Showing papers on "Open quantum system published in 1975"

Quantum fields in curved space--times

Abstract: The problem of obtaining a quantum description of the (real) Klein-Gordon system in a given curved space-time is discussed. An algebraic approach is used. The *-algebra of quantum operators is constructed explicitly and the problem of finding its *-representation is reduced to that of selecting a suitable complex structure on the real vector space of the solutions of the (classical) Klein-Gordon equation. Since, in a static space-time, there already exists, a satisfactory quantum field theory, in this case one already knows what the 'correct' complex structure is. A physical characterization of this 'correct' complex structure is obtained. This characterization is used to extend quantum field theory to non-static space-times. Stationary space-times are considered first. In this case, the issue of extension is completely straightforward and the resulting theory is the natural generalization of the one in static space-times. General, non-stationary space-times are then considered. In this case the issue of extension is quite complicated and we only present a plausible extension. Although the resulting framework is well-defined mathematically, the physical interpretation associated with it is rather unconventional. Merits and weaknesses of this framework are discussed.

Quantum Expansion of Soliton Solutions

Abstract: A method for giving quantum mechanical meaning to particle-like (soliton) classical solutions is described in an attempt to relate particle-like solutions of classical nonlinear field theory to physical hadrons. The method uses the familiar canonical Hilbert space formalism of quantum mechanics and has been applied to the quantum mechanical interpretation of both static and time- dependent classical soliton solutions. (SDF)

On the intuitive understanding of nonlocality as implied by quantum theory

Abstract: We bring out the fact that the essential new quality implied by the quantum theory is non-locality; i.e. that a system cannot be analyzed into parts whose basic properties do not depend on the state of the whole system. We do this in terms of the causal interpretation of the quantum theory, proposed by one of us (D. B.) in 1952, involving the introduction of the ‘quantum potential’, to explain the quantum properties of matter.

General connection between random electrodynamics and quantum electrodynamics for free electromagnetic fields and for dipole oscillator systems

Abstract: A general comparison is presented between random electrodynamics and quantum electrodynamics for the two systems which can be solved exactly in both theories, free electromagnetic fields and point dipole oscillators. The $N$-point correlation functions of the fields are computed in both theories and are found to differ in general because of the dependence upon the order of the quantum operators within products of operators. However, if all products of quantum operators are symmetrized by taking all permutations of the operator order, then the two theories give identical results for the correlation functions. Analogous results hold to all orders in the fine-structure constant for dipole oscllators in quantum and random electrodynamics. The theories agree only if the quantum operator products are symmetrized. In the limit that the oscillator couplings to the radiation fields vanish, th oscllators can be regarded as mechanical oscillators in quantum mechanics and in random mechanics. The theory of random mechanics is defined in terms of this limit which uncouples a mechanical oscillator from the radiation field. The average values of oscillator variables in random mechanics agree with those of symmetrized products in quantum mechanics. The question is then raised as to the physical significance of the many quantum operators which differ only in the order of their factors. It is pointed out that some operator products which are regarded as physically important, such as the square of the angular momentum, indeed involve unsymmetrized products of operators. On this account the average values of the angular momentum squared in the ground state of an isotropic three-dimensional harmonic oscillator differ between the random-mechanical and quantum-mechanical descriptions. However, there seems to be no case in which experiments have shown that the (unsymmetrized) quantum operator value is to be preferred to that provided by random mechanics. The presence of thermal radiation is next treated for free electromagnetic fields and for dipole-oscillator systems. Despite extraordinary differences in the points of view toward thermal radiation taken by the two theories, the conclusion is the same as that found for zero temperature; the two theories agree in their average values if all products of quantum operators are symmetrized. Finally, as a further example of the power of random electrodynamics to give an account of phenomena where Lorentz's classical electron theory failed, we investigate the diamagnetism of a charged three-dimensional isotropic oscillator. The mathematical descriptions at finite temperature are developed in full random electrodynamics and quantum electrodynamics and in second-order perturbation theory in quantum mechanics.

The quantum bouncer

Abstract: Examples in one and two dimensions for motion in a uniform gravitational field are considered quantum mechanically. The examples of bouncing in one dimension and sliding down an incline are proposed for use as conceptual aids in an introductory course.

Quantum-beat phenomena described by quantum electrodynamics and neoclassical theory

Abstract: We propose and analyze the use of quantum-beat phenomena to test neoclassical radiation theory (NCT) and quantum electrodynamics (QED). For a beam-foil type of experiment with atoms having one upper level and two closely spaced lower levels, all coherently excited, NCT predicts the presence of quantum beats in the emitted radiation; beats are not expected in QED. QED predicts beats when many atoms are present, in agreement with recent photon-echo experiments. An experiment to test NCT and QED is suggested.

On the Quantization of Dissipative Systems in the Lagrange-Hamilton Formalism

Abstract: Suppose one knows the classical equation of motion for a certain dissipating system. Of course, the dissipation arises from the system's quantum mechanical interaction with its damping reservoirs. However, the question can be raised how much information one is able to obtain about the quantum mechanical features of the system without having any detailed knowledge concerning the quantum nature of these underlying interactions. In this paper the quantization of dissipative systems is considered in the Lagrange-Hamilton formalism. Making use of complex variables it is possible to formulate a classical Lagrange-Hamilton theory where the Hamiltonian is non-Hermitian. The real part of the Hamiltonian can be quantized in the usual manner. For the imaginary part a procedure is presented, which results in a self-consistent quantum mechanical formulation. It will be seen that the quantum information that can be obtained about the classical dissipation may be expressed in terms of an anti-commutator. In the appendix a dissipation-fluctuation theorem is given which in the case of a simple damped harmonic oscillator yields a well-known expression.

