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Showing papers on "Quantum state published in 1986"


Journal ArticleDOI
TL;DR: In this paper, the Atiyah-Hitchin metric is used to describe the dynamics of two non-relativistic BPS monopoles using the space of collective coordinates of the monopoles.

388 citations


Journal ArticleDOI
TL;DR: In this paper, the quantum noise is evaluated for various simultaneous measurements of two quadrature components: heterodyning, the beam splitter followed by two single quadratures measurements, the parametric amplifier, the (degenerate and/or nondegenerate) four-wave mixer, the Brillouin and Raman amplifiers, and the laser amplifier.
Abstract: The preparation, or generation of coherent states, squeezed states, and photon number states is discussed. The quantum noise is evaluated for various simultaneous measurements of two quadrature components: heterodyning, the beam splitter followed by two single quadrature measurements, the parametric amplifier, the (degenerate and/or nondegenerate) four-wave mixer, the Brillouin and Raman amplifiers, and the laser amplifier. A quantum nondemolition measurement followed by a measurement of the conjugate variable is also categorized as a simultaneous measurement. It is shown that, for all of these schemes, the minimum uncertainty product of the measured variables is exactly equal to that required for a simultaneous measurement of two noncommuting variables. On the other hand, measurements of a single quadrature component are noise-free. Such measurements are degenerate heterodyning, degenerate parametric amplification, and cavity degenerate four-wave mixing and photon counting by a photomultiplier or avalanche photodiode. The Heisenberg uncertainty principle and the quantum-mechanical channel capacity of Shannon are discussed to address the question "How much information can be transmitted by a single photon?" The quantum-mechanical channel capacity provides an upper bound on the achievable information capacity and is ideally realized by photon number states and photon counting detection. Its value is $\frac{\ensuremath{\hbar}\ensuremath{\omega}}{(\mathrm{ln}2)kT}$ bit per photon. The use of coherent or squeezed states and a simultaneous measurement of two quadrature field components or the measurement of one single quadrature field component does not achieve the ultimate limit.

340 citations


Journal ArticleDOI
TL;DR: In this paper, it was shown that in principle a device exists which would duplicate a quantum system within a class of quantum states if and only if those quantum states are mutually orthogonal.

179 citations


Journal ArticleDOI
TL;DR: In this paper, the transition probabilities are expressed in terms of probability tables, which contain only the probabilities of the outcomes of certain special measurements, and are used to represent quantum states instead of state vectors or density matrices.
Abstract: First steps are taken toward a formulation of quantum mechanics which avoids the use of probability amplitudes and is expressed entirely in terms of observable probabilities. Quantum states are represented not by state vectors or density matrices but by “probability tables,” which contain only the probabilities of the outcomes of certain special measurements. The rule for computing transition probabilities, normally given by the squared modulus of the inner product of two state vectors, is re-expressed in terms of probability tables. The new version of the rule is surprisingly simple, especially when one considers that the notion of complex phases, so crucial in the evaluation of inner products, is entirely absent from the representation of states used here.

142 citations


Journal ArticleDOI
TL;DR: In this article, a path integral formulation for measurements distributed in time is proposed. But it has no similar decomposition; the notion of a system quantum state evolving in time has no place.
Abstract: Consider measurements that provide information about the position of a nonrelativistic, one-dimensional, quantum-mechanical system. An outstanding question in quantum mechanics asks how to analyze measurements distributed in time---i.e., measurements that provide information about the position at more than one time. I develop a formulation in terms of a path integral and show that it applies to a large class of measurements distributed in time. For measurements in this class, the path-integral formulation provides the joint statistics of a sequence of measurements. Specialized to the case of instantaneous position measurements, the path-integral formulation breaks down into the conventional machinery of nonrelativistic quantum mechanics: a system quantum state evolving in time according to two rules---between measurements, unitary evolution, and at each measurement, ``collapse of the wave function'' (``reduction of the state vector''). For measurements distributed in time, the path-integral formulation has no similar decomposition; the notion of a system quantum state evolving in time has no place.

