Quantum Classical Analogies

Author : Daniela Dragoman,Mircea Dragoman
Publisher : Springer Science & Business Media
Page : 355 pages
File Size : 50,7 Mb
Release : 2013-04-09
Category : Science
ISBN : 9783662096475

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Quantum-Classical Analogies by Daniela Dragoman,Mircea Dragoman Pdf

It is unanimously accepted that the quantum and the classical descriptions of the physical reality are very different, although any quantum process is "mysteriously" transformed through measurement into an observable classical event. Beyond the conceptual differences, quantum and classical physics have a lot in common. And, more important, there are classical and quantum phenomena that are similar although they occur in completely different contexts. For example, the Schrödinger equation has the same mathematical form as the Helmholtz equation, there is an uncertainty relation in optics very similar to that in quantum mechanics, and so on; the list of examples is very long. Quantum-classical analogies have been used in recent years to study many quantum laws or phenomena at the macroscopic scale, to design and simulate mesoscopic devices at the macroscopic scale, to implement quantum computer algorithms with classical means, etc. On the other hand, the new forms of light – localized light, frozen light – seem to have more in common with solid state physics than with classical optics. So these analogies are a valuable tool in the quest to understand quantum phenomena and in the search for new (quantum or classical) applications, especially in the area of quantum devices and computing.

Author : Olivier Darrigol,Research Director Olivier Darrigol
Publisher : Univ of California Press
Page : 418 pages
File Size : 47,8 Mb
Release : 1992-01-01
Category : Science
ISBN : 0520078225

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From C-numbers to Q-numbers by Olivier Darrigol,Research Director Olivier Darrigol Pdf

The history of quantum theory is a maze of conceptual problems. In this lucid and learned book, Olivier Darrigol tracks the role of formal analogies between classical and quantum theory, from Planck's first introduction of the quantum of action to Dirac's formulation of quantum mechanics. In so doing, Darrigol illuminates not only the history of quantum theory but also the role of analogies in scientific thinking and theory change. The most remarkable result of such analogical argument in quantum theory was Bohr's correspondence principle which, in Darrigol's words, "performed the acrobatic task of bridging two mutually contradictory theories (classical electrodynamics and atomic theory), without diminishing the contrast between them". By analyzing the origins, development, and applications of this principle, From c-Numbers to q-Numbers explains the remarkable fruitfulness of the research done under Bohr's guidance between 1916 and 1925 and shows why Heisenberg claimed that quantum mechanics was born as "a quantitative formulation of the correspondence principle". With a physicist's sure hand, Darrigol examines the formal and the epistemological aspects of the analogy between classical and quantum mechanics. Unlike previous works, which have tended to focus on qualitative, global arguments, he follows the lines of mathematical reasoning and symbolizing, and by doing so he is able to show the motivations of early quantum theorists more precisely - and provocatively - than ever before. For instance, Darrigol demonstrates that a universal principle of elementary chaos underlay Planck's analogies, and that Bohr's correspondence principle was related to his elaboration of a minimal-quantumtheoretical language. Most striking, Darrigol reveals how Dirac's personal conception of the relations among algebra, geometry, use of the analogy between c-numbers and and physics conditioned his highly creative q-numbers. Original, erudite, and witty, From c-Numbers to q-Numbers sets a new standard for the philosophically perceptive and mathematically precise history of quantum mechanics. For years to come it will influence historical and philosophical discussions of twentieth-century physics.

Author : Aydın Cem Keser
Publisher : Springer
Page : 99 pages
File Size : 51,9 Mb
Release : 2018-11-07
Category : Technology & Engineering
ISBN : 9783030004880

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Classical Analogies in the Solution of Quantum Many-Body Problems by Aydın Cem Keser Pdf

This book addresses problems in three main developments in modern condensed matter physics– namely topological superconductivity, many-body localization and strongly interacting condensates/superfluids–by employing fruitful analogies from classical mechanics. This strategy has led to tangible results, firstly in superconducting nanowires: the density of states, a smoking gun for the long sought Majorana zero mode is calculated effortlessly by mapping the problem to a textbook-level classical point particle problem. Secondly, in localization theory even the simplest toy models that exhibit many-body localization are mathematically cumbersome and results rely on simulations that are limited by computational power. In this book an alternative viewpoint is developed by describing many-body localization in terms of quantum rotors that have incommensurate rotation frequencies, an exactly solvable system. Finally, the fluctuations in a strongly interacting Bose condensate and superfluid, a notoriously difficult system to analyze from first principles, are shown to mimic stochastic fluctuations of space-time due to quantum fields. This analogy not only allows for the computation of physical properties of the fluctuations in an elegant way, it sheds light on the nature of space-time. The book will be a valuable contribution for its unifying style that illuminates conceptually challenging developments in condensed matter physics and its use of elegant mathematical models in addition to producing new and concrete results.

