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Elementary Explanation of the Inexistence of Decoherence at Zero
Elementary explanation of the inexistence of decoherence at zero temperature for systems with purely elastic scattering Yoseph Imry Dept. of Condensed-Matter Physics, the Weizmann Institute of science, Rehovot 76100, Israel (Dated: October 31, 2018) This note has no new results and is therefore not intended to be submitted to a ”research” journal in the foreseeable future, but to be available to the numerous individuals who are interested in this issue. Several of those have approached the author for his opinion, which is summarized here in a hopefully pedagogical manner, for convenience. It is demonstrated, using essentially only energy conservation and elementary quantum mechanics, that true decoherence by a normal environment approaching the zero-temperature limit is impossible for a test particle which can not give or lose energy. Prime examples are: Bragg scattering, the M¨ossbauer effect and related phenomena at zero temperature, as well as quantum corrections for the transport of conduction electrons in solids. The last example is valid within the scattering formulation for the transport. Similar statements apply also to interference properties in equilibrium. PACS numbers: 73.23.Hk, 73.20.Dx ,72.15.Qm, 73.21.La I. INTRODUCTION cally in the case of the coupling of a conduction-electron in a solid to lattice vibrations (phonons) 14 years ago [5] and immediately refuted vigorously [6]. Interest in this What diminishes the interference of, say, two waves problem has resurfaced due to experiments by Mohanty (see Eq. 1 below) is an interesting fundamental ques- et al [7] which determine the dephasing rate of conduc- tion, some aspects of which are, surprisingly, still being tion electrons by weak-localization magnetoconductance debated. -
Accommodating Retrocausality with Free Will Yakir Aharonov Chapman University, [email protected]
Chapman University Chapman University Digital Commons Mathematics, Physics, and Computer Science Science and Technology Faculty Articles and Faculty Articles and Research Research 2016 Accommodating Retrocausality with Free Will Yakir Aharonov Chapman University, [email protected] Eliahu Cohen Tel Aviv University Tomer Shushi University of Haifa Follow this and additional works at: http://digitalcommons.chapman.edu/scs_articles Part of the Quantum Physics Commons Recommended Citation Aharonov, Y., Cohen, E., & Shushi, T. (2016). Accommodating Retrocausality with Free Will. Quanta, 5(1), 53-60. doi:http://dx.doi.org/10.12743/quanta.v5i1.44 This Article is brought to you for free and open access by the Science and Technology Faculty Articles and Research at Chapman University Digital Commons. It has been accepted for inclusion in Mathematics, Physics, and Computer Science Faculty Articles and Research by an authorized administrator of Chapman University Digital Commons. For more information, please contact [email protected]. Accommodating Retrocausality with Free Will Comments This article was originally published in Quanta, volume 5, issue 1, in 2016. DOI: 10.12743/quanta.v5i1.44 Creative Commons License This work is licensed under a Creative Commons Attribution 3.0 License. This article is available at Chapman University Digital Commons: http://digitalcommons.chapman.edu/scs_articles/334 Accommodating Retrocausality with Free Will Yakir Aharonov 1;2, Eliahu Cohen 1;3 & Tomer Shushi 4 1 School of Physics and Astronomy, Tel Aviv University, Tel Aviv, Israel. E-mail: [email protected] 2 Schmid College of Science, Chapman University, Orange, California, USA. E-mail: [email protected] 3 H. H. Wills Physics Laboratory, University of Bristol, Bristol, UK. -
Geometric Phase from Aharonov-Bohm to Pancharatnam–Berry and Beyond
