Showing papers on "Phase space published in 1974"
TL;DR: In this article, it is shown that if the phase space of general relativity is defined so as to contain the trajectories representing solutions of the equations of motion then, for asymptotically flat spaces, the Hamiltonian does not vanish but its value is given rather by a nonzero surface integral.
1,365 citations
TL;DR: In this paper, the authors generalized the chemical mechanism of Field, Koros, and Noyes for the oscillatory Belousov reaction by a model composed of five steps involving three independent chemical intermediates.
Abstract: The chemical mechanism of Field, Koros, and Noyes for the oscillatory Belousov reaction has been generalized by a model composed of five steps involving three independent chemical intermediates. The behavior of the resulting differential equations has been examined numerically, and it has been shown that the system traces a stable closed trajectory in three dimensional phase space. The same trajectory is attained from other phase points and even from the point corresponding to steady state solution of the differential equations. The model appears to exhibit limit cycle behavior. By stiffly coupling the concentrations of two of the intermediates, the limit cycle model can be simplified to a system described by two independent variables; this coupled system is amenable to analysis by theoretical techniques already developed for such systems.
1,172 citations
TL;DR: In this paper, a quasi-isometric transformation of a phase space that allows passing from a diffusion process with nonzero drift coefficient to a process without drift is presented, and strong solutions of stochastic differential equations with a "bad" drift coefficient are constructed.
Abstract: In this paper we construct a one-to-one (and quasi-isometric) transformation of a phase space that allows us to pass from a diffusion process with nonzero drift coefficient to a process without drift. Using this transformation we construct strong solutions of stochastic differential equations with a "bad" drift coefficient and give other applications. Bibliography: 21 items.
445 citations
TL;DR: In this paper, the phase space factor for allowed β-decay is parametrized in the form: ƒ = ǫ Z = 0 expΣ3n = 0 an(1n E0)n for |Z| ≦ 101 and for β-particle kinetic energy end points in the range 10 keV to 20 MeV.
110 citations
TL;DR: In this article, the statistical mechanics of Hamiltonian systems with bounded phase space were investigated and it was shown that they can exist in negative temperature states which show observable intrinsic characteristics, such as the formation of clusters of particles.
Abstract: The two-dimensional guiding centre plasma and a system of interacting line vortices in an ideal fluid are examples of Hamiltonian systems with bounded phase space. The statistical mechanics of such systems is investigated. An interesting feature is that they can exist in negative temperature states which show observable intrinsic characteristics, such as the formation of clusters of particles.
74 citations
TL;DR: The difference in the available volume in phase space between collinear and full 3D dynamical computations is referred to as dimensionality bias as mentioned in this paper, and correction for this phase space factor allows for a more realistic estimate of reaction cross sections, branching ratios and 3D product energy distributions.
51 citations
TL;DR: In this paper, the generator of the time translation can be written in terms of a Hamiltonian and a set of Poisson brackets for the phase space variables when the velocity vector is in an n dimensional phase space.
Abstract: In an n dimensional phase space, the generator of the time translation can be written in terms of a Hamiltonian and a set of Poisson brackets for the phase space variables When the velocity vector
22 citations
TL;DR: In this article, it was shown that phase-space tunneling is not only classically forbidden, but also quantum-mechanically forbidden as well, and the existence of this tunneling process is undesirable.
Abstract: By analyzing the simple cosmological model consisting of a real massless Klein-Gordon field with vanishing spatial derivatives in the Friedmann universe, we conclude that this model can be successfully quantized only by using an extrinsic time. If one attempts to quantize using an intrinsic time, one is faced with the problem of either not having a point of maximum expansion, which violates the correspondence principle, or a necessity to devise a new interpretation for a zero-normed quantum mechanics (in addition to the particle-antiparticle interpretation). However, if one uses an extrinsic time, none of these difficulties occur. In analyzing the distinction between these two quantization procedures, we have noted that there are two distinct types of quantum-mechanical tunneling. The first type is the usual quantum-mechanical tunneling which we call "coordinate-space tunneling," where the topology of the classical phase space is usually planar and the phase space has no classically forbidden regions, although for a fixed energy, there can exist certain regions of coordinate space that are classically forbidden. The second type occurs when the phase space has classically forbidden regions, and we call tunneling into these regions "phase-space tunneling." In terms of these two types of tunneling, quantization with an intrinsic time allows "phase-space tunneling" to occur, and it is the presence of this type of tunneling that gives this solution its undesirable features. On the other hand, quantization with a particular choice of extrinsic time absolutely forbids the occurrence of "phase-space tunneling," and it is the lack of this type of tunneling that gives this model its desirable features. Thus, based on this model and other general arguments, we propose that although "coordinate-space tunneling" is quantum-mechanically allowed, the distinctly different tunneling process, "phase-space tunneling," is not only classically forbidden, but also must be considered to be quantum-mechanically forbidden as well.