141 citations


Journal ArticleDOI
TL;DR: In this paper, the energy splitting ΔE due to tunnelling between a pair of quantum states which correspond to classical motion on tori in phase space was calculated, and the result of the calculation, ΔE=Aħ 3 2 e -2 h, has canonically invariant expressions for the tunneling actions S and prefactor A, and it is conjectured that the results apply even when the tori overlap in coordinate space.

84 citations


Journal ArticleDOI
TL;DR: The quantum theory of activated events in condensed phases, developed by Wolynes using path integral techniques, was derived via harmonic quantum state theory as discussed by the authors, which is derived via path integral technique.

77 citations


Journal ArticleDOI
TL;DR: In this paper, the authors consider semiclassical Einstein equations in two dimensions and analyze the global properties of the space-time as a function of the quantum matter content both at zero and finite temperature.

31 citations


Journal ArticleDOI
TL;DR: In this article, the authors review the mathematical methods and problems that are specific to the program of stochastic quantum mechanics and quantum spacetime and then the mathematical models are developed, including positive operator-valued measures on a Hilbert space, reproducing kernel Hilbert spaces, and fibre bundle formulations of quantum geometries.
Abstract: In this paper we review the mathematical methods and problems that are specific to the programme of stochastic quantum mechanics and quantum spacetime. The physical origin of these problems is explained, and then the mathematical models are developed. Three notions emerge as central to the programme: positive operator-valued (POV) measures on a Hilbert space, reproducing kernel Hilbert spaces, and fibre bundle formulations of quantum geometries. A close connection between the first two notions is shown to exist, which provides a natural setting for introducing a fibration on the associated overcomplete family of vectors. The introduction of group covariance leads to an extended version of harmonic analysis on phase space. It also yields a theory of induced group representations, which extends the results of Mackey on imprimitivity systems for locally compact groups to the more general case of systems of covariance. Quantum geometries emerge as fibre bundles whose base spaces are manifolds of mean stochastic locations for quantum test particles (i.e., spacetime excitons) that display a phase space structure, and whose fibres and structure groups contain, respectively, the aforementioned overcomplete families of vectors and unitary group representations of phase space systems of covariance.

26 citations


Journal ArticleDOI
TL;DR: In this article, an expression for the distribution of quantum states of the reaction products of unimolecular dissociations is obtained, based on statistical theory, by introducing an adiabatic approximation for motion from transition state to products.
Abstract: An expression for the distribution of quantum states of the reaction products of unimolecular dissociations is obtained, based on statistical theory. A recently formulated RRKM-type treatment of unimolecular reactions with highly flexible transition states is used to obtain a distribution of quantum states of the products, by introducing an adiabatic approximation for motion from transition state to products. Any impulsive (nonadiabatic) exit channel effects are neglected thereby. Both the final yields of the quantum states of the products and the time evolution of these states are considered. The time evolution of the yield of the products can permit a direct test of non-RRKM effects and, additionally via the long-time component, of other aspects of RRKM theory. The long-time component of the yield of individual quantum states of the products then provides a test of the additional (here, adiabatic) approximation. Such tests are the more definitive the narrower the distribution of initial E's and J's of the dissociating molecule.

25 citations


Journal ArticleDOI
TL;DR: In this article, the Schrodinger equation type of description for fundamental processes is analysed, in terms of an alternative theory which describes the fluid behaviour of a polarized vacuum in a hyperspace.
Abstract: The Schrodinger equation type of description for fundamental processes is analysed, in terms of an alternative theory which describes the fluid behaviour of a polarized vacuum in a hyperspace. it is shown that Schrodinger quantum states can always be generated from an impulsive production of mass dipoles by processes which are classically explicable. A set of natural reference frames are introduced in relation to which it is shown that the Schrodinger structure assumes a very simple form in terms of local rotations. A fundamental vector potential that is involved in the underlying electromagnetic fluid movement is examined and Hamilton-Lagrange aspects of the polarized flow paths are discussed.

Journal ArticleDOI
TL;DR: In this paper, a relativistic Hilbert space is defined for the Klein-Gordon case, based on a recent association of quantum observable algebra with stochastic processes in the frame of the causality of quantum mechanics, and it is demonstrated that unitary transformations in Hilbert space reflect canonical transformations in the associated phase space.

