Intrinsic irreversibility of Kolmogorov dynamical systems

We give the mathematical details and various extensions of the results stated in previous work of Courbage and Prigogine. “Intrinsic random systems” are deterministic and conservative dynamical systems for which we can associate two dissipative Markov processes through a one-to-one “change of representation”, the first leading to equilibrium for t→+∞ and the second for t→-∞. The microscopic formulation of the second principle of thermodynamics permits to lift the degeneracy by the exclusion of all states that do not approach equilibrium for t→+∞. The set of admitted initial conditions $\text{D}$⁺ is then characterized by a non-equilibrium entropy functional which is infinite for rejected initial states and takes finite values for admitted initial conditions. Thus, rejected initial states correspond to an infinite amount of information. To realize this selection rule we consider general probability measures on phase space that are not necessarily absolutely continuous and we extend the theory of transition to Markov processes to such measures. Owing to the non-invariance of $\text{D}$⁺ under the time inversion, the evolution of these states in the new representation can only be given by one of the two possible Markov processes.     

Elementary excitations in quadrupolar systems

We consider $\text{S ?}\text{3}\text{2}$ isotropic quadrupolar ordered systems and derive elementary excitations at low temperature. A Holstein-Primakoff type transformation and a linear approximation are used. For $\text{S =}\text{3}\text{2}$, the spectrum is made of four degenerate acoustic branches. For S ? 2, only two degenerate branches satisfy the Goldstone theorem: they describe Δm = ± 1 excitations similar to librons in molecular crystals. The two degenerate branches describing Δm = ± 2 excitations have a gap at k = 0 although the hamiltonian is isotropic. For a special $\text{S =}\text{3}\text{2}$ cubic hamiltonian, a Goldstone mode is found in the spectrum and related to a continuous degeneracy of the ground state. A comparison between $\text{S =}\text{1}\text{2}$ dipolar and $\text{S =}\text{3}\text{2}$ quadrupolar systems is presented.     

Test of amplitude signs in pion photoproduction predicted by the transformation from current to constituent quarks

The transformation from current to constituent quark basis states is discussed as it applies to relating amplitudes for photon-nucleon decays of baryon resonances. The predictions for the relative signs of pion photoproduction amplitudes through baryon resonances in the $\text{70}\text{L = 1}$ and $\text{56}\text{L = 2}$ multiplets are presented and compared with experiment. Theory and experiment are found to be completely, with the pion-nucleom decay amplitudes of resonances in the $\text{70}\text{L = 1}$ having the signs characteristic of the $\text{3,}\text{3}\text{)?(}\text{3}\text{, 3)}$ rather than (8, 1)?(1, 8) term in the transformation axial-vector charge.     

Renormalization group limits for Wick polynomials of Gaussian processes

We consider sequences of Gaussian stationary generalized stochastic processes, admitting formation of Wick polynomials, which converge to infrared singular limit processes for which the Wick powers are not defined. Nevertheless the suitably renormalized Wick polynomials are convergent, the limit processes form a dense set in the space of superpositions of Gaussian processes, i.e. their characteristic functional has the form

$\text{L(?)=?exp{?}\text{1}\text{2}\text{y}{}^2\text{<?|?>}dv(y)}$

where v is a probability measure. In the probabilistic version of renormalization group for continuous systems the sequences can be viewed as orbits under RG transformations having a short scale fixed point.     

On the functional integral for generalized Wiener processes and nonequilibrium phenomena

The attention will be focussed on a generalized Wiener diffusion process for which the macroscopic evolution $\text{y}\text{?}\text{= c}{}_1\text{(}\text{y}\text{)}$ equals zero, of course, and where the variance of the process obeys $\text{g}\text{?}\text{s}{}^2\text{= c}{}_2\text{(}\text{y}\text{)}$. The diffusion function c₂(y) may be state dependent in an arbitrary way. We invoke our treatment of the general time-local Gaussian process as presented in a previous paper. This process will be seen to define a generalized functional Wiener measure. This measure has already been used implicitly in earlier work being concerned with nonlinear, nonequilibrium Markov processes. The sum of the generalized measure over the entire function space will be shown to be exactly related to the general Fokker-Planck equation for the driftless diffusion process. The relation between the well-defined functional sum and its corresponding functional integral will be studied in detail. The analysis demonstrates in clear fashion the origin of the deviations from other approaches, and provides an extension of our previous results on nonequilibrium, nonlinear phenomena to include generalized diffusion processes.     