22 citations
TL;DR: In this article, an analogue of the analytic Hamiltonian formalism in a complex phase space is presented for constructing formal asymptotic solutions of the characteristics and the transport equation.
Abstract: In this paper we give a method for constructing formal asymptotic solutions. This method uses in some sense "approximate solutions" of the equation of the characteristics and the transport equation. The construction of approximate solutions is brought abount by means of an analogue of the analytic Hamiltonian formalism in a complex phase space. Bibliography: 19 items.
19 citations
TL;DR: In this article, the ergodic properties of a general class of infinite systems of independent particles which undergo nontrivial "collisions" with an external field, e.g. fixed convex barriers (the Lorentz gas), were investigated.
Abstract: We investigate the ergodic properties of a general class of infinite systems of independent particles which undergo nontrivial “collisions” with an external field, e.g. fixed convex barriers (the Lorentz gas). We relate the ergodic properties of these systems to the ergodic properties for a single particle moving in a finite box (with periodic boundary conditions) with the same dynamics. We prove that when the one particle system is mixing or aK-system for a sequence of boxes approaching infinity so is the infinite particle system with an equilibrium measure obtained as a Poisson construction over the one particle phase space.
19 citations
TL;DR: In this article, a single diffraction definition for the phase-space region of exclusive double pomeron exchange (DPE) is proposed, which involves two ratios of missing-mass to total energy.
TL;DR: In this article, a modified phase-space theory of reaction rates was coupled with Monte Carlo trajectory calculations to yield rate constants and energy distributions of reactants and products for the three-atom dissociation and recombination reactions of hydrogen at 4000°K.
Abstract: The modified phase‐space theory of reaction rates was coupled with Monte Carlo trajectory calculations to yield rate constants and energy distributions of reactants and products for the three‐atom dissociation and recombination reactions of hydrogen at 4000°K. Sample trajectories selected from those crossing a surface in phase space were calculated in forward and reverse directions to determine the classical rates of formation of bound and quasibound molecules from atoms. The probability of stabilization of quasibound molecules in successive collisions with hydrogen atoms was determined from additional trajectory calculations. The steady state correction factor for recombination, which accounts for dissociation of newly formed bound H2 molecules, was estimated from similar calculations. The computed rate constant for recombination is 3.1×1015 cm6 mole−2 sec−1. For equilibrium between free atoms and quasibound molecules established through tunneling, the over‐all rate constant is estimated to be 75% higher. In either case the process of termolecular recombination to produce bound molecules makes a substantial contribution to the over‐all rate.
TL;DR: In this article, the short range part of two-particle correlations is discussed as it results from the phase space available in cluster decay, and certain variables emerge which should be useful to organize the data and extract interesting information.
TL;DR: In this paper, a heuristic quantum mechanical path integral formula with paths in phase space is given a precise mathematical meaning, and a quantum quantum path integral model with path integral formulas with path integrals in phase spaces is presented.
TL;DR: In this paper, the memory function and derivation of a kinetic equation for one-body phase space correlation functions are discussed. But the analysis is restricted to the case of a single-body additive projection operator and the Liouville operator.
