Showing papers on "Open quantum system published in 1992"
Book•
01 Jan 1992
TL;DR: An Introduction to Quantum Stochastic Calculus aims to deepen our understanding of the dynamics of systems subject to the laws of chance both from the classical and the quantum points of view as discussed by the authors.
Abstract: "Elegantly written, with obvious appreciation for fine points of higher mathematics...most notable is [the] author's effort to weave classical probability theory into [a] quantum framework." - The American Mathematical Monthly "This is an excellent volume which will be a valuable companion both for those who are already active in the field and those who are new to it. Furthermore there are a large number of stimulating exercises scattered through the text which will be invaluable to students." - Mathematical Reviews An Introduction to Quantum Stochastic Calculus aims to deepen our understanding of the dynamics of systems subject to the laws of chance both from the classical and the quantum points of view and stimulate further research in their unification. This is probably the first systematic attempt to weave classical probability theory into the quantum framework and provides a wealth of interesting features: The origin of Ito's correction formulae for Brownian motion and the Poisson process can be traced to communication relations or, equivalently, the uncertainty principle. Quantum stochastic interpretation enables the possibility of seeing new relationships between fermion and boson fields. Quantum dynamical semigroups as well as classical Markov semigroups are realized through unitary operator evolutions. The text is almost self-contained and requires only an elementary knowledge of operator theory and probability theory at the graduate level.
1,273 citations
Book•
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TL;DR: In this article, a pedagogic account of quantum field theory starting from its foundation in quantum mechanics is given, where the path integral formulation is introduced right at the beginning and the method of dimensional continuation is employed to regulate and renormalize the theory.
Abstract: This book develops quantum field theory starting from its foundation in quantum mechanics. Quantum field theory is the basic theory of elementary particle physics. In recent years, many techniques have been developed which extend and clarify this theory. This book incorporates these modern methods, giving a thoroughly modern pedagogic account which starts from first principles. The path integral formulation is introduced right at the beginning. The method of dimensional continuation is employed to regulate and renormalize the theory. This facilitates the introduction of the concepts of the renormalization group at an early stage. The notion of spontaneous symmetry breakdown is also introduced early on by the example of superfluid helium. Topics in quantum electrodynamics are described which have an analog in quantum chromodynamics. Some novel techniques are employed, such as the use of dimensional continuation to compute the Lamb shift. Many problems are included.
288 citations
Book•
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TL;DR: In this article, a compilation of reprint articles on one of the most intriguing phenomena in modern physics, the Quantum Hall Effect, is presented, together with a detailed introduction by the editor, which is intended as a reference for students and research workers in condensed matter physics.
Abstract: This book is a compilation of reprint articles on one of the most intriguing phenomena in modern physics, the Quantum Hall Effect. Together with a detailed introduction by the editor, this volume is intended as a reference for students and research workers in condensed matter physics and for those with a particle physics background. The papers have been chosen with the intention of emphasizing the topological aspects of the Quantum Hall Effect and its connections with other branches of theoretical physics such as topological quantum field theories and string theory. The contents include sections on integer effect, fractional effect, effect of global topology, effective theories, edge states and non-Abelian statistics.
231 citations
TL;DR: In this article, a potential model of a particle moving in a potential of a certain form has been found for which exact solutions are known for only a part of the spectrum (quasi-exactly solvable models).
160 citations
Book•
01 Jan 1992
TL;DR: A collection of selected reprints by Frohlich aims to illustrate the recent history of quantum field theory and its trends, and aims to be a comprehensive guide of the more mathematical aspects of the subject.
Abstract: Compiled to illustrate the recent history of quantum field theory and its trends, this collection of selected reprints by Frohlich aims to be a comprehensive guide of the more mathematical aspects of the subject. Results and methods of the past 15 years are reviewed. The analytical methods employed are non-perturbative and, for the larger part, mathematically rigorous. Most articles are review articles surveying certain important developments in quantum field theory and guiding the reader towards the original literature. The theory of phase transitions and spontaneous symmetry breaking is reviewed in the first section. The second section discusses the non-perturbative quantization of topological solitons. The third section is devoted to the study of gauge fields. A paper on the triviality of (labda phi) to the power of 4 - theory in four and more dimensions is found in the fourth section, while the fifth contains two articles on "random geometry". The sixth and final part addresses topics in low-dimensional quantum field theory, including braid statistics, two-dimensional conformal field theory and an application to condensed matter theory. The volume begins with a comprehensive introduction by Jurg Frohlich.