A generalization of the classical moment problem on $^*$-algebras with applications to relativistic quantum theory. II

Abstract: A (non-commutative) generalization of the classical moment problem is formulated on arbitrary *-algebras with units. This is used to produce aC*-algebra associated with the space of test functions for quantum fields. ThisC*-algebra plays a role in theories of bounded localized observables in Hilbert space which is similar to that of the space of test functions in quantum field theories (namely it is represented in Hilbert space). The case of local quantum fields which satisfy a slight generalization of the growth condition is investigated.

Quantum electrodynamic and semiclassical interference effects in spontaneous radiation

Abstract: The theory of spontaneous decay is studied using both quantum electrodynamics (QED) and semiclassical theories of radiation. There are qualitative differences between the theories in the prediction of interference phenomena. In QED, systems which have been excited with pulsed laser light do not exhibit quantum interference effects associated with lower state splittings. On the other hand, semiclassical treatments of spontaneous decay do indicate the existence of interference effects not present in QED. In addition to this, differences are found between the predictions of fluorescence intensity in the presence of lower-state level crossings under continuous excitation.

Pattern recognition in molecular quantum mechanics

Abstract: It is shown that the classical concept of an open system does not encompass quantal systems but has to be replaced by the non-Boolean notion of an entangled system. Molecular, chemical, or biological phenomena can be considered to be reduced to a fundamental theory like quantum mechanics only if the fundamental and the phenomenological theories are formally and interpretatively connected, and if the classifications used in the empirical sciences are shown to follow from a single set of fundamental dynamical laws. These conditions enforce a non-statistical and ontic interpretation of quantum mechanics, hence a non-Boolean calculus of propositions. In this interpretation the notion of a world state is well-defined, its Schmidt-decomposition defines a background-dependent model state for molecular systems and creates the phenomena we can observe. To any molecular system there is associated in an objective way a nonnegative number which we call the integrity. The integrity measures the inherent fuzziness of the system concept in a holistic theory, and is used to define recognizable molecular patterns.

Multipole expansion in classical and quantum field theory and radiation

Abstract: The properties of a new multipole family of current (toroidal) moments dissimilar to charge and magnetic ones are investigated. Basic effects and conceptual changes arising from these moments are pointed out. A comprehensive formalism of multipole expansion (current parametrization) within the framework of the classical and quantum field theories is presented.

Toward an objective interpretation of quantum mechanics

Abstract: A simple postulate concerning state reduction is shown to allow for an objective interpretation of quantum mechanics and aconsistent explanation of 1) quantum interference, 2) the fact that macrosystems do not appear to exist in superpositions of states and 3) quantum measurement.

Reversible dynamics in a proposition−state structure

Abstract: We propose an intrinsic definition of reversible dynamical evolution of a physical system based on a unified formulation of the principle of superposition within an axiomatic approach to quantum mechanics.

Quantum dynamical semi-groups and the reduction process

Abstract: Taking advantage of some recent results in the theory of quantum dynamical semi-groups we introduce a mathematical model for the evolution of the statistical operator of an ensemble of quantum systems in the presence of a measuring apparatus. The considered dynamical equation induces the wave packet reduction in a continuous way. When the finite size of the apparatus is explicitly taken into account, the model allows a detailed description of the gradual entering of the wave function into the apparatus and of its consequences.

A characterization of clustering states

Abstract: A characterization of states, over quasi-local algebras, which satsfy a strong cluster property is derived. The discussion is applicable to classical systems and quantum systems with Bose or Fermi statistics.

Quasi-Implicative Lattices and the Logic of Quantum Mechanics

Abstract: Mittelstaedt has defined the class of quasi-implicative lattices and shown that an ortholattice (orthocomplemented lattice) is quasi-implicative exactly if it is orthomodular (quasi-modular). He has also shown that the quasi-implication operation is uniquely determined by the quasi-implicative conditions. One of Mittelstaedt's conditions, however, seems to lack immediate intuitive motivation. Consequently, this paper seeks to provide a number of reformulations of the quasi-implicative conditions which are more intuitively plausible. Three sets of conditions are examined, and it is shown that each set of conditions is both necessary and sufficient to ensure that an ortholattice is orthomodular, and each set of conditions uniquely specifies the implication operation to be Mittelstaedt's quasi-implication. Various properties of the quasi-implication are then investigated. In particular, it is shown that the quasi-implication fails to satisfy a number of laws associated with the classical material conditional. Various weakenings of these laws, satisfied by the quasi-implication, are also discussed

Statistical interpretation of quantum theory

Abstract: A new approach to axiomatizing quantum theory is suggested that overcomes some of the problems of the more usual methods. The measurement process is not left as a primitive under the new approach, and the density operator is taken as describing the fundamental physical properties of a system. Some differences from the Bohr and Margenau–Park approaches are mentioned.