Q is for Quantum

In the ultimate guide to the ultimate mystery--the quantum world--an award-winning scientist and a master of popular science writing explains recent breakthroughs and the wondrous possibilities that lie in the future.

Author: John Gribbin

Publisher: Simon and Schuster

ISBN: 9780684863153

Category: Science

Page: 545

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In the ultimate guide to the ultimate mystery--the quantum world--an award-winning scientist and a master of popular science writing explains recent breakthroughs and the wondrous possibilities that lie in the future. Illustrations throughout.
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Q is for Quantum Particle Physics from A Z

A brilliant populariser and award-winning writer John Gribbin tells the whole storyof the micro-world, and the people who made the discoveries.

Author: J. Gribbin

Publisher: Universities Press

ISBN: 8173712433


Page: 552

View: 703

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A brilliant populariser and award-winning writer John Gribbin tells the whole storyof the micro-world, and the people who made the discoveries. An essential complement to Gribbin's Companion to the Cosmos, it is about the inner structure of everything- a quest which, like the quest for the understanding of the Universe at large goes back to the ancient Greeks and touches on all of scientific and philosophic thought since then.
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From C Numbers to Q Numbers

This title is part of UC Press's Voices Revived program, which commemorates University of California Press's mission to seek out and cultivate the brightest minds and give them voice, reach, and impact.

Author: Olivier Darrigol


ISBN: 9780520328273


Page: 418

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This title is part of UC Press's Voices Revived program, which commemorates University of California Press's mission to seek out and cultivate the brightest minds and give them voice, reach, and impact. Drawing on a backlist dating to 1893, Voices Revived makes high-quality, peer-reviewed scholarship accessible once again using print-on-demand technology. This title was originally published in 1992.
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Learn Quantum Computing with Python and Q

Purchase of the print book includes a free eBook in PDF, Kindle, and ePub formats from Manning Publications.

Author: Sarah C. Kaiser

Publisher: Manning Publications

ISBN: 1617296139

Category: Computers

Page: 300

View: 210

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Learn Quantum Computing with Python and Q# demystifies quantum computing. Using Python and the new quantum programming language Q#, you’ll learn QC fundamentals as you apply quantum programming techniques to real-world examples including cryptography and chemical analysis. Learn Quantum Computing with Python and Q# builds your understanding of quantum computers, using Microsoft’s Quantum Development Kit to abstract away the mathematical complexities. You’ll learn QC basics as you create your own quantum simulator in Python, then move on to using the QDK and the new Q# language for writing and running algorithms very different to those found in classical computing. Purchase of the print book includes a free eBook in PDF, Kindle, and ePub formats from Manning Publications.
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Quantum Calculus

Simply put, quantum calculus is ordinary calculus without taking limits. This undergraduate text develops two types of quantum calculi, the q-calculus and the h-calculus.

Author: Victor Kac

Publisher: Springer Science & Business Media

ISBN: 9781461300717

Category: Mathematics

Page: 112

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Simply put, quantum calculus is ordinary calculus without taking limits. This undergraduate text develops two types of quantum calculi, the q-calculus and the h-calculus. As this book develops quantum calculus along the lines of traditional calculus, the reader discovers, with a remarkable inevitability, many important notions and results of classical mathematics. This book is written at the level of a first course in calculus and linear algebra and is aimed at undergraduate and beginning graduate students in mathematics, computer science, and physics. It is based on lectures and seminars given by MIT Professor Kac over the last few years at MIT.
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Compendium of Quantum Physics

A dispositional account of quantum properties is, for instance, arguably implicit in
the early quantum theory in Bohr's ... of a quantum system is ψ, a superposition of
eigenstates of the Hermitian operator that represents the observable Q. The ...

Author: Daniel Greenberger

Publisher: Springer Science & Business Media

ISBN: 3540706267

Category: Science

Page: 901

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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.
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Quantum Oscillators

Then, according to quantum mechanics, one has to write in place of E(R) given
by Eq. (9.29) the following potential operator V(Q): V(Q) = §Mw2Q2 where Q is
the quantum position operator corresponding to the classical elongation Q given
by ...