Journal ArticleDOI
TL;DR: In this article, it was shown that, even if restricted to only self-dual (or anti-selfdual) fields, photon and linearized graviton states of both helicities can be constructed by dropping the restriction to positive-frequency fields.
Abstract: It is pointed out that, even if restricted to only self‐dual (or anti‐self‐dual) fields, photon and linearized graviton states of both helicities can be constructed by dropping the restriction to positive‐frequency fields. Consequently, contrary to the usual belief, it may not be necessary to work with both self‐dual and anti‐self‐dual fields to obtain the Hilbert space of all quantum states in full quantum gravity.

Journal ArticleDOI
TL;DR: In this article, the thermal linear response theory with the inclusion of the non· Markovian effect is formulated based on the thermal cranked Hartree·Fock·Bogoliubov (THFB) theory.
Abstract: The thermal linear response theory with the inclusion of the non· Markovian effect is formulated based on the thermal cranked Hartree·Fock·Bogoliubov (THFB) theory. We propose the proper strength function which is suitable to be compared with y-ray spectra from giant resonances at high spin and high temperature. A clarification is given of the relation between the stability condition of the THFB solution and the equation in the thermal random phase approximation (TRPA).

Journal ArticleDOI
TL;DR: In this paper, the significance and interest of the covariance and correlation coefficient for two physical properties of a quantum system was drawn to the significance of the generalized Heisenberg inequality between two such properties, in terms of their commutator and anticommutator, which was interpreted as setting an upper bound, of quantum nature, on their correlation coefficient.
Abstract: Attention is drawn to the significance and interest of the covariance and correlation coefficient for two physical properties of a quantum system The generalized Heisenberg inequality between two such properties, in terms of their commutator and anticommutator, is interpreted as setting an upper bound, of quantum nature, on their correlation coefficient

Journal ArticleDOI
TL;DR: In this paper, the superposition principle and minimal superposition are satisfied and the transition probability space can be represented by a generalized Hilbert space, and the notions of superposition and the Superposition principle are introduced.
Abstract: Hilbert‐space representations of transition probability spaces are studied. The notions of superposition and the superposition principle are introduced. It is shown that, provided the superposition principle and the postulate of minimal superposition are satisfied, transition probability space can be represented by a generalized Hilbert space.

Journal ArticleDOI
Onishi Naoki1
TL;DR: In this paper, the Bohr-Sommerfeld rule of classical quantization was used to determine the quantum states and their energies for states of 166 Er with ¦j¦ = 30-40 h.

Journal ArticleDOI
TL;DR: In this paper, the authors examined the relaxation of a primary system coupled weakly to a bath of environmental modes from the standpoint of recent developments in the semiclassical theory of molecular bound states.
Abstract: The relaxation of a primary system coupled weakly to a bath of environmental modes is examined from the standpoint of recent developments in the semiclassical theory of molecular bound states. Emphasis is placed upon highly excited, strongly nonlinear (but quasiperiodic) primary systems and zero temperature baths. The starting point for the analysis is a master equation for the populations of the eigenstates of the primary system. The correspondence principle provides semiclassical approximations to the transition rates, allowing quantum state populations to be calculated from classical trajectories. A second semiclassical approximation leads to an equation of motion for a probability density in the classical action variables. As h→0, this density agrees with the density generated by running an ensemble of damped classical trajectories and averaging out the angle variables; retention of terms of order h provides smoothed quantum corrections. Numerical examples of both semiclassical approximations are presented.


Journal ArticleDOI
TL;DR: Within this formalism the construction of physical states for a scalar quantum field in a Bianchi type-I universe is analyzed and the uniqueness of the inflationary vacuum is shown.
Abstract: The construction of physical states for a scalar quantum field in a Bianchi type-I universe is analyzed. A local constraint based upon the Hadamard form of the anticommutator function is implemented. The constraints imposed on the Fock space by this requirement are derived and the unitary equivalence between different representations of canonical commutation relations is shown. Within this formalism we analyze recently proposed Fock-space constructions and we show the uniqueness of the inflationary vacuum.

Journal ArticleDOI
TL;DR: In this article, a nuclear spin and inversion state-selected NH 3 beam is produced by coupling molecular beam electric deflection techniques with the extreme rotational cooling of a pulsed supersonic expansion.

