth writing about math for people who are alienated from it; Lisa Rougetet traces the earliest written descriptions of Nim, a popular game of mathematical strategy; Scott Aaronson looks at the unexpected implications of testing numbers for randomness; and much, much more. In addition to presenting the year’s most memorable writings on mathematics, this must-have anthology includes a bibliography of other notable writings and an introduction by the editor, Mircea Pitici. This book belongs on the shelf of anyone interested in where math has taken us—and where it is headed.

Hypercontractivity in Group von Neumann Algebras

Author : Marius Junge
Publisher : American Mathematical Soc.
ISBN 13 : 1470425653
Total Pages : 102 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Hypercontractivity in Group von Neumann Algebras by : Marius Junge

Download or read book Hypercontractivity in Group von Neumann Algebras written by Marius Junge and published by American Mathematical Soc.. This book was released on 2017-09-25 with total page 102 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, the authors provide a combinatorial/numerical method to establish new hypercontractivity estimates in group von Neumann algebras. They illustrate their method with free groups, triangular groups and finite cyclic groups, for which they obtain optimal time hypercontractive inequalities with respect to the Markov process given by the word length and with an even integer. Interpolation and differentiation also yield general hypercontrativity for via logarithmic Sobolev inequalities. The authors' method admits further applications to other discrete groups without small loops as far as the numerical part—which varies from one group to another—is implemented and tested on a computer. The authors also develop another combinatorial method which does not rely on computational estimates and provides (non-optimal) hypercontractive inequalities for a larger class of groups/lengths, including any finitely generated group equipped with a conditionally negative word length, like infinite Coxeter groups. The authors' second method also yields hypercontractivity bounds for groups admitting a finite dimensional proper cocycle. Hypercontractivity fails for conditionally negative lengths in groups satisfying Kazhdan's property (T).

On Operads, Bimodules and Analytic Functors

Author : Nicola Gambino
Publisher : American Mathematical Soc.
ISBN 13 : 1470425769
Total Pages : 122 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis On Operads, Bimodules and Analytic Functors by : Nicola Gambino

Download or read book On Operads, Bimodules and Analytic Functors written by Nicola Gambino and published by American Mathematical Soc.. This book was released on 2017-09-25 with total page 122 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors develop further the theory of operads and analytic functors. In particular, they introduce the bicategory of operad bimodules, that has operads as -cells, operad bimodules as -cells and operad bimodule maps as 2-cells, and prove that it is cartesian closed. In order to obtain this result, the authors extend the theory of distributors and the formal theory of monads.

Quantum Paradoxes

Author : Yakir Aharonov
Publisher : John Wiley & Sons
ISBN 13 : 3527619127
Total Pages : 299 pages
Book Rating : 4.5/5 (276 download)

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Book Synopsis Quantum Paradoxes by : Yakir Aharonov

Download or read book Quantum Paradoxes written by Yakir Aharonov and published by John Wiley & Sons. This book was released on 2008-09-26 with total page 299 pages. Available in PDF, EPUB and Kindle. Book excerpt: A Guide through the Mysteries of Quantum Physics! Yakir Aharonov is one of the pioneers in measuring theory, the nature of quantum correlations, superselection rules, and geometric phases and has been awarded numerous scientific honors. The author has contributed monumental concepts to theoretical physics, especially the Aharonov-Bohm effect and the Aharonov-Casher effect. Together with Daniel Rohrlich, Israel, he has written a pioneering work on the remaining mysteries of quantum mechanics. From the perspective of a preeminent researcher in the fundamental aspects of quantum mechanics, the text combines mathematical rigor with penetrating and concise language. More than 200 exercises introduce readers to the concepts and implications of quantum mechanics that have arisen from the experimental results of the recent two decades. With students as well as researchers in mind, the authors give an insight into that part of the field, which led Feynman to declare that "nobody understands quantum mechanics". * Free solutions manual available for lecturers at www.wiley-vch.de/supplements/

Optical Superresolution

Author : David Mendlovic
Publisher : Springer
ISBN 13 : 0387347151
Total Pages : 261 pages
Book Rating : 4.3/5 (873 download)

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Book Synopsis Optical Superresolution by : David Mendlovic

Download or read book Optical Superresolution written by David Mendlovic and published by Springer. This book was released on 2012-12-06 with total page 261 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors explore the ways to improve the classical resolution limits of an imaging system, and provide novel approaches for achieving better results than would otherwise be possible with current imaging technology. The book begins by presenting the theoretical foundations, background information, and terminology of super resolution, and then discusses methods and systems used to achieve the super resolution effect. Various approaches to dealing with and exceeding the limitations of the lens aperture, the pixel size of the camera, and the noise generated at the detector are presented and analyzed. The last chapter illustrates several industry-related examples and potential applications to real industrial electro-optical systems. This book is intended for graduate students or researchers in academia or industry, and anyone else looking to improve the performance of their electro-optical system design.

Engineering Optics 2.0

Author : Xiangang Luo
Publisher : Springer
ISBN 13 : 9811357552
Total Pages : 690 pages
Book Rating : 4.8/5 (113 download)

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Book Synopsis Engineering Optics 2.0 by : Xiangang Luo

Download or read book Engineering Optics 2.0 written by Xiangang Luo and published by Springer. This book was released on 2019-02-28 with total page 690 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides comprehensive information on the history and status quo of a new research field, which we refer to as Engineering Optics 2.0. The content covers both the theoretical basis and the engineering aspects in connection with various applications. The field of Engineering Optics employs optical theories to practical applications in a broad range of areas. However, the foundation of traditional Engineering Optics was formed several hundred years ago, and the field has developed only very gradually. With technological innovations in both the fabrication and characterization of microstructures, the past few decades have witnessed many groundbreaking changes to the bases of optics, including the generalizing of refraction, reflection, diffraction, radiation and absorption theories. These new theories enable us to break through the barriers in traditional optical technologies, yielding revolutionary advances in traditional optical systems such as microscopes, telescopes and lithography systems.