Author: Paul Blaise

Publisher: John Wiley & Sons

ISBN: 1118018028

Category: Science

Page: 672

View: 331

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An invaluable reference for an overall but simple approach to the complexity of quantum mechanics viewed through quantum oscillators Quantum oscillators play a fundamental role in many areas of physics; for instance, in chemical physics with molecular normal modes, in solid state physics with phonons, and in quantum theory of light with photons. Quantum Oscillators is a timely and visionary book which presents these intricate topics, broadly covering the properties of quantum oscillators which are usually dispersed in the literature at varying levels of detail and often combined with other physical topics. These properties are: time-independent behavior, reversible dynamics, thermal statistical equilibrium and irreversible evolution toward equilibrium, together with anharmonicity and anharmonic couplings. As an application of these intricate topics, special attention is devoted to infrared lineshapes of single and complex (undergoing Fermi resonance or Davydov coupling) damped H-bonded systems, providing key insights into this rapidly evolving area of chemical science. Quantum Oscillators is a long overdue update in the literature surrounding quantum oscillators, and serves as an excellent supplementary text in courses on IR spectroscopy and hydrogen bonding. It is a must-have addition to the library of any graduate or undergraduate student in chemical physics.
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Ograni ennye Kvantovye Simmetri eskie Prostranstva

A quantum analog of the Shilov boundary S(D) of the matrix ball and the
corresponding degenerate principal spherical series of Uqsun,n-modules was
studied in [33, 318]. In the classical case q = 1, the Shilov boundary S(D) is the
set of ...

Author: Leonid Lʹvovych Vaksman

Publisher: American Mathematical Soc.

ISBN: 9780821849095

Category: Mathematics

Page: 256

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This book provides exposition of the basic theory of quantum bounded symmetric domains. The area became active in the late 1990s at a junction of noncommutative complex analysis and extensively developing theory of quantum groups. It is well known that the classical bounded symmetric domains involve a large number of nice constructions and results of the theory of $C^*$-algebras, theory of functions and functional analysis, representation theory of real reductive Lie groups, harmonic analysis, and special functions. In a surprising advance of the theory of quantum bounded symmetric domains, it turned out that many classical problems admit elegant quantum analogs. Some of those are expounded in the book. Anyone with an interest in the subject will welcome this unique treatment of quantum groups. The book is written by a leading expert in a very clear, careful, and stimulating way. I strongly recommend it to graduate students and research mathematicians interested in noncommutative geometry, quantum groups, $C^*$-algebras, or operator theory. --Vladimir Drinfeld, University of Chicago
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Many Body Problems and Quantum Field Theory

To simplify matters, we consider the case of a single electron of charge e and
mass m under the influence of the potential V(q) of an atomic nucleus . (8.59)
One obtains the Hamiltonian of the quantum system by the correspondence
principle: p ...

Author: Philippe Andre Martin

Publisher: Springer Science & Business Media

ISBN: 3540213201

Category: Science

Page: 435

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Many-Body Problems and Quantum Field Theory introduces the concepts and methods of the topics on a level suitable for graduate students and researchers. The formalism is developed in close conjunction with the description of a number of physical systems: cohesion and dielectric properties of the electron gas, superconductivity, superfluidity, nuclear matter and nucleon pairing, matter and radiation, interaction of fields by particle exchange and mass generation. Emphasis is placed on analogies between the various systems rather than on advanced or specialized aspects, with the purpose of illustrating common ideas within different domains of physics. Starting from a basic knowledge of quantum mechanics and classical electromagnetism, the exposition is self-contained and explicitly details all steps of the derivations. The new edition features a subtantially new treatment of nucleon pairing.
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A von Neumann Algebra Approach to Quantum Metrics Quantum Relations

Let V and W be quantum pseudometrics on von Neumann algebras M C B(H)
and N C B(K) and let p : M → M be a unital weak* continuous *-homomorphism.
Suppose V is reflexive (Definition (a)). Then _sup_* *(*) - #7 (F) (O) with P and Q

Author: Greg Kuperberg

Publisher: American Mathematical Soc.

