Showing papers on "Open quantum system published in 1994"

General relativity as an effective field theory: The leading quantum corrections

Abstract: I describe the treatment of gravity as a quantum effective field theory. This allows a natural separation of the (known) low energy quantum effects from the (unknown) high energy contributions. Within this framework, gravity is a well-behaved quantum field theory at ordinary energies. In studying the class of quantum corrections at low energy, the dominant effects at large distance can be isolated, as these are due to the propagation of the massless particles ( including gravitons) of the theory and are manifested in the nonlocal and/or nonanalytic contributions to vertex functions and propagators. These leading quantum corrections are parameter-free and represent necessary consequences of quantum gravity. The methodology is illustrated by a calculation of the leading quantum corrections to the gravitational interaction of two heavy masses.

Introduction to Quantum Field Theory

Abstract: Part I. Scalar Fields: 1. Classical fields and symmetries 2. Canonical quantization 3. Path integrals, perturbation theory and Feynman rules 4. Scattering and cross sections for scalar fields Part II. Fields with Spin: 5. Spinors, vectors and gauge invariance 6. Spin and canonical quantization 7. Path integrals for fermions and gauge fields 8. Gauge theories at lowest order Part III. Renormalization: 9. Loops, regularization and unitarity 10. Introduction to renormalization 11. Renormalization and unitarity of gauge theories Part IV. The Nature of Perturbative Cross Sections: 12. Perturbative corrections and the infrared problem 13. Analytic structure and infrared finiteness 14. Factorization and evolution in high energy scattering 15. Epilogue: bound states and the limitations of perturbation theory Appendices References Index.

Quantum mechanics as quantum measure theory

Abstract: The additivity of classical probabilities is only the first in a hierarchy of possible sum rules, each of which implies its successor. The first and most restrictive sum rule of the hierarchy yields measure theory in the Kolmogorov sense, which is appropriate physically for the description of stochastic processes such as Brownian motion. The next weaker sum rule defines a generalized measure theory which includes quantum mechanics as a special case. The fact that quantum probabilities can be expressed "as the squares of quantum amplitudes" is thus derived in a natural manner, and a series of natural generalizations of the quantum formalism is delineated. Conversely, the mathematical sense in which classical physics is a special case of quantum physics is clarified. The present paper presents these relationships in the context of a "realistic" interpretation of quantum mechanics.

Symmetries of Equations of Quantum Mechanics

Abstract: Table of

Limit to space-time measurement

Abstract: Applying simultaneously the principles of quantum mechanics and general relativity we find an intrinsic limitation to quantum measurements of space-time distances. The intrinsic uncertainty of a length is shown to be proportional to the one third power of the length itself. This uncertainty in space-time measurements implies an intrinsic uncertainty of the space-time metric and yields quantum decoherence for particles heavier than the Planck mass.

The Quantum Theory of Motion

Abstract: (1994). The Quantum Theory of Motion. Journal of Modern Optics: Vol. 41, No. 1, pp. 168-169.

Dynamics by Semiclassical Methods

Abstract: quantum approa ch. The evaluation of the quantum time evolution of a system requires the solution of the time-dependent Schr6dinger e:quation. A full numerical solution of the quantum problem is generally not feasible for cases involving more than a few degrees of freedom. The: situation is similar for the time-independent calculation of quantum transition probabilities in collision problems. Semiclassical methods build up approximate quantum solutions, which are numerically relatively easy to obtain, even for moderately long times, from information obtained along classical trajectories. Another reason for the attractiveness of semiclassical methods is their intuitive appeal. A semiclassical analysis of a problem allows the results to be interpreted in terms of classical trajectories, and this can provide a clearer picturc of the bchavior of the system than might be possible from quantum calculatio ns. Classical mechanics provides an accurate approximation of the dynamics of macroscopic systems, while quantum effects are very important on the microscopic lev el. Electronic states of atoms and molecules are known to be highly quantized, while the motion of molecules in a liquid are often well described by classical mechani cs. The scattering of molecules at rela

Quantum logic and the histories approach to quantum theory

Abstract: An extensive analysis is made of the Gell‐Mann and Hartle axioms for a generalized ‘histories’ approach to quantum theory. Emphasis is placed on finding analogs of the lattice structure employed in standard quantum logic. Particular attention is given to ‘quasitemporal’ theories in which the notion of time‐evolution in conventional Hamiltonian physics is replaced by something that is much broader; theories of this type are expected to arise naturally in the context of quantum gravity and quantum field theory in a curved space–time. The quasitemporal structure is coded in a partial semigroup of ‘temporal supports’ that underpins the lattice of history propositions. Nontrivial examples include quantum field theory on a non‐globally‐hyperbolic space–time, and a possible cobordism approach to a theory of quantum topology. A key result is the demonstration that the set of history propositions in standard quantum theory can be realized in such a way that each such proposition is represented by a genuine projection operator. This gives valuable insight into the possible lattice structure in general history theories.