Geometric phase from Aharonov-Bohm to Pancharatnam–Berry and beyond Eliahu Cohen1,2,*, Hugo Larocque1, Frédéric Bouchard1, Farshad Nejadsattari1, Yuval Gefen3, Ebrahim Karimi1,* 1Department of Physics, University of Ottawa, Ottawa, Ontario, K1N 6N5, Canada 2Faculty of Engineering and the Institute of Nanotechnology and Advanced Materials, Bar Ilan University, Ramat Gan 5290002, Israel 3Department of Condensed Matter Physics, Weizmann Institute of Science, Rehovot 76100, Israel *Corresponding authors: [email protected], [email protected] Abstract: Whenever a quantum system undergoes a cycle governed by a slow change of parameters, it acquires a phase factor: the geometric phase. Its most common formulations are known as the Aharonov-Bohm, Pancharatnam and Berry phases, but both prior and later manifestations exist. Though traditionally attributed to the foundations of quantum mechanics, the geometric phase has been generalized and became increasingly influential in many areas from condensed-matter physics and optics to high energy and particle physics and from fluid mechanics to gravity and cosmology. Interestingly, the geometric phase also offers unique opportunities for quantum information and computation. In this Review we first introduce the Aharonov-Bohm effect as an important realization of the geometric phase. Then we discuss in detail the broader meaning, consequences and realizations of the geometric phase emphasizing the most important mathematical methods and experimental techniques used in the study of geometric phase, in particular those related to recent works in optics and condensed-matter physics. Published in Nature Reviews Physics 1, 437–449 (2019). DOI: 10.1038/s42254-019-0071-1 1. Introduction A charged quantum particle is moving through space. -
Annual Report to Industry Canada Covering The
Annual Report to Industry Canada Covering the Objectives, Activities and Finances for the period August 1, 2008 to July 31, 2009 and Statement of Objectives for Next Year and the Future Perimeter Institute for Theoretical Physics 31 Caroline Street North Waterloo, Ontario N2L 2Y5 Table of Contents Pages Period A. August 1, 2008 to July 31, 2009 Objectives, Activities and Finances 2-52 Statement of Objectives, Introduction Objectives 1-12 with Related Activities and Achievements Financial Statements, Expenditures, Criteria and Investment Strategy Period B. August 1, 2009 and Beyond Statement of Objectives for Next Year and Future 53-54 1 Statement of Objectives Introduction In 2008-9, the Institute achieved many important objectives of its mandate, which is to advance pure research in specific areas of theoretical physics, and to provide high quality outreach programs that educate and inspire the Canadian public, particularly young people, about the importance of basic research, discovery and innovation. Full details are provided in the body of the report below, but it is worth highlighting several major milestones. These include: In October 2008, Prof. Neil Turok officially became Director of Perimeter Institute. Dr. Turok brings outstanding credentials both as a scientist and as a visionary leader, with the ability and ambition to position PI among the best theoretical physics research institutes in the world. Throughout the last year, Perimeter Institute‘s growing reputation and targeted recruitment activities led to an increased number of scientific visitors, and rapid growth of its research community. Chart 1. Growth of PI scientific staff and associated researchers since inception, 2001-2009. -
David Bohn, Roger Penrose, and the Search for Non-Local Causality
David Bohm, Roger Penrose, and the Search for Non-local Causality Before they met, David Bohm and Roger Penrose each puzzled over the paradox of the arrow of time. After they met, the case for projective physical space became clearer. *** A machine makes pairs (I like to think of them as shoes); one of the pair goes into storage before anyone can look at it, and the other is sent down a long, long hallway. At the end of the hallway, a physicist examines the shoe.1 If the physicist finds a left hiking boot, he expects that a right hiking boot must have been placed in the storage bin previously, and upon later examination he finds that to be the case. So far, so good. The problem begins when it is discovered that the machine can make three types of shoes: hiking boots, tennis sneakers, and women’s pumps. Now the physicist at the end of the long hallway can randomly choose one of three templates, a metal sheet with a hole in it shaped like one of the three types of shoes. The physicist rolls dice to determine which of the templates to hold up; he rolls the dice after both shoes are out of the machine, one in storage and the other having started down the long hallway. Amazingly, two out of three times, the random choice is correct, and the shoe passes through the hole in the template. There can 1 This rendition of the Einstein-Podolsky-Rosen, 1935, delayed-choice thought experiment is paraphrased from Bernard d’Espagnat, 1981, with modifications via P. -