Neutral current anomalies: Difference between dynamical scaling violations and slow rescaling

We discuss the neutral current phenomena in order to discriminate between dynamical scaling violations and heavy quark productions. both of which could explain the charged current anomalies. In the Weinberg-Salam-GIM (W-S) model, “neutral current anomalies” should appear in addition to the charged current anomalies which result from dynamical scaling violations. The “neutral current anomalies” will be observed through the final hadronic invariant mass distributions, especially in $\text{v}$ neutral current processes. The predictions of the W-S model are compared with those of heavy quark models by investigating the changes of the ratios of neutral-to charged-current cross sections for $\text{v}\text{and}\text{v}$ as functions of the $\text{v}\text{/v}$ charged current cross section ratio.     

A slice theorem for the space of solutions of Einstein's equations

A slice for the action of a group G on a manifold X at a point x ? X is, roughly speaking, a submanifold S_x which is transverse to the orbits of G near x. Ebin and Palais proved the existence of a slice for the diffeomorphism group of a compact manifold acting on the space of all Riemannian metrics. We prove a slice theorem for the group $\text{D}$ of diffeomorphisms of spacetime acting on the space $\text{E}$ of spatially compact, globally hyperbolic solutions of Einstein's equations. New difficulties beyond those encountered by Ebin and Palais arise because of the Lorentz signature of the spacetime metrics in $\text{E}$ and because $\text{E}$ is not a smooth manifold- it is known to have conical singularities at each spacetime metric with symmetries. These difficulties are overcome through the use of the dynamic formulation of general relativity as an infinite dimensional Hamiltonian system (ADM formalism) and through the use of constant mean curvature foliations of the spacetimes in $\text{E}$. (We devote considerable space to a review and extension of some special properties of constant mean curvature surfaces and foliations that we need.) The conical singularity structure of $\text{E}$, the sympletic aspects of the ADM formalism, and the uniqueness of constant mean curvature foliations play key roles in the proof of the slice theorem for the action of $\text{D}$ on $\text{E}$. As a consequence of this slice theorem, we find that the space $\text{D}$ = $\text{E}$/$\text{D}$ of gravitational degrees of freedom is a stratified manifold with each stratum being a sympletic manifold. The spaces for homogeneous cosmologies of particular Bianchi types give rise to special finite dimensional symplectic strata in this space $\text{G}$. Our results should extend to such coupled field theories as the Einstein-Yang-Mills equations, since the Yang-Mills system in a given background spacetime admits a slice theorem for the action of the gauge transformation group on the space of Yang-Mills solutions, since there is a satisfactory Hamiltonian treatment of the Einstein-Yang-Mills system, and since the singularity structure of the solution set is known.     

On intrinsic randomness of dynamical systems

We discuss the problem of nonunitary equivalence, via positivity-preserving similarity transformations, between the unitary groups associated with deterministic dynamical evolution and semigroups associated with stochastic processes. Dynamical systems admitting such nonunitary equivalence with stochastic Markov processes are said to beintrinsically random. In a previous work, it was found that the so-called Bernoulli systems (discrete time) are intrinsically random in this sense. This result is extended here by showing that a more general class of dynamical systems—the so-calledK systems andK flows—are intrinsically random. The connection of intrinsic randomness with local instability of motion is briefly discussed. We also show that Markov processes associated through nonunitary equivalence tononisomorphic K flows are necessarily non-isomorphic.Dr. Goldstein's research was supported in part by NSF Grant No. PHY78-03816.     