138 citations
Book•
01 Jan 1992
TL;DR: The boundary conditions in one-loop quantum cosmology have been studied in this paper for space-times with torsion, and the singularity problem has been formulated in the simplest possible way and finally presented and solved at increasing levels of complexity.
Abstract: The first aim of this book is to describe recent work on the problem of boundary conditions in one-loop quantum cosmology The motivation is to understand whether supersymmetric theories are one-loop finite in the presence of boundaries The second aim of the book is to present a recent, entirely new study of the singularity problem for space-times with torsion Throughout the text, problems have been initially formulated in the simplest possible way, and finally presented and solved at increasing levels of complexity Readers will find a detailed and updated study of quantum cosmology, its motivation, and application to perturbative quantum gravity Moreover, this is the first book which enables the reader to learn techniques used in classical gravity and quantum cosmology
136 citations
01 Jan 1992
TL;DR: The new electronic techniques required for quantum nondemolition measurements and the theory underlying them are described and may find application elsewhere in science and technology.
Abstract: Some future gravitational-wave antennas will be cylinders of mass approximately 100 kilograms, whose end-to-end vibrations must be measured so accurately (10(-19) centimeter) that they behave quantum mechanically. Moreover, the vibration amplitude must be measured over and over again without perturbing it (quantum nondemolition measurement). This contrasts with quantum chemistry, quantum optics, or atomic, nuclear, and elementary particle physics, where one usually makes measurements on an ensemble of identical objects and does not care whether any single object is perturbed or destroyed by the measurement. This article describes the new electronic techniques required for quantum nondemolition measurements and the theory underlying them. Quantum nondemolition measurements may find application elsewhere in science and technology.
130 citations
TL;DR: In this article, a deformation of canonical commutation relations based on quantum group arguments is studied and its Hilbert space representation is given and the dynamics of the free hamiltonian is solved.
129 citations
TL;DR: In this article, the authors underline the remarkable convergence of these two trends in physics, and argue that these recent developments may lead to new results and insights into quantum phenomena, and suggest that these developments may also lead to insights into the quantum phenomena.
01 Jul 1992
TL;DR: In this paper, a generalized sum-over-histories quantum theory for quantum cosmology is presented, which does not require either a preferred notion of time or a definition of measurement.
Abstract: These are the author's lectures at the 1992 Les Houches Summer School, "Gravitation and Quantizations". They develop a generalized sum-over-histories quantum mechanics for quantum cosmology that does not require either a preferred notion of time or a definition of measurement. The "post-Everett" quantum mechanics of closed systems is reviewed. Generalized quantum theories are defined by three elements (1) the set of fine-grained histories of the closed system which are its most refined possible description, (2) the allowed coarse grainings which are partitions of the fine-grained histories into classes, and (3) a decoherence functional which measures interference between coarse grained histories. Probabilities are assigned to sets of alternative coarse-grained histories that decohere as a consequence of the closed system's dynamics and initial condition. Generalized sum-over histories quantum theories are constructed for non-relativistic quantum mechanics, abelian gauge theories, a single relativistic world line, and for general relativity. For relativity the fine-grained histories are four-metrics and matter fields. Coarse grainings are four-dimensional diffeomorphism invariant partitions of these. The decoherence function is expressed in sum-over-histories form. The quantum mechanics of spacetime is thus expressed in fully spacetime form. The coarse-grainings are most general notion of alternative for quantum theory expressible in spacetime terms. Hamiltonian quantum mechanics of matter fields with its notion of unitarily evolving state on a spacelike surface is recovered as an approximation to this generalized quantum mechanics appropriate for those initial conditions and coarse-grainings such that spacetime geometry
TL;DR: In this paper, the advantages of using quantum wires and quantum box structures as optoelectronic materials are discussed. And the structural requirements to obtain these desirable properties are clarified, and the advantage and limitation of gate-controlled planar superlattices and other quantum interference devices are examined.
Book•
25 Mar 1992
TL;DR: An Elementary Introduction to Algebraic Topology as discussed by the authors... Topological Methods in Classical Field Theory, Inequivalent Quantizations in Multiply Connected Spaces, Braid Groups and Anyons.
Abstract: An Elementary Introduction to Algebraic Topology..- Topological Methods in Classical Field Theory..- Inequivalent Quantizations in Multiply Connected Spaces. Braid Groups and Anyons..- Topics in Chern-Simons Physics..- A Short Introduction to: Connections on (1) Bundles and Berry's Phase..- Electrons in A Magnetic Field, and A Cursory Look at the Quantum Hall Effect..
