A limit theorem for stochastic acceleration

We consider the motion of a particle in a weak mean zero random force fieldF, which depends on the position,x(t), and the velocity,v(t)= (t). The equation of motion is (t)=F(x(t),v(t), ), wherex(·) andv(·) take values in ^d ,d3, and ranges over some probability space. We show, under suitable mixing and moment conditions onF, that as 0,v (t)v(t/²) converges weakly to a diffusion Markov processv(t), and ² x (t) converges weakly to , wherex=lim ² x (0).     

Quantized IR properties reconfirmed in the CO and SiO surface oscillators present in the surface layer of A bamboo stem

From analysis of diffusion diagrams of CO stretching band (25002180 cm^–1), bending band (800200 cm^–1) and SiO stretching band (1100700 cm^–1) measured in a skin surface layer of a bamboo stem (silicate cellulose), azimuthal directions where oscillators oriented were shown as ('=-90) _N=a·N-b, with a=28.3, 2×28, 22.7, b=25, 47.5, 10. And N=1,2.....14, N=1, .....6. N=1,2.....16. The optical activity (reflection integral) was shown for the CO stret. band as M_i(N)=a·N+b, with a=21.8, b=42 and N =1,2.....9. And for the bending band as M_i(N)=a·N² +b·N–c, with a=1.87×10¹, b=3.73×10³, c=7.06×10² with N=1,2.....9. Six stepnized fine series in CO weak reflection bands were confirmed as, and with N=1,2.....22. Mean values of the vibrational quantized states of the A, B and C-series in the SiO stretching weak band with R1.0% were shown as, (meV) with .     

Computer simulation of shock waves in the completely asymmetric simple exclusion process

We study the evolution of the completely asymmetric simple exclusion process in one dimension, with particles moving only to the right, for initial configurations corresponding to average density _– ( ₊) left (right) of the origin, _{– +}. The microscopic shock position is identified by introducing a second-class particle. Results indicate that the shock profile is stable, and that the distribution as seen from the shock positionN(t) tends, as time increases, to a limiting distribution, which is locally close to an equilibrium distribution far from the shock. Moreover , withV=1– _–– ₊, as predicted, and the dispersion ofN(t), ²(t), behaves linearly, for not too small values of ₊– _–, i.e., , whereS is equal, up to a scaling factor, to the valueS _WA predicted in the weakly asymmetric case. For ₊= _– we find agreement with the conjecture .Dedicated to the memory of Paola Calderoni.     

Masses ofq 2 \bar q 2 states in a Bethe-Salpeter model

Ground-state masses ofq ^{2 –2} states (true and mock baryonium) are investigated in the framework of a Bethe-Salpeter formalism motivated from QCD. The four-particle system is described by pairwise interactions betweenqq orq pairs with a spectator approximation for the non-interacting pair. The quark-quark interactions are Coulomb plus harmonic interactions; the harmonic terms have been modified to produce linear confinement for heavier quarks, in agreement with experimental spectra. The confining interaction is proportional to the strong coupling constant _s. Apart from the quark masses, the confining interaction is characterized by three basic parameters: (i) a universal spring constant ₀; (ii) a constantC ₀/ ₀ ² , which defines the vacuum structure; (iii) a constantA ₀, which provides a smooth transition from quadratic to linear confinement as one goes from light to heavy quark systems. These three constants [ ₀ = 0.158 GeV;C ₀=0.296;A ₀=0.0283] have been shown to produce excellent fits to all quarkonia states [q ,q ,Q ] as well as baryon spectra (qqq); thus our predictions forq ^{2 2} states contain no free parameters. In this model, theL=0 ground states occur in the range 1.8–2 GeV, 2.15–2.3 GeV and 6.72–6.75 GeV foru ^{2 2},s ^{2 2} andc ^{2 2} states, respectively. We discuss the prospects for these states to be seen experimentally. In the case of thes ^{2 2} state, this is likely to have a rather narrow width, and may correspond to theX(2.22 GeV) meson observed in radiative decays of theJ/ meson. Thec ^{2 2} state might also be visible as a resonance with an appreciable width.Research supported in part by the National Science Foundation under grant NSF-PHY 86-06364Research supported in part by the U.S. Department of Energy     

Bound States in a Locally Deformed Waveguide: The Critical Case

We consider the Dirichlet Laplacian for astrip in with one straight boundary and a width , where $f$ is a smooth function of acompact support with a length 2b. We show that in the criticalcase, , the operator has nobound statesfor small .On the otherhand, a weakly bound state existsprovided . In thatcase, there are positive c ₁,c ₂ suchthat the corresponding eigenvalue satisfies for all sufficiently small.     

