Wave Packet Analysis

Author : Christoph Thiele
Publisher : American Mathematical Soc.
Page : 97 pages
File Size : 41,6 Mb
Release : 2006
Category : Linear operators
ISBN : 9780821836613

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Wave Packet Analysis by Christoph Thiele Pdf

The concept of ``wave packet analysis'' originates in Carleson's famous proof of almost everywhere convergence of Fourier series of $L2$ functions. It was later used by Lacey and Thiele to prove bounds on the bilinear Hilbert transform. For quite some time, Carleson's wave packet analysis was thought to be an important idea, but that it had limited applications. But in recent years, it has become clear that this is an important tool for a number of other applications. This book isan introduction to these tools. It emphasizes the classical successes (Carleson's theorem and the Hilbert transform) in the main development. However, the book closes with a dedicated chapter on more recent results. Carleson's original theorem is sometimes cited as one of the most importantdevelopments of 20th century harmonic analysis. The set of ideas stemming from his proof is now seen as an essential element in modern harmonic analysis. Indeed, Thiele won the Salem prize jointly with Michael Lacey for work in this area. The book gives a nice survey of important material, such as an overview of the theory of singular integrals and wave packet analysis itself. There is a separate chapter on ``further developments'', which gives a broader view on the subject, though it does notexhaust all ongoing developments.

Author : Fabio Nicola,S. Ivan Trapasso
Publisher : Springer Nature
Page : 220 pages
File Size : 47,5 Mb
Release : 2022-07-28
Category : Science
ISBN : 9783031061868

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Wave Packet Analysis of Feynman Path Integrals by Fabio Nicola,S. Ivan Trapasso Pdf

The purpose of this monograph is to offer an accessible and essentially self-contained presentation of some mathematical aspects of the Feynman path integral in non-relativistic quantum mechanics. In spite of the primary role in the advancement of modern theoretical physics and the wide range of applications, path integrals are still a source of challenging problem for mathematicians. From this viewpoint, path integrals can be roughly described in terms of approximation formulas for an operator (usually the propagator of a Schrödinger-type evolution equation) involving a suitably designed sequence of operators. In keeping with the spirit of harmonic analysis, the guiding theme of the book is to illustrate how the powerful techniques of time-frequency analysis - based on the decomposition of functions and operators in terms of the so-called Gabor wave packets – can be successfully applied to mathematical path integrals, leading to remarkable results and paving the way to a fruitful interaction. This monograph intends to build a bridge between the communities of people working in time-frequency analysis and mathematical/theoretical physics, and to provide an exposition of the present novel approach along with its basic toolkit. Having in mind a researcher or a Ph.D. student as reader, we collected in Part I the necessary background, in the most suitable form for our purposes, following a smooth pedagogical pattern. Then Part II covers the analysis of path integrals, reflecting the topics addressed in the research activity of the authors in the last years.

Author : Frank S. Levin
Publisher : Cambridge University Press
Page : 812 pages
File Size : 53,5 Mb
Release : 2002
Category : Science
ISBN : 0521598419

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An Introduction to Quantum Theory by Frank S. Levin Pdf

An undergraduate introductory quantum mechanics textbook with a large number of figures and exercises.

Author : Shan Gao
Publisher : Cambridge University Press
Page : 201 pages
File Size : 48,6 Mb
Release : 2017-03-16
Category : Science
ISBN : 9781107124356

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The Meaning of the Wave Function by Shan Gao Pdf

Covering much of the recent debate, this ambitious text provides new, decisive proof of the reality of the wave function.

Author : Daniel Greenberger,Klaus Hentschel,Friedel Weinert
Publisher : Springer Science & Business Media
Page : 901 pages
File Size : 45,6 Mb
Release : 2009-07-25
Category : Science
ISBN : 9783540706267

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Compendium of Quantum Physics by Daniel Greenberger,Klaus Hentschel,Friedel Weinert Pdf

With contributions by leading quantum physicists, philosophers and historians, this comprehensive A-to-Z of quantum physics provides a lucid understanding of key concepts of quantum theory and experiment. It covers technical and interpretational aspects alike, and includes both traditional and new concepts, making it an indispensable resource for concise, up-to-date information about the many facets of quantum physics.