Abstract: This paper is concerned with the calculation of the memory function and derivation of a kinetic equation for one-body phase space correlation functions. The theory uses a one-body additive projection operator and a division of the Liouville operator with an unperturbed part that describes dressed particles. Binary collisions are neglected, for the theory aims at describing the screening and backflow effects of a type contained in the plasma kinetic theory of Balescu and Lenard. We obtain an explicit kinetic equation which is an improvement of these theories for the plasma case, and involves the exact equilibrium pair and triplet distributions. The equation also describes systems with strong short-range forces and shows how the screening effects occur in this case as well. The unifying function is the direct correlation function. The theory is meant to provide understanding for a more complete theory of fluids where a proper account is given of close collisions.
TL;DR: In this paper, the invariant phase space model was used to predict the p p annihilation data and the main features observed in e+e− annihilation experiments and showed that at present energies, phase space effects are dominant in both e + e − and p p − annihilation processes.
TL;DR: In this paper, the radiation of an arbitrary time-dependent quadratic quantum system is calculated by means of the coherent-state method, and the results are shown to be consistent with the results in this paper.
TL;DR: In this article, the nonlocal multiplication of phase space functions is generalized to functions over locally compact Abelian groups or over homogeneous spaces of such groups, and it is shown that such nonlocal algebras of functions are closely related to the ray-representations of the corresponding dual groups.
TL;DR: In this paper, an auxiliary pre-asymptotic space is proposed to deseribing the self-interacting ''ingoing'' and ''outgoing'' multiparticle states.
Abstract: The scattering formalism for the multiparticle systems interacting before and after scattering—in particular for unstable particles, resonances and clusters—is outlined. The main formal tool proposed here is an auxiliary pre-asymptotic spaceH =Hin =Hout deseribing the self-interacting «ingoing» and «outgoing» multiparticle states. The characteristic features of the states in ℋ—continuous mass spectra and virtual propagation—are briefly discussed. We show further that the physical unitarity condition is satisfied and double counting avoided if in the auxiliary space ℋ the phase space is properly defined.
TL;DR: In this article, the effect of modifying Monte-Carlo generated events by a matrix element containing a factor (−bp⊥2) for each outgoing particle and an exponential damping exp (at) in the momentum transfer to each of the final baryons was examined.
TL;DR: In this article, the influence of kinematical constraints on the transverse momentum correlation features in multiparticle processes is studied by means of thedN/(d�r�1>>\d�r�2) distribution, r�1 and r� 2 being the transversal momenta of the particles entering in each pair.
Abstract: The influence of the kinematical constraints on the transverse momentum correlation features in multiparticle processes is studied by means of thedN/(d
r
1
d
r
2) distribution,r
1 andr
2 being the transverse momenta of the particles entering in each pair. Using a limited transverse momentum phase space we obtain for high energy reactions a simple analytical expression fordN/(d
r
1
d
r
2). This expression, similar to a phenomenological parametrization proposed for analyzing¯pp annihilation data, served to define a correlation parameter, the non vanishing value of which is due to the energy-momentum conservation constraints.
TL;DR: In this article, the Vlasov phase was identified as a perturbed particle trajectory in the variable t 0 which emanates from [x, v], where v is the phase space stream of test particles at the fixed time t 0.
Abstract: While the Vlasov phase, [Xv(t, t0), Vv(t, t0)], can be identified as a perturbed particle trajectory in the variable t0, the time‐reversed Vlasov phase may be identified as the phase space stream of test particles at the fixed time t0 which emanates from [x, v].
TL;DR: The equivalence of the non-equilibrium phase space distribution function in the form due to Kawasaki and Gunton and two versions of the Zubarev statistical operator is established.
TL;DR: In this article, the effect of the use of harmonic oscillator nucleonic wavefunctions for the definition of the phase space factor for allowed β-decay is investigated for A.
TL;DR: In this article, the quantum corrections to the phase space distribution function were obtained for general velocity dependent interactions and it was noted that a study of the thermodynamic properties of bulk nuclear matter may settle the question of velocity dependence of nucleon-nucleon interaction.
Abstract: The quantum corrections to the phase space distribution function are obtained for general velocity dependent interactions. It is noted that a study of the thermodynamic properties of bulk nuclear matter may settle the question of velocity dependence of nucleon‐nucleon interaction.
TL;DR: In this article, a semiclassical extension of Levinson's theorem to a model three-body system is presented, where the system chosen is a particle interacting with a harmonic oscillator for collinear configurations.
