Showing papers on "Open quantum system published in 1979"

Functional integration and quantum physics

Abstract: Introduction The basic processes Bound state problems Inequalities Magnetic fields and stochastic integrals Asymptotics Other topics References Index Bibliographic supplement Bibliography.

Quantum electrodynamics

Abstract: THE subject of quantum electrodynamics is extremely difficult, even for the case of a single electron. The usual method of solving the corresponding wave equation leads to divergent integrals. To avoid these, Prof. P. A. M. Dirac* uses the method of redundant variables. This does not abolish the difficulty, but presents it in a new form, which may be dealt with in two ways. The first of these needs only comparatively simple mathematics and is directly connected with an elegant general scheme, but unfortunately its wave functions apply only to a hypothetical world and so its physical interpretation is indirect. The second way has the advantage of a direct physical interpretation, but the mathematics is so complicated that it has not yet been solved even for what appears to be the simplest possible case. Both methods seem worth further study, failing the discovery of a third which would combine the advantages of both.

Geometrization of quantum mechanics

Abstract: Quantum mechanics is cast into a classical Hamiltonian form in terms of a symplectic structure, not on the Hilbert space of state-vectors but on the more physically relevant infinite-dimensional manifold of instantaneous pure states. This geometrical structure can accommodate generalizations of quantum mechanics, including the nonlinear relativistic models recently proposed. It is shown that any such generalization satisfying a few physically reasonable conditions would reduce to ordinary quantum mechanics for states that are “near” the vacuum. In particular the origin of complex structure is described.

Quantum interference and the quantum potential

Abstract: We re-examine the notion of the quantum potential introduced by the Broglie and Bohm and calculate its explicit form in the case of the two-slit interference experiment. We also calculate the ensemble of particle trajectories through the two slits. The results show clearly how the quantum potential produces the bunching of trajectories that is required to obtain the usual fringe intensity pattern. Hence we are able to account for the interference fringes while retaining the notion of a well-defined particle trajectory. The wider implications of the quantum potential particularly in regard to the quantum interconnectedness are discussed.

Evidence for the quantum nature of light

Abstract: A unique property predicted by the quantum theory of light is the phenomenon of photon antibunching. Recent theoretical predictions and experimental observations of photon antibunching in resonance fluorescence from a two-level atom are reviewed.

Local kinetic energy in quantum mechanics

Abstract: The question of local kinetic energy in quantum mechanics is considered by using the phase space formulation of quantum mechanics. We derive the totality of possible quantum mechanical expressions for local kinetic energy and give a subset which satisfy Bader’s criterion. The different definitions that various authors have used are shown to be directly related to particular quasiprobability distributions and correspondence rules.

Is quantum mechanics equivalent to a classical stochastic process

Abstract: The authors analyze the connection between the theory of stochastic processes and quantum mechanics. It is shown that quantum mechanics is not equivalent to a Markovian diffusion process as claimed in recent papers. The origin of a possible confusion about this question is clarified. The authors further demonstrate that there does not even exist a non-Markovian process equivalent to quantum mechanics.

Quantum nondemolition and gravity wave detection

Abstract: A variety of quantum nondemolition measurement schemes are defined and examples are given to demonstrate their theoretical and practical possibilities. They show that the quantum limit of measurement of weak forces does not exist.

Semi-classical ergodicity of quantum eigenstates in the Wigner representation

Abstract: We propose a new definition of ergodicity for a quantum system, pertaining to the semi-classical behavior of its energy eigenstates analyzed in the Wigner representation. This notion of ergodicity, stronger than the usual ones, leads to observable properties of the eigenfunctions. We discuss the possible existence (yet to proved) of such ergodic systems : we conjecture that “semi-classical ergodicity” is implied by the ergodicity of the limiting classical system found at \( ot h = 0\).

Quantum electrodynamic circuits at ultralow temperature

Abstract: Within present low-temperature technology it is possible to construct macroscopic circuits which exhibit quantum behavior, i.e., subcircuit currents and voltages need to be treated as operators rather than numerical quantities. The general theory of “quantum circuits” is discussed with a view toward the experimental verification of quantum electrodynamics on a macroscopic scale.

Atomic Physics Tests of the Basic Concepts in Quantum Mechanics

Abstract: Publisher Summary Quantum mechanics is the theory used to describe microscopic systems such as atoms, molecules, and elementary particles. It grew early in this century from a synthesis of Planck's introduction of the elementary quantum of action to understand the observed spectrum for blackbody radiation, Einstein's use of the quantum of action to explain the photoelectric effect, and Bohr's combination of the planetary model of the atom and the quantum of action to create a description of the hydrogen atom with a distinct set of stationary energy states. The present form of the nonrelativistic theory was developed independently by Schrodinger through the use of a wave equation that was motivated by work by de Broglie and by Heisenberg through an algebraic analysis based on a calculus of observables and motivated by dispersion theory relationships. This chapter first reviews the present conceptual basis for quantum mechanics and then describes the experiments that have been carried out to test these concepts. The relevant experiments are precision measurements of the predicted eigenvalue spectrum, single-photon interference experiments, successive measurements on eigenstates, measurements of photon-photon and spin correlations as a test of Bell's inequality, and the observation of the sign change for the rotation of the neutron through 2 π rad. Earlier reviews that summarize some of the information presented here are given by Paty , Freedman and Holt , and Freedman.