Author : D Mugnai,Anedio Ranfagni,Lawrence S Schulman
Publisher : World Scientific
Page : 486 pages
File Size : 44,9 Mb
Release : 1997-04-19
Category : Electronic
ISBN : 9789814546980

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Tunneling And Its Implications: Proceedings Of The Adriatico Research Conference by D Mugnai,Anedio Ranfagni,Lawrence S Schulman Pdf

The motion of a particle undergoing quantum tunneling has long been an open and debated problem in several aspects. One of the most discussed is the determination of the time spent in such processes, but many other features deserve consideration. In this volume, both theoretical and experimental aspects, such as quantum measurement, optical analogy, experimental tests, solid state devices and time scale for anomalies (quantum Zeno effect and superluminal evanescence), are explored.

Author : Daniela Mugnai,Anedio Ranfagni,Lawrence S. Schulman
Publisher : World Scientific
Page : 486 pages
File Size : 54,7 Mb
Release : 1997
Category : Tunneling (Physics)
ISBN : 9789814530354

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Tunneling And Its Implications by Daniela Mugnai,Anedio Ranfagni,Lawrence S. Schulman Pdf

"The motion of a particle undergoing quantum tunneling has long been an open and debated problem in several aspects. One of the most discussed is the determination of the time spent in such processes, but many other features deserve consideration. In this volume, both theoretical and experimental aspects, such as quantum measurement, optical analogy, experimental tests, solid state devices and time scale for anomalies (quantum Zeno effect and superluminal evanescence), are explored."--Publisher's website

Author : Antonio B. Nassar,Salvador Miret-Artés
Publisher : Springer
Page : 241 pages
File Size : 52,8 Mb
Release : 2017-03-14
Category : Science
ISBN : 9783319536538

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Bohmian Mechanics, Open Quantum Systems and Continuous Measurements by Antonio B. Nassar,Salvador Miret-Artés Pdf

This book shows how Bohmian mechanics overcomes the need for a measurement postulate involving wave function collapse. The measuring process plays a very important role in quantum mechanics. It has been widely analyzed within the Copenhagen approach through the Born and von Neumann postulates, with later extension due to Lüders. In contrast, much less effort has been invested in the measurement theory within the Bohmian mechanics framework. The continuous measurement (sharp and fuzzy, or strong and weak) problem is considered here in this framework. The authors begin by generalizing the so-called Mensky approach, which is based on restricted path integral through quantum corridors. The measuring system is then considered to be an open quantum system following a stochastic Schrödinger equation. Quantum stochastic trajectories (in the Bohmian sense) and their role in basic quantum processes are discussed in detail. The decoherence process is thereby described in terms of classical trajectories issuing from the violation of the noncrossing rule of quantum trajectories.

Author : Anonim
Publisher : Unknown
Page : 1164 pages
File Size : 45,9 Mb
Release : 2003
Category : Meteorology
ISBN : UGA:32108036122847

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Monthly Weather Review by Anonim Pdf

Author : Ángel S. Sanz,Salvador Miret-Artés
Publisher : Springer
Page : 345 pages
File Size : 44,6 Mb
Release : 2013-09-13
Category : Science
ISBN : 9783642179747

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A Trajectory Description of Quantum Processes. II. Applications by Ángel S. Sanz,Salvador Miret-Artés Pdf

Trajectory-based formalisms are an intuitively appealing way of describing quantum processes because they allow the use of "classical" concepts. Beginning as an introductory level suitable for students, this two-volume monograph presents (1) the fundamentals and (2) the applications of the trajectory description of basic quantum processes. This second volume is focussed on simple and basic applications of quantum processes such as interference and diffraction of wave packets, tunneling, diffusion and bound-state and scattering problems. The corresponding analysis is carried out within the Bohmian framework. By stressing its interpretational aspects, the book leads the reader to an alternative and complementary way to better understand the underlying quantum dynamics.

Author : Reik V. Donner,Susana M. Barbosa
Publisher : Springer
Page : 390 pages
File Size : 45,6 Mb
Release : 2008-08-03
Category : Science
ISBN : 9783540789383

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Nonlinear Time Series Analysis in the Geosciences by Reik V. Donner,Susana M. Barbosa Pdf

