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The authors give the proper functional analytic setting in order to study this operator and develop a pseudodifferential calculus, which provides estimates on the hypoelliptic Laplacian's resolvent. When the deformation parameter tends to zero, the hypoelliptic Laplacian converges to the standard Hodge Laplacian of the base by a collapsing argument in which the fibers of the cotangent bundle collapse to a point. For the local index theory, small time asymptotics for the supertrace of the associated heat kernel are obtained.\u003cbr\u003e\u003cbr\u003e\u003cbr\u003e  The Ray-Singer analytic torsion of the hypoelliptic Laplacian as well as the associated Ray-Singer metrics on the determinant of the cohomology are studied in an equivariant setting, resulting in a key comparison formula between the elliptic and hypoelliptic analytic torsions.\u003c\/p\u003e","brand":"None","offers":[{"title":"Paperback","offer_id":46153119039665,"sku":"9780691137322","price":110.0,"currency_code":"CAD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0655\/8980\/5233\/files\/1_22a98708-54d6-46d3-b642-bf9179bc19b8.jpg?v=1763635938"},{"product_id":"the-world-itself","title":"The World Itself: Consciousness and the Everything of Physics","description":"\u003cp\u003e\u003cb\u003e\u003ci\u003eThere is a wonderfully weird but real world out there, and we are a part of it. It is time for physics to take life seriously.\u003c\/i\u003e\u003c\/b\u003e\u003c\/p\u003e\u003cp\u003eCan we ever truly comprehend the universe before we fully understand consciousness and the wonders, and limits, of the mind? Ulf Danielsson, an acclaimed theoretical physicist who has dedicated his career to probing the deepest mysteries of nature, thinks not. As he dismantles the arguments of esteemed mathematicians and scientists, who would substitute their mathematical models for reality and equate the mind to a computer, he makes a lucid and passionate case that it is nature, full of beauty and meaning, which must compel us. In challenging established worldviews, he also takes a fresh look at major philosophical debates, including the notion of free will.\u003c\/p\u003e\u003cp\u003eFearless, provocative, and witty, \u003ci\u003eThe World Itself\u003c\/i\u003e is essential reading for anyone curious about the profound questions surrounding life, the universe, and everything.\u003c\/p\u003e","brand":"None","offers":[{"title":"Paperback","offer_id":46153160687793,"sku":"9781954276116","price":29.5,"currency_code":"CAD","in_stock":true},{"title":"Kobo eBook","offer_id":46153160720561,"sku":"7ad269ce-7df2-3ffc-8191-3d05d38f3070","price":19.99,"currency_code":"CAD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0655\/8980\/5233\/files\/1_b8ab0bfc-e2aa-4b74-aed0-3e3fb5d06104.jpg?v=1763411421"},{"product_id":"the-science-of-light","title":"The Science of Light: From Galileo’s Telescope to Quantum Physics","description":"\u003cp\u003eOdile Jacob Publishing to release The Science of Light, a captivating journey of scientific discovery by Nobel Prize-winning physicist Serge Haroche. The Science of Light will be available for purchase worldwide in digital formats starting on Thursday, March 24, 2022, at odilejacob. com and on all retail platforms. Serge Haroche is professor emeritus at the Collège de France, a member of the Académie des Sciences, a foreign member of the U. S. National Academy of Sciences, and winner of the 2012 Nobel Prize in Physics for discovering methods of manipulating and measuring individual quantum systems. He has taught at Paris VI University, the École Polytechnique, the École Normale Supérieure, Harvard University, and Yale University. Serge HarocheNobel Prize in PhysicsThe Science of LightFrom Galileo’s Telescope to Quantum Physics Light has fascinated mankind since the dawn of time. Elucidating its properties over the centuries has been an adventure intimately linked with the birth and development of modern science; it has led, after many surprising twists, to the theories of relativity and quantum physics which have profoundly changed our view of the world at the microscopic and cosmic scales alike. Placing his own career in a rich lineage of scientific discovery, Nobel Prize–winning physicist Serge Haroche offers a literally enlightening account of what we know about light today, how we learned it, and how that knowledge has led to countless inventions that have revolutionized daily life. From Galileo