Quantum temporal logic and decoherence functionals in the histories approach to generalized quantum theory

Abstract: The recent suggestion that a temporal form of quantum logic provides the natural mathematical framework within which to discuss the proposal by Gell‐Mann and Hartle for a generalized form of quantum theory based on the ideas of histories and decoherence functionals is analyzed and developed herein. Particular stress is placed on properties of the space of decoherence functionals, including one way in which certain global and topological properties of a classical system are reflected in a quantum history theory.

Quantum cellular automata: the physics of computing with arrays of quantum dot molecules

Abstract: We discuss the fundamental limits of computing using a new paradigm for quantum computation, cellular automata composed of arrays of coulombically coupled quantum dot molecules, which we term quantum cellular automata (QCA). Any logical or arithmetic operation can be performed in this scheme. QCA's provide a valuable concrete example of quantum computation in which a number of fundamental issues come to light. We examine the physics of the computing process in this paradigm. We show to what extent thermodynamic considerations impose limits on the ultimate size of individual QCA arrays. Adiabatic operation of the QCA is examined and the implications for dissipationless computing are explored. >

Stochastic wave-function approach to non-markovian systems

Abstract: We extend the quantum Monte Carlo wave-function method of quantum optics to non-Markovian system-reservoir interactions. The finite correlation time of the reservoir and the associated memory effects are incorporated into the dynamics by expanding the initial system using fictitious harmonic-oscillator modes, which have Markovian dissipative interactions. The underlying principle is the fact that a class of reservoir spectral functions can be approximated by a finite superposition of Lorentzian functions with positive coefficients.

Quantum Brownian motion in a bath of parametric oscillators: A model for system-field interactions.

Abstract: The quantum Brownian motion paradigm provides a unified framework where one can see the interconnection of some basic quantum statistical processes such as decoherence, dissipation, particle creation, noise, and fluctuation. The present paper continues the investigation into these issues begun in two earlier papers by Hu, Paz, and Zhang on the quantum Brownian motion in a general environment via the influence functional formalism. Here, the Brownian particle is coupled linearly to a bath of the most general time-dependent quadratic oscillators. This bath of parametric oscillators mimics a scalar field, while the motion of the Brownian particle modeled by a single oscillator could be used to depict the behavior of a particle detector, a quantum field mode, or the scale factor of the Universe. An important result of this paper is the derivation of the influence functional encompassing the noise and dissipation kernels in terms of the Bogolubov coefficients, thus setting the stage for the influence functional formalism treatment of problems in quantum field theory in curved spacetime. This method enables one to trace the source of statistical processes such as decoherence and dissipation to vacuum fluctuations and particle creation, and in turn impart a statistical mechanical interpretation of quantum field processes. With this result we discuss the statistical mechanical origin of quantum noise and thermal radiance from black holes and from uniformly accelerated observers in Minkowski space as well as from the de Sitter universe discovered by Hawking, Unruh, and Gibbons and Hawking. We also derive the exact evolution operator and master equation for the reduced density matrix of the system interacting with a parametric oscillator bath in an initial squeezed thermal state. These results are useful for decoherence and back reaction studies for systems and processes of interest in semiclassical cosmology and gravity. Our model and results are also expected to be useful for related problems in quantum optics.

Primary State Diffusion

Abstract: Primary quantum state diffusion (PSD) theory is an alternative quantum theory from which classical dynamics, quantum dynamics and localization dynamics are derived. It is based on four principles, that a system is represented by an operator, its state by a normalized state vector, the state vector satisfies a Langevin-Ito state diffusion equation, and the resultant density operator for an ensemble must satisfy an equation of elementary Lindblad form. There are three conditions. The ז 0 first determines the operator, to within an undetermined universal time constant ז 0 . The second and third conditions put opposing bounds on ז 0 . Dissipation of coherence is distinguished from destruction of coherence. The state diffusion destroys coherence and produces the localization or reduction that makes classical dynamics possible. PSD theory is a development of the environmental quantum state diffusion theory of Gisin and Percival and particularly resembles earlier proposals by Gisin and by Milburn. It is also related to the spontaneous localization theories of Ghirardi, Rimini and Weber, of Diosi and of Pearle. The non-relativistic PSD theory is of value only for systems which occupy small regions of space. Special relativity is needed for more extended systems even when they contain only slowly moving massive particles. Experiments on coherence lifetimes and matter interferometry are proposed which either measure ז 0 or put bounds on it, and which might distinguish between PSD and ordinary quantum mechanics.

Quantum optics and fundamentals of physics

Abstract: Preface. 1. Introduction. 2. Fundamentals of quantum theory. 3. Quantum theory of measurement. 4. Coherent states. 5. Nonclassical optical phenomena and their relations. 6. Photon interferences and correlations. 7. Quantum optical and Bell's inequalities. 8. Quantum optical experiments supporting quantum theory. 9. Conclusions. References. Index.

Resonance response of the quantum vacuum to an oscillating boundary

Abstract: We present an exact analytic solution to describe the quantum dynamics of the vacuum field coupled with an oscillating boundary (mirror) in a one-dimensional cavity. We show that the finite part of the field energy density grows in the form of two traveling wave packets which become narrower as time increases. We also discover a "sub-Casimir" region where the energy density can be even smaller than the corresponding static vacuum value.