Author : Andon Rangelov
Publisher : Unknown
Page : 0 pages
File Size : 49,8 Mb
Release : 2023-01-17
Category : Electronic
ISBN : 9798215169872

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Quantum Optical Analogues by Andon Rangelov Pdf

The analogy is a fundamental tool for understanding Mother Nature since it associates various phenomena related by common properties or comparable behavior. In particular, the analogies between classical physics and the quantum world show the fact that similar scientific formalisms apply to phenomena that are completely different. The role of mathematics is essential because the analogy principle exists in the fact that totally different systems can be modeled by similar mathematical equations. Specifically, analogies between quantum mechanics and wave optics have been emphasized since the beginning of quantum mechanics: wave effects like interference and diffraction were taken from optics and applied to exhibit the wavy idea of quantum particles, such as electrons, neutrons, and atoms. After the complete development of quantum theory, the exchange of ideas in the opposite way started to happen. In the recent decade quantum-classical analogies have seen a great revival thanks to quantum control schemes for the transfer of populations, such as excitation with the rapid adiabatic passage, stimulated Raman adiabatic passage, and composite pulses. Adiabatic processes in a dynamical system occur when an external perturbation of the system varies very slowly compared to its internal dynamics, allowing the system the time to adapt to the external changes. Mathematically, it means that for the entire dynamical evolution, the system remains at one of the eigenmodes of the system. Composite pulses are solutions to arbitrary optimization problems in a quantum system, driven by an external radiation field. The basic idea is to improve the performance of single-pulse excitation processes by applying multi-pulse (i.e. composite pulse) processes. The phases of the pulses in the composite sequence are appropriately chosen to yield a better performance of the composite excitation process compared to the single-pulse excitation. Now in this book, we will use the concepts of composite pulses and adiabatic evolution, from the realm of coherent quantum control, to demonstrate: (a) novel robust polarization manipulation devices; (b) efficient broadband and scalable frequency conversion schemes as well as optical parametric amplification schemes; (c) several new optical isolators; (d) several control schemes in waveguide arrays. All of this research is done by making the analogy between quantum mechanics and classical optics.

Author : Miroslav Svitek
Publisher : Academic Press
Page : 156 pages
File Size : 49,6 Mb
Release : 2021-06-05
Category : Science
ISBN : 9780323910125

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Information Physics by Miroslav Svitek Pdf

Information Physics: Physics-Information and Quantum Analogies for Complex Modeling presents a new theory of complex systems that uses analogy across various aspects of physics, including electronics, magnetic circuits and quantum mechanics. The book explains the quantum approach to system theory that can be understood as an extension of classical system models. The main idea is that in many complex systems there are incomplete pieces of overlapping information that must be strung together to find the most consistent model. This incomplete information can be understood as a set of non-exclusive observer results. Because they are non-exclusive, each observer registers different pictures of reality. Provides readers with an understanding of the analogies between very sophisticated theories of electrical circuits and currently underdeveloped information circuits, including capturing positive and negative links, as well as serial and parallel ordering of information blocks Integrates coverage of quantum models of complex systems using wave probabilistic functions which extend the classical probability description by phase parameters that allow researchers to model such properties as entanglement, superposition and others Provides readers with illustrative examples of how to use the presented theories of complex systems in specific cases such as hierarchical systems, cooperation of a team of experts, the lifecycle of the company, and the link between short and long-term memory

Author : Bogdan Povh,Mitja Rosina
Publisher : Springer
Page : 264 pages
File Size : 53,6 Mb
Release : 2009-09-02
Category : Science
ISBN : 3540804048