TL;DR: The notion of integrability in quantum mechanics is investigated in this paper in order to prepare rigorous grounds for the study of regular and irregular behaviour of quantum systems, and it is pointed out why the appealing phenomenological distinction between regular and chaotic quantum systems cannot be traced back to the present notion of "quantum integrabilities" in a mathematically rigorous way.
TL;DR: In this paper, it is shown that if the particles of a quantum system are regarded as real, i.e., if their positions are made part of the state description, one obtains a formulation of quantum theory, Bohmian mechanics, in which "quantum chaos" also arises solely from the dynamical law.
Abstract: It is argued that dynamical chaos in quantum mechanics arises solely from the collapse rule applied in measurements. As such it is quite distinct from classical (deterministic) chaos, which arises from the dynamical law itself. It is shown, however, that if the particles of a quantum system are regarded as “real,” i.e., if their positions are made part of the state description, one obtains a formulation of quantum theory, Bohmian mechanics, in which “quantum chaos” also arises solely from the dynamical law. Moreover, this occurs in a manner far simpler than in the classical case.
01 Jan 1992
TL;DR: The role of perturbation theory in the development of physics is discussed in this article, where the authors present a model for irregular scattering in the presence of localization, and the scaling properties of localized quantum Chaos.
Abstract: Quantum Chaos.- The Role of Perturbation Theory in the Development of Physics.- Dynamical Chaos and Many-Body Quantum Systems.- Unbounded Quantum Diffusion and a New Class of Level Statistics.- Quantal Suppression of Chaos and its Realizations.- A Model for Irregular Scattering in the Presence of Localization.- Localization and Delocalization of Quantum Chaos.- Scaling Properties of Localized Quantum Chaos.- Dynamical Localization Mathematical Framework.- Keeping Track of Chaos by Quantum-Nondemolition Measurements.- Tunnelling and the Lazy Baker's Map.- Regular Orbits for the Stadium Billiard.- Banded Random Matrix Ensembles.- Chaotic behaviour of open quantum mechanical systems.- Relativistic Quantum Chaos in de Sitter Cosmologies.- Quantum Measurement.- Quantum Records.- Macroscopic Quantum Objects and their Interaction with External Environments.- Continuously Measured Chaotic Quantum Systems.- Measurement Aspects of Quantum Optics.- On the Completeness of the Classical Limit of Quantum Mechanics.- Looking at the Quantum World with Classical Eyes.- Quantum Mechanics and Real Events.- Negative Probability and the Correspondence between Quantum and Classical Physics.- When Does a Wave Become a Particle?.- Relativistic Model for Statevector Reduction.- Quantum Measurement and Gravity for Each Other.- The Dynamical Reduction Program.
TL;DR: In this paper, the authors present the compelling evidence which supports the notion that quantum mechanics is much too simple a theory to adequately describe a complex world and present a theoretical framework that provides a proper setting for interpreting these surprising results.
Abstract: This elementary review paper presents the compelling evidence which supports the notion that quantum mechanics is much too simple a theory to adequately describe a complex world. Rigorous arguments based on algorithmic complexity theory are used to show that both the quantum Arnol’d cat and a broad category of finite, bounded, undriven, quantum systems do not obey the correspondence principle, implying that quantum mechanics is also not complete. An experiment, well within current laboratory capability, is proposed which can expose the inability of quantum mechanics to adequately describe macroscopic chaos. In its final section, this paper describes a theoretical framework that provides a proper setting for interpreting these surprising results.
TL;DR: In this paper, a new formulation of Bohmian mechanics is proposed, which is the deterministic theory of particles in motion that emerges from Schrodinger's equation for a system of particles when we merely insist that "particles" means particles.
TL;DR: In this paper, the authors present the important aspects of the Jaynes-Cummings model, describing the dipole interaction between a single two-level atom and a single mode of the electromagnetic field.
Abstract: Publisher Summary This chapter discusses the cavity quantum optics and the quantum measurement process. The chapter presents the important aspects of the Jaynes-Cummings model, describing the dipole interaction between a single two-level atom and a single mode of the electromagnetic field. The cavity quantum electrodynamics (QED) is discussed. The effects of enhanced and inhibited spontaneous emission in density-of-modes approach and the coupled-modes approach are also discussed. The central element of most of these experiments is the micromaser. The chapter treats quantum measurements in a way that emphasizes the difference between ensemble averages and repeated measurements on a single quantum system. Quantum nondemolition measurements are proposed as a way to eliminate this back action of the measurements on the state of the system. The chapter examines macroscopic superpositions of quantum states (Schrodinger cats) and of their generation in micromasers pumped by a stream of polarized atoms. Mechanical effects of light on the center-of-mass motion of atoms, combined with cavity QED, open up new opportunities to study the dynamics of the light-matter interaction and investigate the effects and potential uses of quantum measurements on single quantum systems.