Ensemble and trajectory statistics in a nonlinear partial differential equation

We have examined the influence of parametric noise on the solution behavioru(t, x) of a nonlinear initial value() problem arising in cell kinetics. In terms of ensemble statistics, the eventual limiting solution mean and variance are well-characterized functions of the noise statistics, and and depend on . When noise is continuously present along the trajectory, and are independent of the noise statistics and . However, in their evolution toward and , both _u (t, x) and _u ² (t, x) depend on the noise and.     

Nonlocality of Equivariant Star Products on T*( RPn)

Lecomte and Ovsienko constructed SL _n+1(R)-equivariant quantization maps Q for symbols of differential operators on -densities on RP ⁿ . We derive some formulas for the associated graded equivariant star products on the symbol algebra Pol(T* RP ⁿ ). These give some measure of the failure of locality. Our main result expresses (for n odd) the coefficients C _p (·,·) of when = in terms of some new SL _n+1(C)-invariant algebraic bidifferential operators Z _p (·,·) on T* CP ⁿ and the operators (E + n/2 ± s)^–1 where E is the fiberwise Euler vector field and s {1, 2, ..., [p/2]}.     

Internal Lifschitz singularities for one dimensional Schrödinger operators

The integrated density of states of the periodic plus random one-dimensional Schrödinger operator ;f0,q _i ()0, has Lifschitz singularities at the edges of the gaps inSp(H ). We use Dirichlet-Neumann bracketing based on a specifically one-dimensional construction of bracketing operators without eigenvalues in a given gap of the periodic ones.     

Dependence of creep characteristics on temperature and applied stress in Zn-1.0 wt.% Cu during transformation

The change in the transient and steady state creep deformation of zinc-1.0 wt.% Cu alloy was studied under various constant stresses ranging from 45.80 MPa to 56.02 MPa in the temperature range from 473 K to 573 K. From the transient creep results, the peak values of transient creep parametersB andn found in this temperature zone can be ascribed to dissolution of-phase (Cu-rich phase). The transient creep parameterB is related to the steady state creep rate through the exponent. This exponent has been found to range from 0.8 to 0.3. At the dissolution temperature (513 K) of-phase, the steady state strain sensitivity parameter has been 0.30±0.01 at the steady state strain peaks which is characteristic of dislocation climb along-grain boundaries. The activation energies of the transient and steady state creep in the phase transformation region have been found to be 42 kJ/mole and 63 kJ/mole characterizing the cross slipping of dislocations and dislocation climb along grain boundaries, respectively.     

Entropy functionals of Kolmogorov-Sinai type and their limit theorems

Two functionals and are introduced forC ^*-dynamical systems with invariant states and stationary channels. It is shown that the Kolmogorov-Sinai-type theorems hold for these functionals and . Our functionals and are set within the framework of quantum information theory and generalize a quantum KS entropy by CNT and the mutual entropy by Ohya.     

The metal-semiconductor transition in amorphous Si1−x Cr x films:T 0.19-contribution to the metallic conductivity

A detailed phenomenological re-analysis of previously published conductivity data, (T, x), is presented. It is based on the investigation of differences, (T, x ₁)–(T, x ₂). In this way, the cusp-like low-temperature term is amplified against the other temperature dependent contributions. This term can be described by wherep=0.19±0.03. It is present, if (4.2 K,x) exceeds 260 ^–1 cm^–1, at least up to (4.2 K,x)1350 ^–1 cm^–1 and forT60 K. But it is absent, if (4.2 K,x)180 ^–1 cm^–1. The disappearance of this contribution should be related to the metal-semiconductor transition, taking place atx _c 0.14. On the other hand, the presence of a term proportional toT ^1/2, as predicted by Altshuler and Aronov, seems unlikely.It is argued that the term should be related to the interplay of electron-electron interaction and disorder. The comparison with data from the literature shows that this contribution might also be present in heavily doped crystalline semiconductors.     

The van der Waals limit for classical systems

For a -dimensional system of particles with the two-body potentialq(r)+ ^v K(r) and density , it is proved under fairly weak conditions onq andK that the canonical pressure (, ) and chemical potential (, ) tend to definite limits when 0. The limiting functions are absolutely continuous and are given in terms of the derivative of the limiting free energy density which was found in Part I.     

Search for muon to electron neutrino oscillations

A search for _e and oscillations has been carried out with the CHARM II detector exposed to the CERN wide band neutrino beam. The data were collected over five years, alternating beams mainly composed of muon-neutrinos and muon-antineutrinos. The number of interactions of _e and observed is comparable with the number of events expected from flux calculations. For large squared mass differences the upper limits obtained on the mixing angle aresin ²2 < 9.4=" ·=">^–3 for oscillating to _e andsin ²2 < 4.8=" ·=">^–3 for to , at the 90% confidence level. Combining neutrino and antineutrino data the upper limit is 5.6 · 10^–3.On leave of absence from ITEP (Moscow)     

Minimal supersymmetric standard model with the gauge mediated supersymmetry breaking and the neutrinoless double-beta decay

Neutrinoless double-beta decay within Minimal Supersymmetric Standard Model with gauge mediated supersymmetry breaking is considered. Limits on R-parity breaking constant coming from non-observability of 0 in ⁷⁶Ge are found. The dependence of on different parameters at the messenger scale M are shown, with special attention paid to nuclear part of calculations. We have found that strongly depends on the effective supersymmetry breaking scale only and deduced limits imposed on this non-standard parameter by the germanium experiment.     

