Kinetic equation in the kinetic region of the dilute and nonuniform electron plasma

Mori's scaling method is used to derive the kinetic equation for a dilute, nonuniform electron plasma in the kinetic region where the space-time cutoff (b, t _c) satisfies _Dbl _f , _D t _{c f} , with _D the Debye length, _D ^–1= _p the plasma frequency, andl _f and _f the mean free path and time, respectively. The kinetic equation takes account of the nonuniformity of the order ofl _f and _D for the single-and the two-particle distribution function, respectively. Thus the Vlasov term associated with the two-particle distribution function is retained. This kinetic equation is deduced from the kinetic equation in the coherent region obtained by Morita, Mori, and Tokuyama, where the space-time cutoff of the coherent region satisfies _Dbr ₀, _Dt _{c 0}, withr ₀ the Landau length and ₀ the corresponding time scale.     

A study of the decays of tau leptons produced on theZ resonance at LEP

From the analysis of a data sample corresponding to an integrated luminosity of 4.63 pb^–1 taken during the 1990 run of LEP at centre of mass energies between 88.2 GeV an 94.2 GeV, the tau decays and their charge conjugates have been studied. The following branching ratios have been measured; , , Br(^{– –} (K^–)v)=11.9±0.7±0.7%, BR (^{– –} v)= 22.4±0.8±1.3%, in good agreement with world averages. The measured electronic and muonic branching ratios lead to a measurement of the strong coupling constant, _s (m) = 0.26 _–0.12 ^+0.09 . Extrapolating the _s value fromm tom _Z yields _s (m_Z) = 0.109 _–0.028 ^+0.012 .The average polarizationP of taus produced in Z ^{s s} decays has also been measured using the above decay modes. The weighted mean of the polarizations obtained from the four decay modes isP =–0.24±0.07. This value ofP gives, in the improved Born approximation, a ratio between the axial and vector coupling constants of the tau of /a = 0.12 ± 0.04, and hence a value of the effective electroweak mixing parameter sin² _W(m _Z ² ).     

Tau decays into K* mesons

Using the ARGUS detector at the storage ring DORIS II we have measured decays into three charged mesons containingK ^* mesons. Exploiting the good particle identification capabilities of the detector we have determined the following branching ratios: ,B _r (^–K ^*0 K ^– v )= (0.20±0.05±0.04)%, andB _r (^–K ^*– X ⁰ v ) =(1.15±0.15_–0.18 ^+0.13)%.Supported by the German Bundesministerium für Forschung und Technologie, under contract number 054DO51P.     

On the total cross-section for thermal neutrons of hydrogen in niobium

Neutron transmission experiments have been performed to determine the total cross-section of hydrogen interstitially dissolved in niobium. The wavelength and temperature dependence of the total cross-section can be described by a model with the protons as harmonic oscillators. No changes in the total cross-section were found for the different phases of the interstitials in the niobium host lattice. An upper limit for the jump-time of a proton in diffusion _D is given compared to its mean time of localization _L on an interstitial site. _D <0.2 _L is found.     

Effect of Phase-Sensitive Reservoir on the Decoherence of Pair-Cat Coherent States

We study the decoherence of a superposition of four coherent states under the action of a phase sensitive reservoir. We verify that the decoherence times _k,l, k,l=1,2,3,4, between any two coherent states of the superposition can be controlled through the reservoir parameters. The decoherence time between two components of any pair, for instance _1,2 or _3,4, can be significantly increased, compared with the decoherence time when the state is acted by a thermal reservoir. However, this occurs at the expense of decreasing the decoherence time between the ``cat states" (1,2) and (3,4). This can be useful in quantum computation.     