and Newton to Einstein and Feynman, from early measurements of the speed of light to cutting-edge work on quantum entanglement, Haroche takes a detailed and personal look at light’s role in how we see and understand the universe. The Science of Light is at once a colorful history of scientific inquiry and a passionate defense of “blue sky research”—investigations conducted not in pursuit of a particular goal, but out of curiosity and faith that today’s abstract discoveries may well power tomorrow’s most incredible possibilities. A uniquely captivating book about the thrill of discovery. Contents FOREWORD 13 CHAPTER 1: The dawn of a vocation 21First passions: from mathematics to astronomy 23Introduction to modern physics 35Shut up and calculate! 47When atoms and photons are spinning tops: optical pumping 50To see the world as something rich and strange 65An apprenticeship in trust and freedom 77Promises of the laser 81Beginnings in research 85First trip to America and return to my first passion 90“Blue sky” research 93 CHAPTER 2: Reflections in the Observatory square 97Two instruments at the origins of the scientific revolution: the refracting telescope and the pendulum clock 100Measuring the speed of light to survey the universe 106The science of light becomes quantitative: Descartes and Dioptrics 113Nature works by the shortest and simplest ways: Fermat’s principle 118Huygens and the wave theory of light 124Newton, light particles, and color 134Measuring the shape of the Earth 143A passion for precision 156Basic science, business, power, and technology 161 CHAPTER 3: Daydreams in Faraday’s laboratory 165Young v. Newton 169Light is polarized 175Fresnel and the triumph of the waves 177Combining vectors and interfering waves 181A rotating vibration: circular polarization 187Light illuminated by mathematics 193Back to the speed of light 198From the salons of the Enlightenment to Faraday’s laboratory 208Birth of the concept of field 218The confluence of light, electricity, and magnetism 223Some mysteries disappear but others remain 229 CHAPTER 4: The two clouds of Lord Kelvin 239Michelson and the puzzle of the aether 245Einstein comes on the scene: thought experiments 249A relativistic change of perspective 261Space mixes with time 266Mass and energy combine: E = mc2 272Einstein’s “happiest” idea comes from Galileo again 283Gravitation and curvature of space-time 291Relativistic predictions and postdictions 299 CHAPTER 5: Light reveals the strange world of quanta 311The ultraviolet catastrophe 314Light between waves and particles 318Quanta are generalized to matter 322Gregarious photons and atoms that mimic them 329The veil is lifted on matter waves 334Wave function, quantum states, and the superposition principle 339The particle family expands 342A fundamental identity 347The Pandora’s box of quantum physics 352From classical to quantum: a dialogue across centuries between Fermat, Maupertuis, and Feynman 355A journey in orders of magnitude 360The quantum scene: individual objects or statistical ensembles? 365Young’s double slit revisited 368Measurement, complementarity, and uncertainty relations 371Debates around imaginary experiments 380Quantum entanglement 389Schrödinger’s cat and the classical–quantum boundary 399 CHAPTER 6: Lasers, photons, and giant atoms 407An atom dressed by photons 408Introduction to lasers in California 417Beating the Doppler effect 425Quantum beats 434Californian anecdotes 439First major international conference 442The terra incognita of giant atoms 445The birth of cavity quantum electrodynamics 456Research and teaching on both sides of the Atlantic 463The laser cooling revolution 468Trapped ions and quantum jumps 479 CHAPTER 7: Taming Schrödinger’s cat 489The photon box 494The circular atom 498Quantum ping-pong 504Quantum knitting 507How to see photons without destroying them 510Life and death of a photon 514Back to Young’s moving slit experiment 523Counting photons and observing quantum jumps 526Quantum field radiography 538Schrödinger’s cats of light 547Exploring the quantum-to-classical boundary 559Toward a quantum computer: utopia or future reality? 