Preferred Invariant Symplectic Connections on Compact Coadjoint Orbits

Let be the Haag--Kastler net generated by the (2) chiral current algebra at level 1. We classify the SL(2, )-covariant subsystems by showing that they are all fixed points nets ^H for some subgroup H of the gauge automorphisms group SO(3) of . Then, using the fact that the net ₁ generated by the (1) chiral current can be regarded as a subsystem of , we classify the subsystems of ₁. In this case, there are two distinct proper subsystems: the one generated by the energy-momentum tensor and the gauge invariant subsystem .     

On General Plane Fronted Waves. Geodesics

A general class of Lorentzian metrics, , , with any Riemannian manifold, is introduced in order to generalize classical exact plane fronted waves. Here, we start a systematic study of their main geodesic properties: geodesic completeness, geodesic connectedness and multiplicity causal character of connecting geodesics. These results are independent of the possibility of a full integration of geodesic equations. Variational and geometrical techniques are applied systematically. In particular, we prove that the asymptotic behavior of H(x,u) with x at infinity determines many properties of geodesics. Essentially, a subquadratic growth of H ensures geodesic completeness and connectedness, while the critical situation appears when H(x,u) behaves in some direction as , as in the classical model of exact gravitational waves.     

Is the channelH \to b\bar b observable at LHC?

A detailed study of associated Standard Model Higgs production (WH and ) at the LHC (or a possible upgraded Tevatron collider), where the Higgs boson decays to pairs, is reported for 80m _H <120 gev.=" even=" for=">b-tagging performances of the detector, the signal cannot be cleanly extracted from the background. For an integrated luminosity of 10⁴ pb ^–1 andm _H =100 GeV, one can expect at best 110 reconstructed decays fromWH production, above a resonant background of 150WZ events and a non-resonant background of 4800 events, and 100 reconstructed pairs (of which 50 from decay) from production, above a background of 4000 events. The main difficulty in extracting these two channels is in the expected low signal rate after reconstruction, the need for accurate control of all the background sources and for extremely goodb-tagging performance. Nevertheless, for a few years of running at a luminosity of 10³³ cm^–2s^–1, channel may be the best way to probe the region 80m _H <100>     

Eigenvalue Asymptotics for the Schrödinger Operator with a δ-Interaction on a Punctured Surface

Given n2, we put r=min . Let be a compact, C ^r -smooth surface in ⁿ which contains the origin. Let further be a family of measurable subsets of such that as . We derive an asymptotic expansion for the discrete spectrum of the Schrödinger operator in L ²( ⁿ ), where is a positive constant, as . An analogous result is given also for geometrically induced bound states due to a interaction supported by an infinite planar curve.     

On two “self-creation” cosmologies

An attempt to produce a continuous creation theory by adapting the Brans-Dicke theory is described. The universe is seen to be created out of self-contained gravitational, scalar, and matter fields. However, the solution of the one-body problem reveals unsatisfactory characteristics of the theory, and in particular the principle of equivalence is severely violated. A second theory is described which retains the attractive features of the first theory and which does not fall foul of its objections. There do exist empirical tests for the theory which are described and which will require further examination. In the limit this theory approaches general relativity in every respect.Notation ² gf the invariant d'Alembertian - t ₀ Hubble time - H Hubble's constant - scalar field - coupling constant - T _M energy-momentum tensor of matter and nongravitational energy, and nonscalar field energy - T _M energy-momentum tensor of scalar field energy - T _M covariant form - T _M contravariant form - T _M mixed form - T _M T _M trace - T _{M ;} covariant differentiation - contravariant differentiation - T Ricci tensor - R curvature scalar (in tensorial equations) - Kronecker symbol - () a function of used in the text - density - p pressure - g the metric tensor - R(t) scale factor (in cosmological equations) - U the fluid 4-velocity (covariant) - U the fluid 4-velocity (contravariant) - functions differentiated once with respect to time ( , differenciated twice) - k the Robertson-Walker curvature constant=+1, 0, or –1 - proportional to - g gravitational coefficient - parameter - angle of deflection, or coordinate - angle of precession or coordinate - angle of precession - G _v the force density - ³( – _n (t)) the Dirac delta function - proper time - K an unknown function definingG - total angle of deflection - r ₀ minimum radius of approach of a light ray grazing the sun