ISBN: 9780821853412

Category: Mathematics

Page: 140

View: 408

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In A von Neumann Algebra Approach to Quantum Metrics, Kuperberg and Weaver propose a new definition of quantum metric spaces, or W*-metric spaces, in the setting of von Neumann algebras. Their definition effectively reduces to the classical notion in the atomic abelian case, has both concrete and intrinsic characterizations, and admits a wide variety of tractable examples. A natural application and motivation of their theory is a mutual generalization of the standard models of classical and quantum error correction. In Quantum Relations Weaver defines a ``quantum relation'' on a von Neumann algebra $\mathcal{M}\subseteq\mathcal{B}(H)$ to be a weak* closed operator bimodule over its commutant $\mathcal{M}'$. Although this definition is framed in terms of a particular representation of $\mathcal{M}$, it is effectively representation independent. Quantum relations on $l^\infty(X)$ exactly correspond to subsets of $X^2$, i.e., relations on $X$. There is also a good definition of a ``measurable relation'' on a measure space, to which quantum relations partially reduce in the general abelian case. By analogy with the classical setting, Weaver can identify structures such as quantum equivalence relations, quantum partial orders, and quantum graphs, and he can generalize Arveson's fundamental work on weak* closed operator algebras containing a masa to these cases. He is also able to intrinsically characterize the quantum relations on $\mathcal{M}$ in terms of families of projections in $\mathcal{M}{\overline{\otimes}} \mathcal{B}(l^2)$.
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Recent Developments in Quantum Affine Algebras and Related Topics

The quantum group U, sl(2). Let q be a complex number different from +1. Let p
be a complex number such that q = exp(Ti/p). We always assume Rep < 0. For a
complex number a, by q" we mean exp(Tia/p). Let eq, f, q", q " be generators of U,

Author: Naihuan Jing

Publisher: American Mathematical Soc.

ISBN: 9780821811993

Category: Mathematics

Page: 469

View: 855

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This volume reflects the proceedings of the International Conference on Representations of Affine and Quantum Affine Algebras and Their Applications held at North Carolina State University (Raleigh). In recent years, the theory of affine and quantum affine Lie algebras has become an important area of mathematical research with numerous applications in other areas of mathematics and physics. Three areas of recent progress are the focus of this volume: affine and quantum affine algebras and their generalizations, vertex operator algebras and their representations, and applications in combinatorics and statistical mechanics. Talks given by leading international experts at the conference offered both overviews on the subjects and current research results. The book nicely presents the interplay of these topics recently occupying 'center stage' in the theory of infinite dimensional Lie theory.
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Dissipative Quantum Mechanics of Nanostructures

Suppose we are interested in the probability for the particle q to have the
coordinate q = qf at a time t provided at t = 0, it had the coordinate q = qi. By
definition, this probability W is given by the square of a quantum mechanical
transition ...

Author: Andrei D. Zaikin

Publisher: CRC Press

ISBN: 9781000024203

Category: Science

Page: 926

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Continuing miniaturization of electronic devices, together with the quickly growing number of nanotechnological applications, demands a profound understanding of the underlying physics. Most of the fundamental problems of modern condensed matter physics involve various aspects of quantum transport and fluctuation phenomena at the nanoscale. In nanostructures, electrons are usually confined to a limited volume and interact with each other and lattice ions, simultaneously suffering multiple scattering events on impurities, barriers, surface imperfections, and other defects. Electron interaction with other degrees of freedom generally yields two major consequences, quantum dissipation and quantum decoherence. In other words, electrons can lose their energy and ability for quantum interference even at very low temperatures. These two different, but related, processes are at the heart of all quantum phenomena discussed in this book. This book presents copious details to facilitate the understanding of the basic physics behind a result and the learning to technically reproduce the result without delving into extra literature. The book subtly balances the description of theoretical methods and techniques and the display of the rich landscape of the physical phenomena that can be accessed by these methods. It is useful for a broad readership ranging from master’s and PhD students to postdocs and senior researchers.
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Quantum Entanglement and Information Processing

... position coordinate as being the flux <t> in the inductor, while the role of the
conjugate momentum is played by the charge Q on the capacitor. The variables <
t> and Q have to be treated as canonically conjugate quantum operators that
obey ...

