Showing papers on "Open quantum system published in 1991"

Quantum signatures of chaos

Abstract: The distinction between level clustering and level repulsion is one of the quantum analogues of the classical distinction between globally regular and predominantly chaotic motion (see Figs. 1, 2, 3). In order to reveal level repulsion under conditions of global classical chaos special care may be necessary: (i) subspectra referring to different values of the quantum numbers related to symmetries must be dealt with separately and (ii) for systems with quantum localization only levels whose wavefunctions have overlapping support must be admitted. A “level” may either be an energy eigenvalue E in the case of autonomous systems or, for periodically driven systems, a quasi-energy φ, i.e. an eigenphase of the unitary Floquet operator transporting the wavevector from period to period.

Decoherence and the transition from quantum to classical

Abstract: Quantum mechanics works exceedingly well in all practical applications. No example of conflict between its predictions and experiment is known. Without quantum physics we could not explain the behavior of solids, the structure and function of DNA, the color of the stars, the action of lasers or the properties of superfluids. Yet well over half a century after its inception, the debate about the relation of quantum mechanics to the familiar physical world continues. How can a theory that can account ith precision for everything we can measure still be deemed lacking? The environment surrounding a quantum system can, in effect, monitor some of the system's observobles. As a result, the eigenstates of those observables continuously decohere and can behave like classical states.

The quantum theory of measurement

Abstract: The amazing accuracy in verifying quantum effects experimentally has recently renewed interest in quantum mechanical measurement theory. In this book the authors give within the Hilbert space formulation of quantum mechanics a systematic exposition of the quantum theory of measurement. Their approach includes the concepts of unsharp objectification and of nonunitary transformations needed for a unifying description of various detailed investigations. The book addresses advanced students and researchers in physics and philosophy of science. In this second edition Chaps. II-IV have been substantially rewritten. In particular, an insolubility theorem for the objectification problem has been formulated in full generality, which includes unsharp object observables as well as unsharp pointers.

Quantum optical tests of complementarity

Abstract: Simultaneous observation of wave and particle behaviour is prohibited, usually by the position–momentum uncertainty relation New detectors, constructed with the aid of modern quantum optics, provide a way around this obstacle in atom interferometers, and allow the investigation of other mechanisms that enforce complementarity

Quantum Mechanics: An Empiricist View

Abstract: Part 1 Determinism and inderterminism in classical perspective: determinism indeterminism and probability. Part 2 How the phenomena demand quantum theory: the empirical basis of quantum theory new probability models and their logic. Part 3 Mathematical foundations: the basic theory of quantum mechanics composite systems, interaction, and measurement. Part 4 Questions of interpretation: critique of the standard interpretation modal interpretation of quantum mechanics EPR - when is a correlation not a mystery? the problem of identical particles indentical particles - individuation and modality.

Quantum mechanics near closed timelike lines

Abstract: The methods of the quantum theory of computation are used to analyze the physics of closed timelike lines. This is dominated, even at the macroscopic level, by quantum mechanics. In classical physics the existence of such lines in a spacetime imposes "paradoxical" constraints on the state of matter in their past and also provides means for knowledge to be created in ways that conflict with the principles of the philosophy of science. In quantum mechanics the first of these pathologies does not occur. The second is mitigated, and may be avoidable without such spacetimes being ruled out. Several novel and distinctive (but nonparadoxical) quantum-mechanical effects occur on and near closed timelike lines, including violations of the correspondence principle and of unitarity. It becomes possible to "clone" quantum systems and to measure the state of a quantum system. A new experimental test of the Everett interpretation against all others becomes possible. Consideration of these and other effects sheds light on the nature of quantum mechanics.

Measurements continuous in time and a posteriori states in quantum mechanics

Abstract: Measurements continuous in time have been consistently introduced in quantum mechanics and applications worked out, mainly in quantum optics. In this context a quantum filtering theory has been developed giving the reduced state after a measurement when a certain trajectory of the measured observables is registered (the a posteriori states). In this paper a new derivation of filtering equations is presented for the cases of counting processes and of measurement processes of diffusive type. It is also shown that the equation for the a posteriori dynamics in the diffusive case can be obtained, by a suitable limit, from that in the counting case. Moreover, the paper is intended to clarify the meaning of the various concepts involved and to discuss the connections among them. As an illustration of the theory, simple models are worked out.

Quantum reference systems

Abstract: The author argues that only by taking into account the quantum properties of the bodies that form the reference frames, physical quantum operators can be defined in quantum gravity. The theory of general relativity coupled to matter introduced in a companion paper is considered. Its formal canonical quantization yields two surprising results: the diffeomorphism constraint can be exactly solved; and the Hamiltonian constraint reduces, in the context of a well defined approximation, to a Schrodinger evolution equation. By using the solutions of the quantum constraints of vacuum general relativity recently obtained in the loop representation, and in the context of a 'realistic' local material reference system, he defines a quantum gravitational theory in which the constraints can be solved, the only remaining equation is a regularized Schrodinger equation which expresses the dynamics in the internal clocks, and a class of gauge-invariant physical observables is explicitly displayed.