Diffusion processes and atomic collisions of Na-rare gas systems studied by laser induced population grating method

Diffusion processes and atomic collisions of Na-He and Na-Ar systems have been studied by measurement of the time development of population gratings (Laser-Induced Population Grating; LIPG) induced in atomic levels by two intersecting resonant laser pulses and monitored through the Bragg diffraction of a probe laser beam. The diffusion process in the systems was observed through the decay of the LIPGs in the sodium ground-state $\text{(3}{}^2\text{S}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{)}$ sublevels. The pressure dependence of the diffusion constants were measured. The values showed rough agreement with the previously reported values which had been measured indirectly by the optical-pumping method. The gaussian process model and a simple collision kernel model were considered for the diffusion process. It was also found that with increasing buffer-gas pressure, the population gratings in the excited state $\text{3}{}^2\text{P}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$ were transferred to $\text{3}{}^2\text{P}{}_{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$, which was interpreted as an effect of fine-structure state-changing collisions.     

Atomic short-range order and its relation to the magnetic behavior of noble-metal based spin-glass alloys

We have investigated the spatial distribution of magnetic atoms (Mn or Fe) by determining the short range order parameters for the archetypal spin-glass alloys: $\text{Cu}$Mn, $\text{Au}$Mn, $\text{Au}$Fe and $\text{Pt}$Mn in the dilute limit. All four systems possess atomic short-range order (ASRO) such as to enhance local ferromagnetic regions. In the latter three systems the ASRO is relatively strong and initiates long-range structures which develop with increasing concentration and which eventually destroy the spin-glass state.     

Double inelastic interactions in pd collisions in the 1.6–4.3 GeV/c incident p momentum range

We present results on $\text{p}\text{d}$ multiplicity distributions at 3.9 and $\text{4.3}\text{GeV}\text{/c}\text{p}$ incident momenta obtained from a bubble chamber experiment. An excess is observed for the even-prong multiplicities as compared with $\text{p}$ collisions on free protons. This excess as well as that observed in other existing $\text{p}\text{d}$ data in the 1.6–2.9 GeV/c range was analysed in terms of double interaction processes inside the deuteron.     

Baryon-antibaryon bound states and annihilation

In order to gain some insight into the problem of the widths of quasi-nuclear levels in the $\text{B}\text{B}$ systems, we investigate a simple multichannel model for the influence of decay channels on a bound state. The shift and width of a bound-state level is found to depend strongly not only on the range of the annihilation and the $\text{B}\text{B}$ wave function at small distances but also on the position of the level relative to the thresholds. We point out a new mechanism through which a level in the vicinity of open thresholds can remain narrow even for strong coupling to the decay channels.     

Properties of a spin fluid in a Riemann-Cartan spacetime

In this paper we extend to the case of spin fluids in the Einstein-Cartan theory some results obtained by Taub and Lichnerowicz for a perfect fluid in general relativity. So doing we also give an extension of the Bernoulli theorem. We show a connection between torsion and a macroscopical quantity, the tensor $\text{Ω}{}_{\mathrm{ij}}\text{=2?[}{}_{\mathrm{j}}{}^{\mathrm{V}}{}_{\mathrm{i}}\text{]}$.     

Heavy-quark production by hadrons: Gluon jet fragmentation versus fusion

We show that at $\text{p}\text{p}$ collider energies heavy quarks are dominantly produced by the fragmentation of gluon jets into $\text{Q}\text{Q}$ with Q = c,b. This is because the underlying gg → gg jet cross section exceeds the fusion process $\text{gg → Q}\text{Q}$ by over two orders of magnitude. We compute the perturbative contribution to the gluon fragmentation from 2 → 3 processes such as gg $\text{→ gQ}\text{Q}$. We point out the observable consequences for single-lepton production and same-opposite charge dileptons. In particular, the observed production of dileptons with large p_T and low effective mass is explained.     