The enormous progress over the last decades in our understanding of the mechanisms behind the complex system “Earth” is to a large extent based on the availability of enlarged data sets and sophisticated methods for their analysis. Univariate as well as multivariate time series are a particular class of such data which are of special importance for studying the dynamical p- cesses in complex systems. Time series analysis theory and applications in geo- and astrophysics have always been mutually stimulating, starting with classical (linear) problems like the proper estimation of power spectra, which hasbeenputforwardbyUdnyYule(studyingthefeaturesofsunspotactivity) and, later, by John Tukey. In the second half of the 20th century, more and more evidence has been accumulated that most processes in nature are intrinsically non-linear and thus cannot be su?ciently studied by linear statistical methods. With mat- matical developments in the ?elds of dynamic system’s theory, exempli?ed by Edward Lorenz’s pioneering work, and fractal theory, starting with the early fractal concepts inferred by Harold Edwin Hurst from the analysis of geoph- ical time series,nonlinear methods became available for time seriesanalysis as well. Over the last decades, these methods have attracted an increasing int- est in various branches of the earth sciences. The world’s leading associations of geoscientists, the American Geophysical Union (AGU) and the European Geosciences Union (EGU) have reacted to these trends with the formation of special nonlinear focus groups and topical sections, which are actively present at the corresponding annual assemblies.

Author : Sergej O. Demokritov
Publisher : CRC Press
Page : 436 pages
File Size : 47,7 Mb
Release : 2017-09-07
Category : Science
ISBN : 9781351617215

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Spin Wave Confinement by Sergej O. Demokritov Pdf

Since the publication of the first edition of Spin-Wave Confinement, the magnetic community’s interest in dynamic excitations in magnetic systems of reduced dimensions has been increasing. Although the concept of spin waves and their quanta (magnons) as propagating excitation of magnetic media was introduced more than 80 years ago, this field has been repeatedly bringing us fascinating new physical phenomena. The successful development of magnonics as an emerging subfield of spintronics, which considers confined spin waves as a basis for smaller, faster, more robust, and more power-efficient electronic devices, inevitably demands reduction in the sizes and dimensions of the magnetic systems being studied. The unique features of magnons, including the possibility of carrying spin information over relatively long distances, the possibility of achieving submicrometer wavelength at microwave frequencies, and controllability by electronic signal via magnetic fields, make magnonic devices distinctively suited for implementation of novel integrated electronic schemes characterized by high speed, low power consumption, and extended functionalities. Edited by S. O. Demokritov, a prominent magnonics researcher who has successfully collected the results of cutting-edge research by almost all main players in the field, this book is for everyone involved in nanotechnology, spintronics, magnonics, and nanomagnetism.

Author : Slobodan Danko Bosanac
Publisher : CRC Press
Page : 224 pages
File Size : 51,5 Mb
Release : 2018-01-31
Category : Science
ISBN : 9781351091060

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Long Lived States In Collisions by Slobodan Danko Bosanac Pdf

This book contains essentially two parts. A Review of the classical, quantum, and semi-classical theories of collision are given in the first part, while their applications to the atom and molecule collisions are given in the second part. The book is useful to scientists other than atom and molecular physicists, and is as general as possible, however, with the emphasis on the atom and molecule collisions.

Author : Peter R. Bergethon
Publisher : Springer Science & Business Media
Page : 581 pages
File Size : 49,6 Mb
Release : 2013-03-14
Category : Science
ISBN : 9781475729634

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The Physical Basis of Biochemistry by Peter R. Bergethon Pdf

The objective of this book is to provide a unifying approach to the study of biophysical chemistry for the advanced undergraduate who has had a year of physics, organic chem istry, calculus, and biology. This book began as a revised edition of Biophysical Chemistry: Molecules to Membranes, which Elizabeth Simons and I coauthored. That short volume was written in an attempt to provide a concise text for a one-semester course in biophysical chemistry at the graduate level. The experience of teaching biophysical chemistry to bi ologically oriented students over the last decade has made it clear that the subject requires a more fundamental text that unifies the many threads of modem science: physics, chem istry, biology, mathematics, and statistics. This book represents that effort. This volume is not a treatment of modem biophysical chemistry with its rich history and many contro versies, although a book on that topic is also needed. The Physical Basis of Biochemistry is an introduction to the philosophy and practice of an interdisciplinary field in which biological systems are explored using the quantitative perspective of the physical scientist. I have three primary objectives in this volume: one, to provide a unifying picture of the interdisciplinary threads from which the tapestry of biophysical studies is woven; two, to provide an insight into the power of the modeling approach to scientific investigation; and three, to communicate a sense of excitement for the activity and wholesome argument that characterize this field of study.

Author : United States. National Aeronautics and Space Administration
Publisher : Unknown
Page : 556 pages
File Size : 50,7 Mb
Release : 1959
Category : Aeronautics
ISBN : UIUC:30112008547769

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NASA Technical Note by United States. National Aeronautics and Space Administration Pdf