The Abel Prize Laureate 2017
The Abel Prize Laureate 2017 Yves Meyer École normale supérieure Paris-Saclay, France www.abelprize.no Yves Meyer receives the Abel Prize for 2017 “for his pivotal role in the development of the mathematical theory of wavelets.” Citation The Abel Committee The Norwegian Academy of Science and or “wavelets”, obtained by both dilating infinite sequence of nested subspaces Meyer’s expertise in the mathematics Letters has decided to award the Abel and translating a fixed function. of L2(R) that satisfy a few additional of the Calderón-Zygmund school that Prize for 2017 to In the spring of 1985, Yves Meyer invariance properties. This work paved opened the way for the development of recognised that a recovery formula the way for the construction by Ingrid wavelet theory, providing a remarkably Yves Meyer, École normale supérieure found by Morlet and Alex Grossmann Daubechies of orthonormal bases of fruitful link between a problem set Paris-Saclay, France was an identity previously discovered compactly supported wavelets. squarely in pure mathematics and a theory by Alberto Calderón. At that time, Yves In the following decades, wavelet with wide applicability in the real world. “for his pivotal role in the Meyer was already a leading figure analysis has been applied in a wide development of the mathematical in the Calderón-Zygmund theory of variety of arenas as diverse as applied theory of wavelets.” singular integral operators. Thus began and computational harmonic analysis, Meyer’s study of wavelets, which in less data compression, noise reduction, Fourier analysis provides a useful way than ten years would develop into a medical imaging, archiving, digital cinema, of decomposing a signal or function into coherent and widely applicable theory. -
Mathematics Nomad Wins Abel Prize (Pdf)
Mathematics Nomad Wins Abel Prize Give me a museum and I’ll fill it. Indeed, his contributions thereafter cru- – Pablo Picasso cially changed common practices in signal processing. As an example, the compres- rolific mathematician Yves Meyer, sion standard in JPEG2000 is entirely based could be described as the Picasso of on the ability of sparsely representing P the mathematical sciences. On 23 images in a wavelet basis and the work of May 2017 the French mathematician was Martin Vetterli and his team who turned awarded the Abel Prize, which is often Meyer’s insight into usable computational described as the mathematics Nobel. In the algorithms. The discovery of wavelets as a laudatio the Abel recognised Meyer in par- sciences des | Académie Eymann © B. tool for sparsely representing images also ticular ‘for his pivotal role in the develop- turned them into one of the central compo- ment of mathematical theory of wavelets’. nents in compressed sensing, i.e. the non- Wavelets are functions that can explain adaptive compressed acquisition of data. complex structures in signals and images, And in 2015 and 2016 wavelets played a in solutions of partial differential equa- central role in the detection of gravitational tions, by decomposing them into translated waves by LIGO. Wavelets separated the and dilated versions of a mother wavelet gravitational waves from instrumental arte- (see Figure 1). facts and random noise using an algorithm They form an orthonormal basis of square integrable func- designed by Sergey Klimenko. tions and can be seen as a further development of the Fourier Recent works by Stéphane Mallat and colleagues also show transform, characterising signals in time-frequency by spatially the role of wavelets in understanding the mechanisms behind localised, somewhat oscillatory, building blocks of different deep learning. -
2. Superoscillations.Pdf