Author: Daniel Esteve

Publisher: Elsevier

ISBN: 0444517286

Category: Science

Page: 608

View: 947

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Presents the lecture notes of the Les Houches Summer School on Quantum entanglement and information processing. This book aims to establish connections between the communities of quantum optics and of quantum electronic devices working in the area of quantum computing. It is useful for graduate students with a basic knowledge of quantum mechanics.
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Continuous Quantum Measurements and Path Integrals

Therefore q hereafter will be a real number (a point in R!) unless stated otherwise
. The time dependence of a wavefunction is determined by the Schrödinger
equation iñ0 is tot–H^\p t (3.1) wheriffthe quantum Hamiltonian can be obtained
from ...

Author: M.B Mensky

Publisher: Routledge

ISBN: 9781351458023

Category: Science

Page: 188

View: 106

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Advances in technology are taking the accuracy of macroscopic as well as microscopic measurements close to the quantum limit, for example, in the attempts to detect gravitational waves. Interest in continuous quantum measurements has therefore grown considerably in recent years. Continuous Quantum Measurements and Path Integrals examines these measurements using Feynman path integrals. The path integral theory is developed to provide formulae for concrete physical effects. The main conclusion drawn from the theory is that an uncertainty principle exists for processes, in addition to the familiar one for states. This implies that a continuous measurement has an optimal accuracy-a balance between inefficient error and large quantum fluctuations (quantum noise). A well-known expert in the field, the author concentrates on the physical and conceptual side of the subject rather than the mathematical.
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Connections in Classical and Quantum Field Theory

Let { Aq } be a set of C * -algebras parameterized by points of a locally compact
topological space Q. Let all C * -algebras Aq are isomorphic to each other and to
some ... One can consider a quantum system characterized by this C * -algebra .

Author: L. Mangiarotti

Publisher: World Scientific

ISBN: 9812813748

Category: Connections (Mathematics)

Page: 516

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Geometrical notions and methods play an important role in both classical and quantum field theory, and a connection is a deep structure which apparently underlies the gauge-theoretical models. This collection of basic mathematical facts about various types of connections provides a detailed description of the relevant physical applications. It discusses the modern issues concerning the gauge theories of fundamental interactions. This text presents several levels of complexity, from the elementary to the advanced, and provides a considerable number of exercises. The authors have tried to give all the necessary mathematical background, thus making the book self-contained. This book should be useful to graduate students, physicists and mathematicians who are interested in the issue of deep interrelations between theoretical physics and geometry.
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Consistent Quantum Theory

Robert B. Griffiths. The preceding remarks also apply to the quantum case. In
particular, (4.53) is valid if P and Q are projectors. However, P + Q – PQ is a
projector if and only if PQ = QP. Thus as long as P and Q commute, we can use (
4.50) to ...

Author: Robert B. Griffiths

Publisher: Cambridge University Press

ISBN: 0521539293

Category: Science

Page: 391

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A clear and accessible presentation of quantum theory, suitable for researchers yet accessible to graduates.
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Entanglement Information and the Interpretation of Quantum Mechanics

Whatever the nature of this innovation, it appears increasingly likely that it will be
related to quantum entanglement and have ... To see how the L ̈uders rule is
naturally picked out, consider a generalized probability function q on the set of ...

Author: Gregg Jaeger

Publisher: Springer Science & Business Media

ISBN: 9783540921288

Category: Science

Page: 307

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Entanglement was initially thought by some to be an oddity restricted to the realm of thought experiments. However, Bell’s inequality delimiting local - havior and the experimental demonstration of its violation more than 25 years ago made it entirely clear that non-local properties of pure quantum states are more than an intellectual curiosity. Entanglement and non-locality are now understood to ?gure prominently in the microphysical world, a realm into which technology is rapidly hurtling. Information theory is also increasingly recognized by physicists and philosophers as intimately related to the foun- tions of mechanics. The clearest indicator of this relationship is that between quantum information and entanglement. To some degree, a deep relationship between information and mechanics in the quantum context was already there to be seen upon the introduction by Max Born and Wolfgang Pauli of the idea that the essence of pure quantum states lies in their provision of probabilities regarding the behavior of quantum systems, via what has come to be known as the Born rule. The signi?cance of the relationship between mechanics and information became even clearer with Leo Szilard’s analysis of James Clerk Maxwell’s infamous demon thought experiment. Here, in addition to examining both entanglement and quantum infor- tion and their relationship, I endeavor to critically assess the in?uence of the study of these subjects on the interpretation of quantum theory.
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Path Integrals in Quantum Mechanics