Holes in the probability density of strongly colored noise driven systems

A qualitative change in the topology of the joint probability densityP(,x), which occurs for strongly colored noise in multistable systems, has recently been observed first by analog simulation (F. Moss and F. Marchesoni,Phys. Lett. A 131:322 (1988)) and confirmed by matrix continued fraction methods (Th. Leiber and H. Riskin, unpublished), and by analytic theory (P. Hänggi, P. Jung, and F. Marchesoni,J. Stat. Phys., this issue). Systems studied were of the classx=–U(x)/x+(t,), whereU(x) is a multistable potential and (t, ) is a colored, Gaussian noise of intensityD, for which =0, and (t) (s)=(D/)exp(–t–s/). When the noise correlation time is smaller than some critical value ₀, which depends onD, the two-dimensional densityP(,x) has the usual topology [P. Jung and H. Risken,Z. Phys. B 61:367 (1985); F. Moss and P. V. E. McClintock,Z. Phys. B 61:381 (1985)]: a pair of local maxima ofP(,x), which correspond to a pair of adjacent local minima ofU(x), are connected by a single saddle point which lies on thex axis. When >₀, however,the single saddle disappears and is replaced by a pair of off-axis saddles. A depression, or hole, which is bounded by the saddles and the local maxima thus appears. The most probable trajectory connecting the two potential wells therefore does not pass through the origin for >₀, but instead must detour around the local barrier. This observation implies that successful mean-first-passage-time theories of strongly colored noise driven systems must necessarily be two dimensional (Hänggiet al.). We have observed these holes for several potentialsU(x): (1)a soft, bistable potential by analog simulation (Moss and Marchesoni); (2) a periodic potential [Th. Leiber, F. Marchesoni, and H. Risken,Phys. Rev. Lett. 59:1381 (1987)] by matrix continued fractions; (3) the usual hard, bistable potential,U(x)=–ax ²/2+bx ⁴/4, by analog simulations only; and (4) a random potential for which the forcingf(x)=–U(x)/x is an approximate Gaussian with nonzero correlation length, i.e., colored spatiotemporal noise, by analog simulation. There is a critical curve ₀(D) in the versusD plane which divides the two topological behaviors. For a fixed value ofD, this curve is shifted toward larger values of ₀ for progressively weaker barriers between the wells. Therefore, strong barriers favor the observation of this topological transformation at smaller values of . Recently, an analytic expression for the critical curve, valid asymptotically in the small-D limit, has been obtained (Hänggiet al.).This paper will appear in a forthcoming issue of theJournal of Statistical Physics.     

A study of ultraviolet renormalon ambiguities in the determination of α s from τ decay

The divergent large-order behaviour of the perturbative series relevant for the determination of _s from decay is controlled by the leading ultraviolet (UV) renormalon. Even in the absence of the first infrared (IR) renormalon, an ambiguity of order ²/m ² is introduced. We make a quantitative study of the practical implications of this ambiguity. We discuss the magnitude of UV renormalon corrections obtained in the large-N _f limit, which, although unrealistic, is nevertheless interesting to some extent. We then study a number of improved approximants for the perturbative series, based on a change of variable in the Borel representation, such as to displace the leading UV renormalon singularity at a larger distance from the origin than the first IR renormalon. The spread of the resulting values of _s (m ²) obtained by different approximants, at different renormalization scales, is exhibited as a measure of the underlying ambiguities. Finally, on the basis of mathematical models, we discuss the prospects of an actual improvement, given the signs and magnitudes of the computed coefficients, the size of _s (m ²) and what is known of the asymptotic properties of the series. Our conclusion is that a realistic estimate of the theoretical error cannot go below _s (m ²)±0.060, or _s (m _Z ²)±0.006.On leave of absence from INFN, Sezione di Milano, Milan, Italy     

How to measure the magnetic moment of the tau lepton

We present a method for obtaining bounds on the magnetic moment of the lepton. In order to do this, we study the radiative decayW as a function of the anomalous magnetic moment of the ,a . One can obtain bounds as good asa < 4.05×10^–2, 2.25×10^–2, 4.5×10^–3, and 2.5×10^–3 at the present Fermilab, future Fermilab, SSC, and LHC, respectively.     