Exclusive processes in QCD:: Two-photon physics involving baryons

Exclusive two-photon processes involving baryons have been calculated within the framework of perturbative QCD. In particular, the angular dependence of the process $\text{γγ →}\text{p}\text{p}$ is predicted as a function of the universal baryonic distribution amplitudes φ(x_i). The overall normalization is then found by a comparison with the process $\text{Ψ →}\text{p}\text{p}$, so that we can present a unique, absolutely normalized QCD prediction for the two-photon processes. We argue that these predictions, based on the $\text{Ψ →}\text{p}\text{p}$ decay rate, should be more reliable than those based on baryonic form factors. Presently not enough data exist to give a meaningful differential cross section for the process $\text{γγ →}\text{p}\text{p}$. Nevertheless, a total cross section has been obtained. Excluding the region close to threshold, quite good agreement between our predictions and experimental data is found. The analysis in this paper is trivially generalized to other baryons as well.     

Gluon condensate and the interquark potential

We construct a potential for qurkonium systems using as the basic ingredients the gluon condensate, i.e., 〈0∥G_μν^aG_μν^a∥0〉 ≠ 0 to incorporate nonperturbative effects and using quark screening. The potential is able to account satisfactorily for the s$\text{s}$, c$\text{c}$ and b$\text{b}$ bound states with a flavor independent, essentially constant value for the effective coupling constant $\text{(}\text{α}{}_{\mathrm{<mtext>S</mtext>}}\text{≈ 0.45)}$. We also investigate heavier quark systems with the constant $\text{α}{}_{\mathrm{S}}$ and find that for quark mass ? 20 GeV the potential is essentially coulombic.     

The non-linear sigma model in the 1N expansion and the inverse scattering transformation in the angular momentum

We develop an inverse scattering transformation in the angular momentum to deal with rotationally invariant problems in higher dimensions. We consider the two-dimensional non-linear σ-model in the $\text{1}\text{N}$ expansion. We succeed in expressing the action (a renormalized determinant) in terms of spectral data and we show that no real saddle points exist. This relates to an instability under dilatations connected with the asymptotic freedom of the model. This result together with Zamolodchikov's S-matrix lead us to conjecture that the $\text{1}\text{N}$ series may be convergent for this model.     

Resistivity of dilute AlMg and AlMn between 0° and 100°C a generalized approach

We have measured the resistivity of $\text{Al}$Mg and $\text{Al}$Mn up to 0.5 at. % impurity concentration between 0° and 100°C. The results for the resistivity for both systems can be analysed within one generalized model in which spinfluctuations as well as changes in the electron-phonon interaction are considered. For $\text{Al}$Mn a calculation of the impurity contribution to d?/dT is attempted. For $\text{Al}$Mg there are indications that the superconducting T_c will increase with Mg concentration.     

Soft phonon mode at the martensitic phase transformation of AuCuZn2

The lattice dynamical property of AuCuZn₂ has been investigated by means of inelastic neutron scattering technique in connection with its martensitic phase transformation. The temperature dependent soft phonon was observed transformation. The temperature dependent soft phonon was observed around $\text{q =}\text{2}\text{3}\text{[110]}$ of TA₂ phonon branch. We have also found a premartensitic metastable phase, in which new satellite reflections at (H± $\text{2}\text{3}$, K ? $\text{2}\text{3}$, 0) have been observed around fundamental reflections with H + K = 4n. The atomic displacements of the soft phonon mode correspond to the atomic arrangement of the premartensitic phase.     

On universality for area-preserving maps of the plane

We present detailed evidence that one-parameter families of area-preserving maps exhibit cascades of period doubling with universal geometric scaling in the parameter. We relate this behaviour to a fixed point equation of the form

$\text{Λ}{}^{\mathrm{?1}}\text{°Φ°Φ°Λ = Φ}$

and

$\text{det}\text{DΦ = 1}$

, Φ:$\text{R}$²→$\text{R}$². In particular we argue that the scaling transformation Λ:$\text{R}$²→$\text{R}$² is conjugate to the transformation Λ₀:(x, y)→(λx, μy), with λ² ≠ μ, and in fact λ² >μ. We present some numerical evidence that

$\text{δ = 8.721}$

…,

$\text{?}\text{1}\text{λ}\text{= 4.018}$

…,

$\text{1}\text{μ}\text{= 16.36}$

…, where δ is the asymptotic ratio of the differences of the parameter values corresponding to the successive periods 2^k described above.