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The Mathematics of Superoscillations

Author: Yakir Aharonov

Publisher:

Published: 2017

Total Pages: 107

ISBN-13: 9781470437091

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"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.

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.

Published: 2017-04-25

Total Pages: 120

ISBN-13: 1470423243

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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.

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.

Recent Developments in Operator Theory, Mathematical Physics and Complex Analysis

Author: Daniel Alpay

Publisher: Springer Nature

Published: 2023-04-11

Total Pages: 424

ISBN-13: 3031214609

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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.

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

Published: 1990

Total Pages: 564

ISBN-13: 9780521289641

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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.

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.

A Half-Century of Physical Asymptotics and Other Diversions

Author: Michael Berry

Publisher: World Scientific

Published: 2017-07-19

Total Pages: 200

ISBN-13: 9813221224

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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.

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.

Noncommutative Analysis, Operator Theory and Applications

Author: Daniel Alpay

Publisher: Birkhäuser

Published: 2016-06-30

Total Pages: 285

ISBN-13: 3319291165

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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.

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.

Quantum Theory: A Two-Time Success Story

Author: Daniele C. Struppa

Publisher: Springer Science & Business Media

Published: 2013-09-12

Total Pages: 402

ISBN-13: 8847052173

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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.

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.

Theoretical Physics, Wavelets, Analysis, Genomics

Author: Patrick Flandrin

Publisher: Springer Nature

Published: 2023-05-31

Total Pages: 650

ISBN-13: 3030458474

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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.

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

Published: 2024-03-20

Total Pages: 198

ISBN-13: 1803561912

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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”.

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”.

The Best Writing on Mathematics 2015

Author: Mircea Pitici

Publisher: Princeton University Press

Published: 2016-01-12

Total Pages: 408

ISBN-13: 1400873371

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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.

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.