Classical Topology and Quantum States

Abstract: Any two infinite-dimensional (separable) Hilbert spaces are unitarily isomorphic. The sets of all their self-adjoint operators are also therefore unitarily equivalent. Thus if all self-adjoint operators can be observed, and if there is no further major axiom in quantum physics than those formulated for example in Dirac’s ‘quantum mechanics’, then a quantum physicist would not be able to tell a torus from a hole in the ground. We argue that there are indeed such axioms involving observables with smooth time evolution: they contain commutative subalgebras from which the spatial slice of spacetime with its topology (and with further refinements of the axiom, its C K - and C --structures) can be reconstructed using Gel’fand-Naimark theory and its extensions. Classical topology is an attribute of only certain quantum observables for these axioms, the spatial slice emergent from quantum physics getting progressively less differentiable with increasingly higher excitations of energy and eventually altogether ceasing to exist. After formulating these axioms, we apply them to show the possibility of topology change and to discuss quantized fuzzy topologies. Fundamental issues concerning the role of time in quantum physics are also addressed.

The Quantum Mechanics of Cosmology

Abstract: Notes from the lectures by the author at the 7th Jerusalem Winter School 1990 on Quantum Cosmology and Baby Universes. The lectures covered quantum mechanics for closed systems like the universe, generalized quantum mechanics, time in quantum mechanics, the quantum mechanics spacetime, and practical quantum cosmology. References have not been updated.

Learning quantum field theory from elementary quantum mechanics

Abstract: The study of the Dirac delta potentials in more than one dimension allows the introduction within the framework of elementary quantum mechanics of many of the basic concepts of modern quantum field theory: regularization, renormalization group, asymptotic freedom, dimensional transmutation, triviality, etc. It is also interesting, by itself, as a nonstandard quantum mechanical problem.

Spectral and stability aspects of quantum chaos.

Abstract: The relation between the spectrum of a generalized quasienergy operator and the stability of quantum systems driven by quasiperiodic time‐dependent forces is discussed.

Relativistic quantum mechanics and quantum fields

Abstract: A sequel to the well received book, Quantum Mechanics by T Y Wu, this book carries on where the earlier volume ends. This present volume follows the generally pedagogic style of Quantum Mechanics. The scope ranges from relativistic quantum mechanics to an introduction to quantum field theory with quantum electrodynamics as the basic example and ends with an exposition of important issues related to the standard model. The book presents the subject in basic and easy-to-grasp notions which will enhance the purpose of this book as a useful textbook in the area of relativistic quantum mechanics and quantum electrodynamics.

Quantum mechanics of radiation damping.

Abstract: We develop a nonrelativistic formulation for the quantum dynamics of an electron coupled to its own radiation field. For this purpose, we have applied the Feynman-Vernon approach to the composite system in order to obtain the reduced density operator of the electron. In the classical limit, some well-known results, such as the Abraham-Lorentz equation of motion, are reproduced. We have applied the resulting formalism to the problem of interference in order to investigate the possible effects of the incoherent modes of the electromagnetic radiation on the interference fringes. The results allow us to conclude that the coupling to the radiation field is not enough for one to observe a strong influence of those modes on the interference phenomenon.

Missing integral quantum Hall effect in a wide single quantum well.

Abstract: We report magnetotransport measurements in a weakly coupled double-layer electron system realized in a wide quantum well. This system has the unique property that the distance and the coupling between the layers can be changed continuously by varying the electron density in the well. We observe the absence of quantum Hall states at odd filling factors. Our results complement earlier experimental work and are consistent with a recent theoretical model proposed for the magnetic-field-driven destruction of the quantum Hall effect in double quantum wells.

Algebraic theory of superselection sectors and the measurement problem in quantum mechanics

Abstract: A synthesis is attempted between the algebraic theory of superselection sectors (not necessarily of infinite systems), which is based on the representation theory of C* algebras (which we review), and recent ideas on the measurement problem, classical behavior in open quantum systems, and the peculiar nature of subsystems in quantum mechanics. The key point is a proper use of the notion of a state, in combination with an appropriate choice of algebras of observables for which the superposition “principle” may be invalid. In this way, a major part of the measurement problem becomes equivalent to the study of superselection sectors in models for a measurement situation, and can in principle be resolved unambiguously. Special emphasis is placed on the transition from pure to mixed states, and the (non)uniqueness of the decomposition of the latter into pure states.

Chaotic scattering, unstable periodic orbits, and fluctuations in quantum transport.

Abstract: The field of quantum chaos has recently focused attention on the quantum description of chaotic scattering processes. The new physical intuition, analytical methods, and numerical tools developed in the study of the quantum behavior of classically chaotic bound systems, like quantum billiards or atoms in strong fields, has led to exciting new predictions for the scattering of electromagnetic waves in curved waveguides, electrons in mesoscopic wires, and atoms off molecules. After a brief review of recent progress in the field of quantum chaos, this paper focuses on specific results relating to ballistic electron transport in small, mesoscopic devices. Several specific geometries are suggested for experimental studies of this ‘‘game’’ of quantum pinball with explicit predictions for the fluctuations in the electrical conductivity as functions of the electron Fermi energy and of an applied magnetic field.

Elementary inelastic radiation-induced processes

Abstract: This collection of articles covers the "quiet revolution" that took place in quantum optics in the 1980s. Explores far-reaching repercussions in methods of light field generation, propagation, and detection in the quantum rather than in the classical regime. Throughout, theory is discussed with supporting experimental data. Newcomers and experienced researchers will find this a useful introduction and an excellent reference. Contents: Introduction. The early years. Photon antibunching and sub- Poissonian photon statistics. Squeezed states of light. Quantum non- demolition. Quantum effects in photon interference. Cavity quantum electrodynamics. Quantum noise reduction in lasers.

Dynamical quasidegeneracies and quantum tunneling.

Abstract: A Comment on the Letter by W. A. Lin and L. E. Ballentine, Phys. Rev. Lett. 65, 2927 (1990).