TL;DR: In this article, lifetime measurements of levels near 2 MeV in 114 Cd give quantitative evidence for collective 3-phonon vibrational states and an analysis of the level scheme reveals a remarkable ambiguity with origins in the basic properties of quantum mechanical mixing.
TL;DR: In this paper, the quantum potential interpretation of quantum mechanics due to Bohm is applied to the Wheeler-De Witt equation for minisuperspace, and the potential interpretation was applied to minisupperspace.
TL;DR: In this paper, the free Maxwell field in Minkowski space is quantized using a loop representation and shown to be equivalent to the standard Fock quantization, which may be useful in quantum optics.
Abstract: Quantization of the free Maxwell field in Minkowski space is carried out using a loop representation and shown to be equivalent to the standard Fock quantization. Because it is based on coherent state method, this framework may be useful in quantum optics. It is also well suited for the discussion of issues related to flux quantization in condensed matter physics. The authors' own motivation, however, came from a non-perturbative approach to quantum gravity. The concrete results obtained in this work for the Maxwell field provide independent support for that approach. In addition, they offer some insight into the physical interpretation of the mathematical structures that play, within this approach, an essential role in the description of the quantum geometry at Planck scale.
01 Jan 1992
TL;DR: In this paper, the authors make a coarser distinction and combine all sectors which coincide in their information about the content of outgoing (or incoming) massive particles in their respective folia of states into one class.
Abstract: One consequence of the possible appearance of infrared clouds is that in quantum electrodynamics there are innumerably many sectors satisfying the Borchers selection criterion even for states with the same charge It is then convenient to make a coarser distinction and combine all sectors which coincide in their information about the content of outgoing (or incoming) massive particles in their respective folia of states into one class Since electrically charged particles are massive such a class fixes in particular the electric charge and for this reason it was called a charge class in [Buch 82b] We shall keep this terminology here though these classes still give a much finer distinction than that provided by the charge quantum numbers
TL;DR: In this paper, the quantum fluctuations in optical systems are treated in the framework of the semiclassical linear input output theory, and the quantum properties of the parametric generation in an optical cavity, including two regimes below and above the oscillation threshold.
Abstract: Publisher Summary This chapter discusses the quantum fluctuations in optical systems. Quantum fluctuations are present in every measurement. In the measurement device, quantum fluctuations have an effect similar to that of the instrumental noise or thermal fluctuations. The chapter describes the principal experiments that have generated light with reduced quantum fluctuations, and the applications of such light. Straightforward calculations involving squeezed fields help to explain the experimental results. The squeezed fields are treated in the framework of the semiclassical linear input output theory, which models the quantum fluctuations by classical random fields. The standard representations of quantum optics are used to treat the quantum fluctuations and properties of the squeezed states, and to study the ideal parametric interaction Hamiltonian in detail. The chapter also discusses the quantum properties of the parametric generation in an optical cavity, including the two regimes below and above the oscillation threshold.
Book•
01 Jan 1992
TL;DR: The Fibre Framework for Classical General Relativity and Quantum Geometries for Spin-1/2 Massive Fields is described in this article, as well as quantum geometry for Yang-Mills Fields.
Abstract: Preface. 1. Principles and Physical Interpretation of Quantum Geometries. 2. The Fibre Framework for Classical General Relativity. 3. Stochastic Quantum Mechanics on Phase Space. 4. Nonrelativistic Newton-Carton Quantum Geometries. 5. Relativistic Klein-Gordon Quantum Geometries. 6. Relativistic Dirac Quantum Geometries. 7. Relativistic Quantum Geometries for Spin-O Massive Fields. 8. Relativistic Quantum Geometries for Spin-1/2 Massive Fields. 9. Quantum Geometries for Electromagnetic Fields. 10. Classical and Quantum Geometries for Yang-Mills Fields. 11. Geometro-Stochastic Quantum Gravity. 12. Historical and Epistemological Perpectives on Developments in Relativity and Quantum Theory. References. Index.