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Scattering and Structures by Bogdan Povh,Mitja Rosina Pdf

Quantum physics may appear complicated, especially if one forgets the "big picture" and gets lost in the details. However, it can become clearer and less tangled if one applies a few fundamental concepts so that simplified approaches can emerge and estimated orders of magnitude become clear. Povh and Rosina’s Scattering and Structures presents the properties of quantum systems (elementary particles, nucleons, atoms, molecules, quantum gases, quantum liquids, stars, and early universe) with the help of elementary concepts and analogies between these seemingly different systems. The original German-language edition of this book was written for students preparing for their final oral examination in physics. By and large, the scope of the book in English has been essentially enlarged and thus may also be of interest for physicists in general.

Author : Hernán Pringe
Publisher : Walter de Gruyter
Page : 265 pages
File Size : 55,7 Mb
Release : 2011-10-18
Category : Philosophy
ISBN : 9783110971750

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Critique of the Quantum Power of Judgment by Hernán Pringe Pdf

The Critique of the Quantum Power of Judgement analyzes the a priori principles which underlie the empirical knowledge provided by quantum theory. In contrast to other transcendental approaches to quantum physics, none of the transcendental principles established by Kant is modified in order to cope with the new epistemological situation that arises with the asumption of the quantum postulate. Rather, by considering Bohr’s views, it is argued that classical concepts provide the mathematical formalism of quantum theory with physical reference through symbolic analogies in the strict Kantian sense. The main result of the investigation is the determination of the highest principle under which quantum objects are subsumed. This principle states that the conditions of the possibility of the systematic unity of contextual experience are at the same time the conditions of the possibility of quantum objects. Upon this principle rests the possibility of any a priori synthetic knowledge of quantum objects. Therefore, the Critique of the Quantum Power of Judgement yields the prolegomena to any future quantum metaphysics.

Author : A. O. Bolivar
Publisher : Springer Science & Business Media
Page : 196 pages
File Size : 41,6 Mb
Release : 2013-04-09
Category : Science
ISBN : 9783662096499

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Quantum-Classical Correspondence by A. O. Bolivar Pdf

At what level of physical existence does "quantum behavior" begin? How does it develop from classical mechanics? This book addresses these questions and thereby sheds light on fundamental conceptual problems of quantum mechanics. It elucidates the problem of quantum-classical correspondence by developing a procedure for quantizing stochastic systems (e.g. Brownian systems) described by Fokker-Planck equations. The logical consistency of the scheme is then verified by taking the classical limit of the equations of motion and corresponding physical quantities. Perhaps equally important, conceptual problems concerning the relationship between classical and quantum physics are identified and discussed. Graduate students and physical scientists will find this an accessible entrée to an intriguing and thorny issue at the core of modern physics.

Author : David Park
Publisher : Unknown
Page : 348 pages
File Size : 51,6 Mb
Release : 1990-06-28
Category : Electronic
ISBN : 3642749232

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Classical Dynamics and Its Quantum Analogues by David Park Pdf

Author : Stuart A. Rice
Publisher : John Wiley & Sons
Page : 558 pages
File Size : 51,6 Mb
Release : 2005-07-13
Category : Science
ISBN : 9780471445265

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Advances in Chemical Physics, Volume 131 by Stuart A. Rice Pdf

This series provides the chemical physics field with a forum for critical, authoritative evaluations of advances in every area of the discipline. Volume 131 includes chapters on: Polyelectrolyte Dynamics; Hydrodynamics and Slip at the Liquid-Solid Interface; Structure of Ionic Liquids and Ionic Liquid Compounds: Are Ionic Liquids Genuine Liquids in the Conventional Sense?; Chemical Reactions at Very High Pressure; Classical Description of Nonadiabatic Quantum Dynamics; and Non-Born Oppenheimer Variational Calculations of Atoms and Molecules with Explicitly Correlated Gaussian Basis Functions.