Square root singularity in the viscosity of neutral colloidal suspensions at large frequencies

The asymptotic frequency, , dependence of the dynamic viscosity of neutral hard-sphere colloidal suspensions is shown to be of the form ₀A()(_p)^-1/2, whereA() has been determined as a function of the volume fraction , for all concentrations in the fluid range, ₀ is the solvent viscosity, and _p is the Péclet time. For a soft potential it is shown that, to leading order in the steepness, the asymptotic behavior is the same as that for the hard-sphere potential and a condition for the crossover behavior to 1/_p, is given. Our result for the hardsphere potential generalizes a result of Cichocki and Felderhof obtained at low concentrations and agrees well with the experiments of van der Werffet al. if the usual Stokes-Einstein diffusion coefficientD ₀ in the Smoluchowski operator is consistently replaced by the short-time self-diffusion coefficientD _s() for nondilute colloidal suspensions.     

From the eden model to the kinetic growth walk: A generalized growth model with a finite lifetime of growth sites

We propose a new class of cluster growth models where growth sites have a finite lifetime , which contains as special cases the Eden model ( = ) and the kinetic growth walk ( = 1). For finite but large values the growth process can be characterized by a crossover timet _X; for times belowt _X an Eden-type cluster is formed, while for times abovet _X the growth process belongs to the universality class of the self-avoiding random walk. The crossover time increases monotonically with . We develop a scaling theory for the time evolution of the mean end-to-end distance between the seed and the last-added site, and for the average number of growth sites by which the kinetics of the growth process can be characterized. We test this scaling theory by extensive Monte Carlo simulations. We also extend our results to inhomogeneous media (percolation systems).     

The Landau-Pomeranchuk effect and soft lepton-pair production in heavy ion collisions

The most general angular decay distribution of the hadronic system in the decay of a polarized into one pseudoscalar plus a vector is calculated. Emphasis is put on decays ine ⁺ e ^– experiments where the neutrino escapes detection and the restframe cannot be reconstructed. We propose a model for the decay intov involving both a vector- and a second class axial vector-current contribution. Then we present numerical results for this decay channel.     

The magnetic structures of NdCu2 determined by single crystal neutron diffraction

We investigated the magnetic structure of NdCu₂ by means of neutron diffraction as a function of temperature between 1.5 K and 8 K in zero external field. The diffraction data were obtained on two single crystals with different orientations using the triple-axis-spectrometer TAS6 at the DR-3 reactor at Risø. Two magnetic phases were observed between 1.5K andT _N =6.5K. From 1.5 K to 4.1 K the magnetic reflections can be described by the commensurate wave vector =(3/5 0 0) and its higher harmonics 3 and 5. Below 2.5K the structure is completely squared-up. For 4.1 KT6.5 K the magnetic structure is incommensurate with the chemical lattice and can be described by the wave vector=(3/5 0 0) and its higher harmonies 3 and 5M. Below 2.5 K the structure is completely squared-up. For 4.1 K T 6.5 K the magnetic structure is incommensurate with the chemical lattice and can be described by the wave vector ^*=(0.62 0.044 0). In both phases the Nd-moments are oriented along the easyb-direction.     

Percolation cluster numbers by real-space renormalization

The average numbern _s (p) of percolation clusters withs sites is calculated for the triangular lattice using real-space renormalization. Fors up to 2,000 the whole range of concentrationsp was analyzed;n _s varied over sixty decades. We found logn _s –s forp belowp _c =0.5, andn _s s ^–, =2.35 atp=p _c . For smallp one hasn _s (p · ) ^s . Nearp _c we found the scaling fromn _s s ^– f((p _c –p) ·s ) with=0.53. Presumably for the first time renormalization methods were used to calculate percolation properties not only nearp _c but also far away from the critical point.Sonderforschungsbereich 125 Aachen-Jülich-Köln     

Closed timelike smooth curves in the general theory of relativity

For a space-time which admits a closed timelike smooth curve it is estimated that 2 · 10^–24 · l ², where is the real time andl the spatial length associated with the timelike curve, and is the density of material.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, Vol. 16, No. 9, pp. 33–36, September, 1973.     