570Feynman’s dream: quantum simulation 575Spooky action at a distance, quantum cryptography, and quantum teleportation 578Quantum metrology and optical clocks 582 POSTFACE: Science and truth 593 BIBLIOGRAPHY: Some works to complement the reading of this book 599 INDEX OF CITED SCIENTISTS 605 ACKNOWLEDGMENTS 613\u003c\/p\u003e\r\n","brand":"None","offers":[{"title":"Kobo eBook","offer_id":46153160523953,"sku":"6cd284ed-f110-348b-8553-c36fa8cec8d7","price":14.49,"currency_code":"CAD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0655\/8980\/5233\/files\/image_acba89d5-5612-4d8d-906a-86c8613b581e.jpg?v=1762726579"},{"product_id":"simulation-and-the-monte-carlo-method","title":"Simulation and the Monte Carlo Method","description":"\u003cp\u003e\u003cb\u003eThis accessible new edition explores the major topics in Monte Carlo simulation that have arisen over the past 30 years and presents a sound foundation for problem solving\u003c\/b\u003e\u003cb\u003e \u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003ci\u003eSimulation and the Monte Carlo Method, Third Edition \u003c\/i\u003ereflects the latest developments in the field and presents a fully updated and comprehensive account of the state-of-the-art theory, methods and applications that have emerged in Monte Carlo simulation since the publication of the classic First Edition over more than a quarter of a century ago. While maintaining its accessible and intuitive approach, this revised edition features a wealth of up-to-date information that facilitates a deeper understanding of problem solving across a wide array of subject areas, such as engineering, statistics, computer science, mathematics, and the physical and life sciences. The book begins with a modernized introduction that addresses the basic concepts of probability, Markov processes, and convex optimization. Subsequent chapters discuss the dramatic changes that have occurred in the field of the Monte Carlo method, with coverage of many modern topics including: Markov Chain Monte Carlo, variance reduction techniques such as importance (re-)sampling, and the transform likelihood ratio method, the score function method for sensitivity analysis, the stochastic approximation method and the stochastic counter-part method for Monte Carlo optimization, the cross-entropy method for rare events estimation and combinatorial optimization, and application of Monte Carlo techniques for counting problems. An extensive range of exercises is provided at the end of each chapter, as well as a generous sampling of applied examples.\u003c\/p\u003e \u003cp\u003eThe \u003ci\u003eThird Edition \u003c\/i\u003efeatures a new chapter on the highly versatile splitting method, with applications to rare-event estimation, counting, sampling, and optimization. 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In addition, the \u003ci\u003eThird Edition \u003c\/i\u003efeatures new material on\u003ci\u003e:\u003c\/i\u003e\u003c\/p\u003e \u003cp\u003e• Random number generation, including multiple-recursive generators and the Mersenne Twister\u003c\/p\u003e \u003cp\u003e• Simulation of Gaussian processes, Brownian motion, and diffusion processes\u003c\/p\u003e \u003cp\u003e• Multilevel Monte Carlo method\u003c\/p\u003e \u003cp\u003e• New enhancements of the cross-entropy (CE) method, including the “improved” CE method, which uses sampling from the zero-variance distribution to find the optimal importance sampling parameters\u003c\/p\u003e \u003cp\u003e• Over 100 algorithms in modern pseudo code with flow control\u003c\/p\u003e \u003cp\u003e• Over 25 new exercises\u003c\/p\u003e \u003cp\u003e\u003ci\u003eSimulation and the Monte Carlo Method, Third Edition \u003c\/i\u003eis an excellent text for upper-undergraduate and beginning graduate courses in stochastic simulation and Monte Carlo techniques. 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For this reason we take an algorithmic approach, emphasizing estimates of the efficiency of the techniques that arise from the theory.","brand":"None","offers":[{"title":"Paperback","offer_id":46153870704817,"sku":"9781461264422","price":33.95,"currency_code":"CAD","in_stock":true},{"title":"Hardcover","offer_id":46153870737585,"sku":"9780387942933","price":84.5,"currency_code":"CAD","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0655\/8980\/5233\/files\/1_f50f93de-0bca-4bf8-98f0-6252d3b4835e.jpg?v=1763514373"},{"product_id":"experiments-with-mixtures","title":"Experiments with Mixtures: Designs, Models, and the Analysis of Mixture Data","description":"The most comprehensive, single-volume guide to conductingexperiments with mixtures\u003cbr\u003e \u003cbr\u003e \"If one is involved, or heavily interested, in experiments onmixtures of ingredients, one must obtain this book. 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