Author : Mario BUNGE
Publisher : Springer Science & Business Media
Page : 434 pages
File Size : 44,9 Mb
Release : 1983-08-31
Category : Science
ISBN : 9027715114

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Epistemology & Methodology I: by Mario BUNGE Pdf

In this Introduction we shall state the business of both descriptive and normative epistemology, and shall locate them in the map oflearning. This must be done because epistemology has been pronounced dead, and methodology nonexisting; and because, when acknowledged at all, they are often misplaced. 1. DESCRIPTIVE EPISTEMOLOGY The following problems are typical of classical epistemology: (i) What can we know? (ii) How do we know? (iii) What, if anything, does the subject contribute to his knowledge? (iv) What is truth? (v) How can we recognize truth? (vi) What is probable knowledge as opposed to certain knowledge? (vii) Is there a priori knowledge, and if so of what? (viii) How are knowledge and action related? (ix) How are knowledge and language related? (x) What is the status of concepts and propositions? In some guise or other all of these problems are still with us. To be sure, if construed as a demand for an inventory of knowledge the first problem is not a philosophical one any more than the question 'What is there?'. But it is a genuine philosophical problem if construed thus: 'What kinds of object are knowable-and which ones are not?' However, it is doubtful that philosophy can offer a correct answer to this problem without the help of science and technology. For example, only these disciplines can tell us whether man can know not only phenomena (appearances) but also noumena (things in themselves or self-existing objects).

Author : W. van Haeringen,D. Lenstra
Publisher : Springer Science & Business Media
Page : 257 pages
File Size : 40,9 Mb
Release : 2012-12-06
Category : Science
ISBN : 9789400920095

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Analogies in Optics and Micro Electronics by W. van Haeringen,D. Lenstra Pdf

This book gives an account of a number of recent developments in two different subfields of research, optics and micro--electronics. The leading principle in presenting them together in one book is the striking similarity between a variety of notions in these two research areas. We mention in this respect tunneling, quantum interference and localization, which are important concepts in quantummechanics and more specifically in condensed matter physics. Miniaturization in solid state engineering has led to new phenomena in which these concepts play their significant roles. As it is the wave character of electrons which is strongly emphasized in these phenomena one's attention is quite naturally directed to the field of optics in which the above quantum-mechanical notions all seem to have their direct classical wavemechanical counterparts. Both micro--electronics and optics have been and still are in a mode of intensifying activity. The possibilities to technically "translate" devices developed within one research field to similar devices in the other field are strongly increasing. This opens, among other things, a door leading to "quantummechanics" on a macroscopic scale with visible light under relatively easily accessible experimental conditions, or to "wave optics II in the domain of solid state physics. Thinking in terms of analogies is important anyhow, but it is especially the cross-fertilization between optics and micro--electronics which according to the editors will lead to deepened insights and a new type of technology.

Author : William Unruh,Ralf Schützhold
Publisher : Springer
Page : 306 pages
File Size : 45,5 Mb
Release : 2007-04-14
Category : Science
ISBN : 9783540708599

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Quantum Analogues: From Phase Transitions to Black Holes and Cosmology by William Unruh,Ralf Schützhold Pdf

Recently, analogies between laboratory physics (e.g. quantum optics and condensed matter) and gravitational/cosmological phenomena such as black holes have attracted an increasing interest. This book contains a series of selected lectures devoted to this new and rapidly developing field. Various analogies connecting (apparently) different areas in physics are presented in order to bridge the gap between them and to provide an alternative point of view.

Author : Ilya Prigogine,Stuart A. Rice
Publisher : John Wiley & Sons
Page : 608 pages
File Size : 49,9 Mb
Release : 2003-04-23
Category : Science
ISBN : 9780471461524

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Advances in Chemical Physics by Ilya Prigogine,Stuart A. Rice Pdf

Advances in Chemical Physics covers recent advances at the cutting edge of research relative to chemical physics. The series, Advances in Chemical Physics, provides a forum for critical, authoritative evaluations of advances in every area of the discipline.

Author : Brigitte Falkenburg
Publisher : Springer Science & Business Media
Page : 393 pages
File Size : 52,5 Mb
Release : 2007-03-21
Category : Science
ISBN : 9783540337324

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Particle Metaphysics by Brigitte Falkenburg Pdf

Are the particles of modern physics "real" or are they virtual entities, their existence deduced merely by abstract theories? This book examines the continuing debate regarding the inner constitution of matter by exploring the particle concept in physics. It investigates if the particles of particle physics are real or not. Readers interested in the "true meaning" of such physical concepts will find this book informative and thought provoking.