When the Whole Vibrates Faster than Any of its Parts Computational Superoscillation Theory Nicholas Wheeler December 2017 Introduction. The phenomenon/theory of “superoscillations”—brought to my attention by my friend Ahmed Sebbar1—originated in the time-symmetric formulation of quantum mechanics2 that gave rise to the theory of “weak measurements.” Recognition of the role that superoscillations play in that work was brought into explicit focus by Aharonov et al in 1990, and since that date the concept has found application to a remarkable variety of physical subject areas. Yakir Aharonov took his PhD in 1960 from the University of Bristol, where he worked with David Bohm.3 In 1992 a conference was convened at Bristol to celebrate Aharonov’s 60th birthday. It was on that occasion that the superoscillation phenomenon came first to the attention of Michael Berry (of the Bristol faculty), who in an essay “Faster than Fourier” contributed to the proceedings of that conference4 wrote that “He [Aharonov] told me that it is possible for functions to oscillate faster than any of their Fourier components. This seemed unbelievable, even paradoxical; I had heard nothing like it before. ” Berry was inspired to write a series of papers relating to the theory of superoscillation and its potential applications, as also by now have a great many other authors. 1 Private communication, 17 November 2017. 2 Y. Aharonov, P. G. Bergmann & J. L. Libowitz, “Time symmetry in the quantum meassurement process,” Phys. Rev. B 134, 1410–1416 (1964). 3 It was, I suspect, at the invitation of E. P Gross—who had collaborated with Bohm when both were at Princeton—that Aharonov spent 1960–1961 at Brandeis University, from which I had taken the first PhD and departed to Utrecht/CERN in February of 1960, so we never met. -
Yves Meyer: Restoring the Role of Mathematics in Signal and Image Processing
Yves Meyer: restoring the role of mathematics in signal and image processing John Rognes University of Oslo, Norway May 2017 The Norwegian Academy of Science and Letters has decided to award the Abel Prize for 2017 to Yves Meyer, École Normale Supérieure, Paris–Saclay for his pivotal role in the development of the mathematical theory of wavelets. Yves Meyer (1939-, Abel Prize 2017) Outline A biographical sketch From Fourier to Morlet Fourier transform Gabor atoms Wavelet transform First synthesis: Wavelet analysis (1984-1985) Second synthesis: Multiresolution analysis (1986-1988) Yves Meyer: early years I 1939: Born in Paris. I 1944: Family exiled to Tunisia. I High school at Lycée Carnot de Tunis. Lycée Carnot University education I 1957-1959?: École Normale Supérieure de la rue d’Ulm. I 1960-1963: Military service (Algerian war) as teacher at Prytanée national militaire. “Beginning a Ph.D. to avoid being drafted would be like marrying a woman for her money.” “From teaching in high school I understood that I was more happy to share than to possess.” Prytanée national militaire Doctoral degree I 1963-1966: PhD at Strasbourg (unsupervised, formally with Jean Pierre Kahane). 1 I Operator theory on Hardy space H . I Advice from Peter Gabriel: “Give up classical analysis. Switch to algebraic geometry (à la Grothendieck). People above 40 are completely lost now. Young people can work freely in this field. In classical analysis you are fighting against the accumulated training and experience of the old specialists.” I Meyer’s PhD thesis was soon outdone by Elias Stein. Jean-Pierre Kahane (1926-) Elias Stein (1931-) Meyer sets = almost lattices I 1966-1980: Université Paris-Sud at Orsay. -
EMS Newsletter September 2012 1 EMS Agenda EMS Executive Committee EMS Agenda
NEWSLETTER OF THE EUROPEAN MATHEMATICAL SOCIETY Editorial Obituary Feature Interview 6ecm Marco Brunella Alan Turing’s Centenary Endre Szemerédi p. 4 p. 29 p. 32 p. 39 September 2012 Issue 85 ISSN 1027-488X S E European M M Mathematical E S Society Applied Mathematics Journals from Cambridge journals.cambridge.org/pem journals.cambridge.org/ejm journals.cambridge.org/psp journals.cambridge.org/flm journals.cambridge.org/anz journals.cambridge.org/pes journals.cambridge.org/prm journals.cambridge.org/anu journals.cambridge.org/mtk Receive a free trial to the latest issue of each of our mathematics journals at journals.cambridge.org/maths Cambridge Press Applied Maths Advert_AW.indd 1 30/07/2012 12:11 Contents Editorial Team Editors-in-Chief Jorge Buescu (2009–2012) European (Book Reviews) Vicente Muñoz (2005–2012) Dep. Matemática, Faculdade Facultad de Matematicas