The Mathematics of Superoscillations

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.


The Mathematics of the Bose Gas and its Condensation

The Mathematics of the Bose Gas and its Condensation

Author: Elliott H. Lieb

Publisher: Springer Science & Business Media

Published: 2006-01-17

Total Pages: 204

ISBN-13: 3764373377

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This book contains a unique survey of the mathematically rigorous results about the quantum-mechanical many-body problem that have been obtained by the authors in the past seven years. It addresses a topic that is not only rich mathematically, using a large variety of techniques in mathematical analysis, but is also one with strong ties to current experiments on ultra-cold Bose gases and Bose-Einstein condensation. The book provides a pedagogical entry into an active area of ongoing research for both graduate students and researchers. It is an outgrowth of a course given by the authors for graduate students and post-doctoral researchers at the Oberwolfach Research Institute in 2004. The book also provides a coherent summary of the field and a reference for mathematicians and physicists active in research on quantum mechanics.


The Multifaceted Skyrmion

The Multifaceted Skyrmion

Author: Gerald Edward Brown

Publisher: World Scientific

Published: 2010

Total Pages: 460

ISBN-13: 9814280704

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1. Skyrmions and nuclei / R.A. Battye, N.S. Manton and P.M. Sutcliffe -- 2. Electromagnetic form factors of the nucleon in chiral soliton models / G. Holzwarth -- 3. Exotic baryon resonances in the Skyrme model / D. Diakonov and V. Petrov -- 4. Heavy-quark skyrmions / N.N. Scoccola -- 5. Skyrmion approach to finite density and temperature / B.-Y. Park and V. Vento -- 6. Half-skyrmion hadronic matter at high density / H.K. Lee and M. Rho -- 7. Superqualitons : baryons in dense QCD / D.K. Hong -- 8. Rotational symmetry breaking in baby skyrme models / M. Karliner and I. Hen -- 9. Spin and isospin : exotic order in quantum hall ferromagnets / S.M. Girvin -- 10. Noncommutative skyrmions in quantum hall systems / Z.F. Ezawa and G. Tsitsishvili -- 11. Skyrmions and merons in bilayer quantum hall system / K. Moon -- 12. Spin and pseudospin textures in quantum hall systems / H.A. Fertig and L. Brey -- 13. Half-skyrmion theory for high-temperature superconductivity / T. Morinari -- 14. Deconfined quantum critical points / T. Senthil [und weitere] -- 15. Skyrmion and string theory / S. Sugimoto -- 16. Holographic baryons / P. Yi -- 17. The Cheshire cat principle from holography / H.B. Nielsen and I. Zahed -- 18. Baryon physics in a five-dimensional model of hadrons / A. Pomarol and A. Wulzer


Higgs Discovery

Higgs Discovery

Author: Lisa Randall

Publisher: Harper Collins

Published: 2012-07-24

Total Pages: 94

ISBN-13: 0062245317

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On July 4, 2012, physicists at the Large Hadron Collider in Geneva madehistory when they discovered an entirely new type of subatomic particle that many scientists believe is the Higgs boson. For forty years, physicists searched for this capstone to the Standard Model of particle physics—the theory that describes both the most elementary components that are known in matter and the forces through which they interact. This particle points to the Higgs field, which provides the key to understanding why elementary particles have mass. In Higgs Discovery, Lisa Randall explains the science behind this monumental discovery, its exhilarating implications, and the power of empty space.


The Physics of the B Factories

The Physics of the B Factories

Author: Adrian Bevan

Publisher: Springer

Published: 2015-03-23

Total Pages: 0

ISBN-13: 9783662449905

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This comprehensive work thoroughly introduces and reviews the set of results from Belle and BaBar - after more than two decades of independent and complementary work - all the way from the detectors and the analysis tools used, up to the physics results, and the interpretation of these results. The world’s two giant B Factory collaborations, Belle at KEK and BaBar at SLAC, have successfully completed their main mission to discover and quantify CP violation in the decays of B mesons. CP violation is a necessary requirement to distinguish unambiguously between matter and antimatter. The shared primary objective of the two B Factory experiments was to determine the shape of the so-called unitarity triangle, an abstract triangle representing interactions of quarks, the elementary constituents of matter. The area of the triangle is a measure of the amount of CP violation associated with the weak force. Many other measurements have been performed by the B Factories and are also discussed in this work.