Abstract: A semiclassical extension of Levinson's theorem to a model three‐body system is presented. The system chosen is a particle interacting with a harmonic oscillator for collinear configurations. The theorem predicts the number N of three‐body bound states that a potential energy surface can support, and this number is calculated for a set of surfaces for this model collinear system. The calculation involves the extrapolation of the S matrix to zero collision energy, where S matrix elements needed in the extrapolation are found in the classical limit. For comparison, N is also calculated in a purely classical fashion from the multidimensional phase space volume integral. The results from the semiclassical and purely classical calculations are in fairly good agreement.
TL;DR: In this paper, the parton model was used to analyze massive J.J-pair trajectories and obtain expressions for general cross sections, dcr/d4Q, in the J-pair momentum.
Abstract: LBL-3021 PIT'l'-122 We analyze massive J.J-pair production in.hadron-haarcn collisions using. the parton model, and obtain expressions for general ~ifferential cross sections, dcr/d4Q, in the J.J-pair momentum. .We indicate ways in which the parton distributions inboth longitudinal and transverse momenta may oe probed in detail. Finally, we apply our results to -tne data by using part on distribution functionS With threshold behavior 1 (w=--+1) . X ~mplied by the interchange model for large angle scattering, Our results are: (1) the calculated cross section is only five percent of the observed cross section at Brookhaven energies; (2) the-shape, if not the_normalization, of the observed longitudinal momentum distribution, dcr/dC': 11 , is accurately reproduced; (3) the shape or the invariant mass distribution, 2 dcr/dQ , can be approximately reproduced if the partons are given nonpointlike struc+ ture' as suggested by recent e e co_lliding beam experiments. -2INTRODUCTION 1 The ability or the parton model to \"explain\" the apparent scaling of the electroproduction data in the SLAG-MIT experiments 2 does not in itself provide. conclusive evidence for sucn a composite hadronic picture. Theories based on vector-meson aominance3 and, indeed, any models with appropriate light cone behavior4 are viable alternatives. The importance of extracting and_experimentally testing predictions of the parton model for other processes is manifest. Particularly important examples are: electron-positron annihiJ.ation; 5 high transverse molilentum reactions;6 and massive J.J-pair proauction. 79 + 'h'l. • 10,11 . The existing e -e ann~ ~ at~on data is not easily interpreted within the parton framework without modifications to the pointlike structure of the partons. 12 On the other haria, high transverse momentum phenomena seem to lend considerable support to parton model ideas.l5 Indeed there is a definite consistency between deep inelastic and high PJ. processes. The wave functionsl3,l4 describing the breakup of a haaron into partons, suggested by the intercnange and dimensional counting models of high transverse momentum interactions, seem to be in remarkable agreement with the deep inelastic data~ Of particular importance is the very different behavior .of parton vs. antiparton distribution functions. This·difference leads to substantial alterations i~ the expectations of the parton model for the, as yet, incompletely measured cross section for massive J.J-pair production. A rough treatment of these alterations has been glven in Ref. 12. In this paper, we shall employ the more precise distribution t'1,!Ilctions of Ref. 11 to analyze the J.J-pair production data in detail. -3We shall also prepare a large),y kinematical modification of the traditional analysis which is vital in making reliable parton model predictions at subasymptotic energies. We give a method for taking account of the phase space limitations of the ~-pair invariant mass squared up to order I{S. At the energies.of the tlrookhavenColumbia experiment15 the modifications are substantial. Finally; we shall discuss the importance of measuring the longitudinal and-transverse momentum distributions of the ~~pair. In particular, a definite correlation between the transverse and longitudinal momentum distributions is expected as the edge of phase space is approached. I. KINEMATICS AND CROSS SECTION FORMULAE We first discuss the necessary corrections to and amplifications of the asymptotic. cross section formulae contained in the literature. 7 It is convenient ana perhaps interesting to use a slightly different technique for deriving the results. Neither naive parton model calculations nor the relatively more complicated Sudakov ana1ysis16 need be .employed. The invariant cross section for production of·a massive ~-pair (Fig. 1) may be written as,
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