with N(q) ∼ε→0(2πε)−n/2 n∏ [det ̄g(q)]1/2. (10.49) i=1 It has the form of an
infinite quantum correction (it has no 1/ factor) to the classical action: t′′ N(q)
∝ exp [ 1 2ε ∫ t′ lndetg[q(t)] dt ] , (10.50) or, equivalently, using the identity ln
detg ...

Author: Jean Zinn-Justin

Publisher: Oxford University Press

ISBN: 9780198566755

Category: Mathematics

Page: 320

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Quantum field theory is hardly comprehensible without path integrals: the goal of this book is to introduce students to this topic within the context of ordinary quantum mechanics and non-relativistic many-body theory, before facing the problems associated with the more involved quantum field theory formalism.
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Quantum Triangulations

Moduli Spaces, Strings, and Quantum Computing Mauro Carfora, Annalisa
Marzuoli. q(/<)—2 q(k)—1 = Z d<¢<<1+1.k>-¢<<1.k>>4 Z <¢><fl+1.k)-¢<fl.k>). 01:
1 }5:a+l from which it easily follows that, in passing from q(k) to q(k) + 1, we have
the ...

Author: Mauro Carfora

Publisher: Springer Science & Business Media

ISBN: 9783642244407

Category: Science

Page: 284

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Research on polyhedral manifolds often points to unexpected connections between very distinct aspects of Mathematics and Physics. In particular triangulated manifolds play quite a distinguished role in such settings as Riemann moduli space theory, strings and quantum gravity, topological quantum field theory, condensed matter physics, and critical phenomena. Not only do they provide a natural discrete analogue to the smooth manifolds on which physical theories are typically formulated, but their appearance is rather often a consequence of an underlying structure which naturally calls into play non-trivial aspects of representation theory, of complex analysis and topology in a way which makes manifest the basic geometric structures of the physical interactions involved. Yet, in most of the existing literature, triangulated manifolds are still merely viewed as a convenient discretization of a given physical theory to make it more amenable for numerical treatment. The motivation for these lectures notes is thus to provide an approachable introduction to this topic, emphasizing the conceptual aspects, and probing, through a set of cases studies, the connection between triangulated manifolds and quantum physics to the deepest. This volume addresses applied mathematicians and theoretical physicists working in the field of quantum geometry and its applications.
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Quantum Plasmadynamics

The set q corresponds to a complete set of commuting variables, and the choice
need not be unique. The set q usually includes both discrete and continuous
quantum numbers, including the spin. For the Klein-Gordon equation the spin is
zero ...

Author: D. B. Melrose

Publisher: Springer Science & Business Media

ISBN: 9780387739021

Category: Science

Page: 464

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The idea of synthesizing quantum electrodynamics (QED) and the kinetic theory of plasmas ?rst occurred to me in the early 1970s [1, 2]. The project to do so has been carried out bit by bit over the subsequent years. The name “quantum plasmadynamics” (QPD) is my own jargon [3] for the synthesized theory. Both QED and the kinetic theory of plasmas areconcerned with the int- action between charged particles and the electromagnetic ?eld, but they are radically di?erent in the way the interaction is described. The kinetic theory of plasmas is a collective-medium theory: a plasma is not a collection of - dependent particles in a given electromagnetic ?eld, but a medium in which the particles collectively modify the ?eld, and the ?eld modi?es the par- cles. The charge and current densities associated with the particles are part of a self-consistent ?eld. Conventionally, the kinetic theory of plasmas is a classical theory: the motions of particles are treated using classical dynamics.
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