Journal ArticleDOI
TL;DR: The notion of coherent algebra allows one to apply the formalism to spaces for which the Wigner mapping is not known as mentioned in this paper, and the quantum mechanics of a particle in a plane in polar coordinates is discussed as an example.
Abstract: Quantum mechanics is formulated on a quantum mechanical phase space. The algebra of observables and states is represented by an algebra of functions on a phase space that fulfils a certain coherence condition, expressing the quantum mechanical superposition principle. The trace operation is an integration over phase space. In the case where the canonical variables independently run from - infinity to + infinity formalism reduces to the representation of quantum mechanics by Wigner distributions. However, the notion of coherent algebra allows one to apply the formalism to spaces for which the Wigner mapping is not known. The quantum mechanics of a particle in a plane in polar coordinates is discussed as an example.


Journal ArticleDOI
TL;DR: In this paper, it was shown that in the logical-algebraic approach there is no kind of dependence (i.e. arbitrary two Boolean algebras may be the centres of two logics whose state spaces are identical).

Journal ArticleDOI
TL;DR: In this paper, the authors examined the classical limits to the orbital and energy sudden approximations and showed that at large orbital and rotational quantum numbers the transformations which diagonalized the coupling matrix in the sudden limit also diagonalize the coupling matrices in the classical limit.
Abstract: We have examined the classical limits to the orbital and energy sudden approximations. It is shown that at large orbital and rotational quantum numbers the transformations which diagonalize the coupling matrix in the sudden limit also diagonalize the coupling matrix in the classical limit. The eigenvalues are no longer a delta function fixed in position during the collision but become a narrow wave packet moving with the classical velocity. The result is a uniform approximation valid in both the sudden and classical limits. A key feature of the theory is the use of the discrete‐variable representation which allows an accurate counting of quantum states in the sudden representation. The theory should improve the accuracy of the sudden approximation while requiring little additional computer time.

Journal ArticleDOI
TL;DR: In this paper, a simple formula relating the input and output quantum states of a beamsplitter is derived and applied to the analysis of an interferometer with a photon duplicator along one arm.

Journal ArticleDOI
TL;DR: The origin of the Bohr-de Broglie quantum condition for the stability of atomic and nuclear systems can be interpreted in terms of a locally high Gaussian curvature of space-time equivalent to a large value of the gravitational constant along the lines suggested by Motz.
Abstract: The origin of the Bohr-de Broglie quantum condition for the stability of atomic and nuclear systems can be interpreted in terms of a locally high Gaussian curvature of space-time equivalent to a large value of the gravitational constant along the lines suggested by Motz’ for the stability of the electron. Assuming the mass is purely electromagnetic in origin and that hadrons are composed of highly relativistic electron-positron pairs in “charmonium” or heavy, integrally charged, quarklike arrangements, and also by adopting a symmetrical definition of the electromagnetic force between two moving particles as proposed by Einstein in 1905, one arrives a t the existence of a minimum approach distance as well as a changing source size or rest mass for the electron and positron in highly relativistic orbits of pion mass that form the basis of all hadrons (FIGURE I).’ The existence of a minimum approach distance between the fundamental entities is equivalent to a non-Euclidean geometry with a high local G similar to that of Motz, except that this local G is found to increase inversely as the square root of the pair mass during the course of the evolution of the universe by internal pair-production. This process begins with the Newtonian value of G and increases up to a maximum value of e2/m2, starting with a single massive “Lemaitre-atom”-like electron-pair of mass equal to that of the universe, MU, a t the Planck density, c * / ~ G ’ . ~ As a result, the charges in equilibrium orbits move along geodesics of the local space so that they do not radiate, which is contrary to classical electromagnetic theory. In these orbits, the tangential Lorentz contraction of the field source is exactly equaled by the radial contraction produced by the local space-curvature, thus reducing the source to the spherical shape associated with a state of rest. This provides a simple physical or geometrical explanation of the Bohr-de Broglie quantum condition, which can be applied to the stability of electron orbits and, thus, to all matter. Because hadrons appear to be describable as molecular arrangements of highly relativistic electrons and positrons whose masses, sizes, and lifetimes can be accounted for in terms of the basic electromagnetic constants, e, m,, c, and h , without any other arbitrary constants or adjustable parameters: and because the electron and positron may in turn be regarded as self-stabilized, spinning sources of a single field’ analogous to “twisted geons,” “vortex rings,” or “strings” in a fluidlike space-time continuum or ether, the wave-particle nature of matter finds a simple physical explanation. In this model, there is no “hard” or “ponderable” matter. Instead, all matter “particles” consist of stable, spinning sources of electromagnetic fields of finite inner size, with the size of the source determining the rest mass. This explains the relation of heavy quarks to leptons, including their small, pointlike size and spin ‘/2. In this model, the strong force is explained as a relativistic form of the electromag-