Dynamical quantum Zeno effect

Abstract: A purely dynamical explanation for the quantum Zeno effect is proposed. It is argued that a quantum system undergoes a quantum-Zeno-type dynamics as a consequence of a particular type of evolution involving a series of frequent spectral decompositions. The role of quantum measurements and of the ``collapse of the wave function'' is investigated and it is clarified that, provided a final observation is performed, the dynamical quantum Zeno effect can be obtained without making use of von Neumann's projection postulate. The meaning of infinitely frequent measurements is critically discussed and it is argued that it should be regarded as a mathematical idealization, impossible to realize from a physical point of view.

Quantum stochastic resonance

Abstract: We demonstrate that stochastic resonance, where an increase in the noise acting on a nonlinear dynamical system increases the signal-to-noise ratio describing the response to periodic driving, can occur in quantum systems as well as classical ones. We show that quantum stochastic resonance can be observed experimentally by measuring conductance fluctuations in mesoscopic metals and describe the experimental parameters for which it occurs.

On Quantum Mechanics

Abstract: We reformulate the problem of the "interpretation of quantum mechanics" as the problem of DERIVING the quantum mechanical formalism from a set of simple physical postulates. We suggest that the common unease with taking quantum mechanics as a fundamental description of nature could derive from the use of an incorrect notion, as the unease with the Lorentz transformations before Einstein derived from the notion of observer independent time. Following an an analysis of the measurement process as seen by different observers, we propose a reformulation of quantum mechanics in terms of INFORMATION THEORY. We propose three different postulates out of which the formalism of the theory can be reconstructed; these are based on the notion of information about each other that systems contain. All systems are assumed to be equivalent: no observer-observed distinction, and information is interpreted as correlation. We then suggest that the incorrect notion that generates the unease with quantum mechanichs is the notion of OBSERVER INDEPENDENT state of a system.

Quantum chaos: An entropy approach

Abstract: A new definition of the entropy of a given dynamical system and of an instrument describing the measurement process is proposed within the operational approach to quantum mechanics. It generalizes other definitions of entropy, in both the classical and quantum cases. The Kolmogorov–Sinai (KS) entropy is obtained for a classical system and the sharp measurement instrument. For a quantum system and a coherent states instrument, a new quantity, coherent states entropy, is defined. It may be used to measure chaos in quantum mechanics. The following correspondence principle is proved: the upper limit of the coherent states entropy of a quantum map as ℏ→0 is less than or equal to the KS‐entropy of the corresponding classical map. ‘‘Chaos umpire sits, And by decision more imbroils the fray By which he reigns: next him high arbiter Chance governs all.’’ John Milton, Paradise Lost, Book II

Quantum, classical and intermediate: An illustrative example

Abstract: We present a model that allows one to build structures that evolve continuously from classical to quantum, and we study the intermediate situations, giving rise to structures that are neither classical nor quantum. We construct the closure structure corresponding to the collection of eigenstate sets of these intermediate situations, and demonstrate how the superposition principle disappears during the transition from quantum to classical. We investigate the validity of the axioms of quantum mechanics for the intermediate situations.

Matrix models, one-dimensional fermions, and quantum chaos

Abstract: Recent studies of universal parametric correlations in quantum chaotic spectra have revealed an astonishing connection to an integrable one-dimensional quantum system. We introduce a continuous matrix model which establishes a direct connection between the quantum Hamiltonian and the exact eld the-oretic description of spectral correlations. This reveals a common mathematical structure which underlies quantum chaos, matrix models, and a quantum Hamiltonian.

Nondemolition principle of quantum measurement theory

Abstract: We give an explicit axiomatic formulation of the quantum measurement theory which is free of the projection postulate. It is based on the generalized nondemolition principle applicable also to the unsharp, continuous-spectrum and continuous-in-time observations. The “collapsed state-vector” after the “objectification” is simply treated as a random vector of the a posterioristate given by the quantum filtering, i.e., the conditioning of the a prioriinduced state on the corresponding reduced algebra. The nonlinear phenomenological equation of “continuous spontaneous localization” has been derived from the Schrodinger equation as a case of the quantum filtering equation for the diffusive nondemolition measurement. The quantum theory of measurement and filtering suggests also another type of the stochastic equation for the dynamical theory of continuous reduction, corresponding to the counting nondemolition measurement, which is more relevant for the quantum experiments.

Fundamental limits upon the measurement of state vectors.

Abstract: Using the Shannon information theory and the Bayesian methodology for inverting quantum data [K. R. W. Jones, Ann. Phys. (N.Y.) 207, 140 (1991)] we prove a fundamental bound upon the measurability of finite-dimensional quantum states. To do so we imagine a thought experiment for the quantum communication of a pure state , known to one experimenter, to his colleague via the transmission of N identical copies of it in the limit of zero temperature. Initial information available to the second experimenter is merely that of the allowed manifold of superpositions upon which the chosen may lie. Her efforts to determine it, in an optimal way, subject to the fundamental constraints imposed by quantum noise, define a statistical uncertainty principle. This limits the accuracy with which can be measured according to the number N of transmitted copies. The general result is illustrated in the physically realizable case of polarized photons.