Interaction between classical and quantum systems; a new approach to quantum measurement. II. Theoretical considerations

Abstract: We develop further a new approach to the quantum measurement process. In this approach, which we proposed in a recent paper, the apparatus is treated as a classical system; however, the classical apparatus is directly coupled to the quantum system. A principle of integrity, which requires that the observables of the classical apparatus retain their classical integrity, is introduced. We examine the constraints which this principle places upon the coupling between the apparatus and the quantum system. To illustrate our approach we use a model loosely based on the Stern-Gerlach experiment. For this model we exhibit a coupling which satisfies the principle of integrity.

The quantum harmonic oscillator revisited: A new look from stochastic electrodynamics

Abstract: We apply the theory of stochastic electrodynamics to the study of the (nonrelativistic) harmonic oscillator by using the Fokker–Planck method. It is demonstrated that the equilibrium distribution in phase space is exactly equal to that given by quantum statistical mechanics, i.e., the corresponding Wigner distribution, and that analysis of this distribution by means of a decomposition in terms of canonical densities leads automatically to the usual description of quantum mechanics in terms of excited states. All fundamental equations of quantum mechanics are recovered as aprproximations to zero order in the radiation terms; the first‐order terms lead to the radiative corrections predicted by quantum electrodynamics, namely, the decay of states and the Lamb shift of the energy levels. The necessary differences between both treatments of the oscillator and their implications are briefly discussed.

A dynamical theory of Markovian diffusion

Abstract: A dynamical treatment of Markovian diffusion is presented and several applications discussed. The stochastic interpretation of quantum mechanics is considered within this framework. A model for Brownian movement which includes second order quantum effects is derived.

The quasi-classical limit of quantum scattering theory

Abstract: We study the quasi-classical limit of the quantum mechanical scattering operator for non-relativistic simple scattering system. The connection between the quantum mechanical and classical mechanical scattering theories is obtained by considering the asymptotic behavior as ħ → 0 of the quantum mechanical scattering operator on the state exp(—ip·a/ħ)f(p) in the momentum representation.

Quantum Field Theory and Fibre Bundles in a General Space-Time

Abstract: There is as yet no complete and consistent quantum theory of gravity. Indeed some practitioners of this art still argue about what would even constitute such a theory. However, irrespective of the final format, it seems likely that something rather dramatic will happen if the system is probed at distances of the fundamental Planck length \(L = \,{\left( {\frac{{hG}}{{{C^3}}}} \right)^{\frac{1}{2}}} \simeq \,{10^{ - 33}}cms.\) It is often suggested that at this order of distance there will be violent quantum fluctuations in the space-time structure itself (rather than in just the metric tensor) and in particular the topological structure may be subject to quantum laws. Whether such an idea can be sensibly implemented is not yet clear and it. might even be too conservative! However, in order to obtain any understanding of this problem it seems reasonable to first study the situation in which a quantum field is defined on a fixed (unquantized) manifold and to ask what role global space-time topology plays in the quantum field theory.

Stochastic Quantization: A Review

Abstract: The present status of the work on the application of the stochastic quantization procedure is reviewed. A compact mathematical introduction to the basic notions of random processes such as Markov processes, Martingales and Fokker-Planck equations is presented. The stochastic quantization procedure is explained in much detail and it is found to possess remarkable features which can not be achieved within the conventional framework of quantum theory. This admits us to give systematic analyses of irreversible quantum dynamics of dissipative systems and the vacuum tunneling phenomena in non-Abelian gauge theory

Filtering theory and quantum fields

Abstract: : In this paper we describe certain remarkable connections that exist between mathematical developments in quantum field theory (and enclidean field theory) and filtering theory (and in general system theory). Roughly speaking, the Kalman filter is the mathematical analog of a free quantum field (in a precise sense) and the study of non-linear filtering is the analog of the study of interacting quantum fields. Due to lack of space we only sketch this theory in this paper and the details of this work will be presented elsewhere. (Author)

Non-local charges: A new concept in quantum field theory

Abstract: Non-local charges are defined as a natural generalization of standard charges in relativistic quantum field theory. The general form of a non-local charge in terms of asymptotic fields is given and preliminary results on the restrictions imposed on non-local charges in interacting theories are reported [8].

Momentum Space Techniques for Curved Space-Time Quantum Field Theory

Abstract: A momentum space formulation of curved space-time quantum field theory is presented. Such a formulation allows the riches of momentum space calculational techniques already existing in nuclear physics to be exploited in the application of quantum field theory to cosmology and astrophysics. It is demonstrated that one such technique can allow exact, or very accurate approximate, results to be obtained in cases which are intractable in coordinate space. An efficient method of numerical solution is also described.

Comparison of classical and quantum mechanical uncertainties

Abstract: A comparison of classical and quantum uncertainties is presented for the particle‐in‐a‐box, the harmonic oscillator, and the one‐electron atom. It is found that the quantum results reduce to the classical in the limit of either very large quantum numbers or h→0. A classical uncertainty principle is derived and compared with its quantum analogue. A possible relationship between zero‐point motion and the uncertainty principle is noted.