Journal ArticleDOI
TL;DR: In this article, the probability of presence at a given point in space and time of a one-dimensional quantum system which interacts with an external system is derived in terms of a double path integral which contains memory effects.
Abstract: We define and derive the probability of presence at a given point in space and time of a one-dimensional quantum system which interacts with an external system. The probability is expressed in terms of a double path integral which contains memory effects. We show that it is possible to get a simple compact algebraic expression of the probability as the continuum limit of a discretized form of the path integrals.

Journal ArticleDOI
TL;DR: The stochastic mechanics of Nelson and Guerra is formulated for the hydrogen atom and it is demonstrated that this simple quantum system can be described in terms of three independent Gaussian Markov processes which are driven (controlled) by the classical Kepler problem, establishing an apparent link between the quantized and classical versions of the Kepler problem.
Abstract: The stochastic mechanics of Nelson and Guerra is formulated for the hydrogen atom. We demonstrate that this simple quantum system can be described in terms of three independent Gaussian Markov processes which are driven (controlled) by the classical Kepler problem. It reveals a manifest connection between the classical and quantized versions of the Kepler problem. I. MOTIVATION The idea of stochastic quantization, as developed in Refs. 1 and 2, amounts to associating the stochastic processes to quantum states of the dynamical system. The procedure works quite successfully as long as ground states of the simplest models are considered; the determination of the Madelung fiuid representation for higher excited states is much more involved. In fact, the stochastic strategy works in full generality for an example of the harmonic oscillator and its most straightforward generalizations (see also the studies of its two-level, Fermi version ' ). However, the formulation of the stochastics mechanics for another simple quantum system, that of the hydrogen atom, except for the ground state, is yet to be accomplished. This fact is a bit puzzling since, like many other simple quantum systems, the quantized Kepler problem admits a realization in terms of (a quartet of) harmonic oscillators, " and should in principle allow for the generalization of the arguments of Refs. 2 and 12. Moreover the concept of related coherent states was introduced in Ref. 11, and the construction of oscillator stochastic processes is most transparent with respect to the coherent basis. It is our aim to take advantage of the oscillator reconstruction of the Kepler problem, to formulate the stochastic mechanics of the latter. While working with the fouroscillator system, the functions of Madelung densityphase variables p;(x), S;(x), i=1,2,3,4, arise through computing the coherent-state expectation values (a ~ A ~ a) =Z(p, S) of operator-valued quantities. To recover the hydrogen problem, the constraints must be accounted for. As we demonstrate in the course of the paper, the (analytic) stochastic mechanics of the problem, if formulated in the Madelung [p(x),S(x)] parametrization, is in all respects equivalent to the standard classical mechanics of the singular (constrained) Hamiltonian system, whose phase manifold is parametrized by holom orphic coherent-state labels (a,a): 4 ~ a)=exp g (a;tt — a;tt;) ~ 0) . consequence, we identify the coherent-state domain for the Kepler problem, whose a~, az, a3, a4 parameters are completely determined in terms of the canonical variables of the standard classical Kepler problem. It allows for the final conclusion that the three independent GaussianMarkov processes can be associated with the hydrogen atom. Moreover, these processes are driven (controlled in the language of Ref. 12) by the classical Kepler motion. It establishes an apparent link between the quantized and classical versions of the Kepler problem, the connection which could hardly have been seen from the path-integral computation presented in Ref. 6.

Journal ArticleDOI
TL;DR: In this article, it was shown that topologically massive Yang-Mills therries lack a fermionic sector of quantum states similar to that of non-linear sigma models with a Wess-Zumino term in the lagrangian.