The Mathematics of Superoscillations PDF Download
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Author: Yakir Aharonov
Publisher: American Mathematical Soc.
ISBN: 1470423243
Category : Mathematics
Languages : en
Pages : 120
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Book Description
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.
Author: Yakir Aharonov
Publisher: American Mathematical Soc.
ISBN: 1470423243
Category : Mathematics
Languages : en
Pages : 120
Get Book Here
Book Description
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.
Author: Daniel Alpay
Publisher: Springer Nature
ISBN: 3031214609
Category : Mathematics
Languages : en
Pages : 424
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Book Description
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.
Author: Adam Ostaszewski
Publisher: Cambridge University Press
ISBN: 9780521289641
Category : Mathematics
Languages : en
Pages : 564
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Book Description
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.
Author: Michael Berry
Publisher: World Scientific
ISBN: 9813221224
Category : Science
Languages : en
Pages : 200
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Book Description
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.
Author: Daniel Alpay
Publisher: Birkhäuser
ISBN: 3319291165
Category : Mathematics
Languages : en
Pages : 285
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Book Description
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.
Author: Patrick Flandrin
Publisher: Springer Nature
ISBN: 3030458474
Category : Mathematics
Languages : en
Pages : 650
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Book Description
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.
Author: Jose M. Balthazar
Publisher: BoD – Books on Demand
ISBN: 1803561912
Category : Technology & Engineering
Languages : en
Pages : 198
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Book Description
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”.
Author: Donatella Daniell
Publisher: American Mathematical Soc.
ISBN: 1470425475
Category : Mathematics
Languages : en
Pages : 116
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Book Description
The authors give a comprehensive treatment of the parabolic Signorini problem based on a generalization of Almgren's monotonicity of the frequency. This includes the proof of the optimal regularity of solutions, classification of free boundary points, the regularity of the regular set and the structure of the singular set.
Author: Mircea Pitici
Publisher: Princeton University Press
ISBN: 1400873371
Category : Mathematics
Languages : en
Pages : 408
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Book Description
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.
Author: Nicola Gigli
Publisher: American Mathematical Soc.
ISBN: 1470427656
Category : Mathematics
Languages : en
Pages : 174
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Book Description
The author discusses in which sense general metric measure spaces possess a first order differential structure. Building on this, spaces with Ricci curvature bounded from below a second order calculus can be developed, permitting the author to define Hessian, covariant/exterior derivatives and Ricci curvature.