Derivations commuting with abelian gauge actions on lattice systems

Let be an action of a compact abelian groupG on aC*-algebraA, and assume that the fixed-point subalgebraA is an AF-algebra. We show that if is a closed *-derivation onA commuting with , and the restriction of toA generates a one-parameter group of *-automorphisms, then itself is a generator. In particular, the result applies if is an infinite product action ofG on a UHF algebra. Furthermore, if in this situation ₁ and ₂ are two derivations both satisfying the hypotheses on , and ₁ and ₂ have the same restriction toA , then there exists a one-parameter subgroup of the action with generator ₀ such thatD(₁)D(₂)D(₀) is a joint core for the three derivations, and ₂=₁+₀ on this core.     

Estimates of general Mayer graphs. II. Long-range behavior of graphs with two root points occurring in the theory of ionized systems

We find the asymptotic behavior of general Mayer 2-graphs (Mayer graphs with two root points), which occur in the theory of ionized systems. This problem arises when one wants to compute corrections to the Debye length for large values of the plasma parameter. For a given 2-graph (r) with Debye-Hückel linese ^– /r, we prove the inequalitiesC _m r ^– e ^– (r) (r ₀)C_Mr^3k–l e ^– , for anyrr ₀, and whereC _m andC _M are positive and finite constants which depend only on . These bounds are finite whenever (r) is not infinite everywhere. The integersl, k, and denote, respectively, the number of lines of the graph , its number of field points, and its local line connectivity (the maximum number of chains linking the root points, which have no line in common). From this result, we deduce that the simple irreducible 2-graphs dominant at large distances decay exponentially likee ^– and have an isthmus between the root points (an isthmus is a line whose deletion separates the graph into two disjoint components, each one containing a root point). We prove also that 2-graphs that have a number of linesl > 3k+ are infinite. We exhibit simple, irreducible prototypes satisfying this condition, for anyk 6. This implies that the Abe-Meeron theory of ionized gases as applied to a classical plasma is not free from divergences. Finally, we extend the preceding results to 2-graphs with lines F_L=(e ^– /r)^k L, withk _L real positive. We prove that they still decay exponentially likee ^– , where is now the maximal flow in a network associated to by assigning the capacityk _L to each lineL.     

A matrix method for estimating the Liapunov exponent of one-dimensional systems

Let : [0, 1][0, 1] be a piecewise monotonie expanding map. Then admits an absolutely continuous invariant measure. A result of Kosyakin and Sandler shows that can be approximated by a sequence of absolutely continuous measures _n invariant under piecewise linear Markov maps _itn. Each _itn is constructed on the inverse images of the turning points of . The easily computable measures _n are used to estimate the Liapunov exponent of . The idea of using Markov maps for estimating the Liapunov exponent is applied to both expanding and nonexpanding maps.     

Measurement of the magnetic dipole moment of the 57 keV state of143Pr by time-differential perturbed angular correlation technique

The magnetic dipole interaction of the 57 keV state of¹⁴³Pr in an environment of metallic cerium and in an aqueous solution of Ce(NO₃)₃ has been investigated by time-differential perturbed angular correlation experiments. The measurements were performed in external magnetic fields between 0.94 T and 2.24 T and at temperatures between 77 K and 1200 K. From the temperature dependence of the observed spin rotation the ionicity of the Pr ion is determined as Pr⁴⁺ in the Ce(NO₃)₃ and as Pr³⁺ in Ce metal in the intermediate nuclear state. The magnetic dipole moment of the 57 keV state is derived as = +(3.4±0.1)_K. From the room temperature relaxation constants ₂ = (0.19±0.03)10⁹s^–1 for Ce(NO₃)₃ and ₂= (0.07±0.02)10⁹s^–1 for Ce metal the correlation times _J = (3.8±0.7)10^–13s and _J = (1.4±0.4)10^–13s respectively are deduced. The angular correlation coefficientA ₂=+0.17±0.02 is in good agreement with the result of a decoupling experiment.     

Infrared behaviour of metallic systems in one, two and three dimensions

A simple approximate expression for the electron lifetime() in metals is rederived and discussed for different dimensions. In the 3D-case we get the well known Drude behaviour, i.e. a constant. In one dimension() is strongly frequency-dependent in the IR. The 2D-case is intermediate to the preceding ones. These results are essentially due to the different form of the Fermi surface for an electron gas in one, two and three dimensions.