de Ciências, Edifício C6, Universidad Complutense Piso 2 Campo Grande Mathematical de Madrid 1749-006 Lisboa, Portugal e-mail: [email protected] Plaza de Ciencias 3, 28040 Madrid, Spain Eva-Maria Feichtner e-mail: [email protected] (2012–2015) Society Department of Mathematics Lucia Di Vizio (2012–2016) Université de Versailles- University of Bremen St Quentin 28359 Bremen, Germany e-mail: [email protected] Laboratoire de Mathématiques Newsletter No. 85, September 2012 45 avenue des États-Unis Eva Miranda (2010–2013) 78035 Versailles cedex, France Departament de Matemàtica e-mail: [email protected] Aplicada I EMS Agenda .......................................................................................................................................................... 2 EPSEB, Edifici P Editorial – S. Jackowski ........................................................................................................................... 3 Associate Editors Universitat Politècnica de Catalunya Opening Ceremony of the 6ECM – M. -
Cuatro Matemáticos Ganan El Premio Princesa De Asturias De Investigación Científica Y Técnica 2020
CIENCIAS Cuatro matemáticos ganan el Premio Princesa de Asturias de Investigación Científica y Técnica 2020 Los trabajos de Yves Meyer, Ingrid Daubechies, Terence Tao y Emmanuel Candès, líderes mundiales en el campo de las matemáticas, han permitido la compresión de vídeos e imágenes digitales, incluidas las del telescopio Hubble, los detectores de ondas gravitacionales y las resonancias magnéticas. SINC 23/6/2020 15:16 CEST Ives Meyer, Ingrid Daubechies, Terence Tao y Emmanuel Candès. / FPA Los matemáticos Yves Meyer (francés), Ingrid Daubechies (belga y estadounidense), Terence Tao (australiano y estadounidense) y Emmanuel Candès (también francés) han sido galardonados con el Premio Príncipe de Asturias de Investigación Científica y Técnica de este año, según ha comunicado hoy el jurado. Estos cuatro matemáticos han realizado contribuciones pioneras y trascendentales a las teorías y técnicas modernas del procesamiento matemático de datos y señales. Estas son base y soporte de la era digital – para, por ejemplo, comprimir archivos gráficos sin apenas pérdida de resolución–, de la imagen y el diagnóstico médicos –al permitir reconstruir imágenes precisas a partir de un reducido número de datos– y de la CIENCIAS ingeniería y la investigación científica –eliminado interferencias y ruido de fondo–. En este último punto, estas técnicas están siendo clave, por ejemplo, en la llamada deconvolución (operación inversa a la convolución para restaurar señalas y recuperar datos) de las imágenes del telescopio espacial Hubble, y han sido cruciales -
Invitation to Quantum Mechanics
i Invitation to Quantum Mechanics Daniel F. Styer ii Invitation to Quantum Mechanics Daniel F. Styer Schiffer Professor of Physics, Oberlin College copyright c 31 May 2021 Daniel F. Styer The copyright holder grants the freedom to copy, modify, convey, adapt, and/or redistribute this work under the terms of the Creative Commons Attribution Share Alike 4.0 International License. A copy of that license is available at http://creativecommons.org/licenses/by-sa/4.0/legalcode. You may freely download this book in pdf format from http://www.oberlin.edu/physics/dstyer/InvitationToQM: It is formatted to print nicely on either A4 or U.S. Letter paper. You may also purchase a printed and bound copy from World Scientific Publishing Company. In neither case does the author receive monetary gain from your download/purchase: it is reward enough for him that you want to explore quantum mechanics. Love all God's creation, the whole and every grain of sand in it. Love the stars, the trees, the thunderstorms, the atoms. The more you love, the more you will grow curious. The more you grow curious, the more you will question. The more you question, the more you will uncover. The more you uncover, the more you will love. And so at last you will come to love the entire universe with an agile and resilient love founded upon facts and understanding. | This improvisation by Dan Styer was inspired by the first sentence, which appears in Fyodor Dostoyevsky's The Brothers Karamazov. iii iv Dedicated to Linda Ong Styer, adventurer Contents Synoptic Contents 1 Welcome 3 1.