Maximum of a Fractional Brownian Motion: Probabilities of Small Values

Let b _γ (t), b _γ(0)= 0 be a fractional Brownian motion, i.e., a Gaussian process with the structure function , 0 < γ < 2. We study the logarithmic asymptotics of P _T = P{b _γ (t) < 1,□t∈TΔ} as T→∞, where Δ is either the interval (0,1) or a bounded region that contains a vicinity of 0 for the case of multidimensional time. It is shown that ln P _T = - D ln T(1 + o(1)), where D is the dimension of zeroes of b _γ (t) in the former case and the dimension of time in the latter. Received: 28 September 1998 / Accepted: 19 February 1999     

Study of the reaction γp → pπ0η

The reaction γp → pπ⁰η has been studied with the CBELSA detector at the tagged photon beam of the Bonn electron stretcher facility. The reaction shows contributions from Δ⁺(1232)η , N(1535)⁺π⁰ and pa ₀(980) as intermediate states. A partial-wave analysis suggests that the reaction proceeds via formation of six Δ -resonances, Δ(1600)P ₃₃ , Δ(1920)P ₃₃ , Δ(1700)D ₃₃ , Δ(1940)D ₃₃ , Δ(1905)F ₃₅ , Δ(2360)D ₃₃ , and two nucleon resonances N(1880)P ₁₁ and N(2200)P ₁₃ , for which pole positions and decay branching ratios are given.     

Quark momentum-space charge distribution in deuteron and neutron/proton structure functions ratio

The electromagnetic polarizabilities of the nucleon are shown to be essentially composed of the nonresonant α _p(E ₀₊) = + 3.2, α _n(E ₀₊) = + 4.1, the t-channel α ^t _{p, n} = - β ^t _{p, n} = + 7.6 and the resonant β _{p, n}(P ₃₃(1232)) = + 8.3 contributions (in units of 10^-4fm^3). The remaining deviations from the experimental data Δα _p = 1.2±0.6, Δβ _p = 1.2±0.6, Δα _n = 0.8±1.7 and Δβ _n = 2.0±1.8 are contributed by a larger number of resonant and nonresonant processes with cancellations between the contributions. This result confirms that dominant contributions to the electric and magnetic polarizabilities may be represented in terms of two-photon coupling to the σ-meson having the predicted mass m _σ = 666MeV and two-photon width Γ _γγ = 2.6keV.     

Kinetic processes of muonium formation by thermalized electrons in the spur model

Diffusion of a thermalized electron in the field of a Coulomb centre is considered. The time dependence of the probability for the electron not to be captured by the Coulomb centre ( ⁺) at the momentt,P _D (t), is obtained. The quantityP _D (t) coincides with the precession amplitude at the muon frequency and is determined by the parameter/l _CT ( is an averaged distance from an electron to a muon att=0 andl _CT =e ²/(2T) is the Onsager length) that reflects the relation between electron potential and kinetic energies at t=0. When/l _CT –1 the precession amplitudeP _D (t) decreases up to 30% during the timel _CT ² /D-(D-is the diffusion coefficient) and then it becomes almost constant. The dependence ofP _D () on/l _CT is presented.     

Diffusing wave spectroscopy of dense colloids: Liquid,crystal and glassy states

Using intensity autocorrelation of multiply scattered light, we show that the increase in interparticle interaction in dense, binary colloidal fluid mixtures of particle diameters 0.115μm and 0.089μm results in freezing into a crystalline phase at volume fractionφ of 0.1 and into a glassy state atφ=0.2. The functional form of the field autocorrelation functiong ⁽¹⁾(t) for the binary fluid phase is fitted to exp[−γ(6k ₀ ² D _eff t)^1/2] wherek ₀ is the magnitude of the incident light wavevector andγ is a parameter inversely proportional to the photon transport mean free pathl*. TheD _eff is thel* weighted average of the individual diffusion coefficients of the pure species. Thel* used in calculatingD _eff was computed using the Mie theory. In the solid (crystal or glass) phase, theg ⁽¹⁾(t) is fitted (only with a moderate success) to exp[−γ(6k ₀ ² W(t))^1/2] where the mean-squared displacementW(t) is evaluated for a harmonically bound overdamped Brownian oscillator. It is found that the fitted parameterγ for both the binary and monodisperse suspensions decreases significantly with the increase of interparticle interactions. This has been justified by showing that the calculated values ofl* in a monodisperse suspension using Mie theory increase very significantly with the interactions incorporated inl* via the static structure factor.     

The high-pressure-induced spin-reorientation transition in a ferromagnetic semiconductor Cd<Subscript>0.7</Subscript>Mn<Subscript>0.3</Subscript>GeAs<Subscript>2</Subscript>

The dependences of the longitudinal magnetoresistance (Δρ _zz /ρ₀)(P), transverse magnetoresistance (Δρ _xx /ρ₀)(P), and magnetic susceptibility (χ/χ₀(P)) on hydrostatic pressure P ≤ 7 GPa in the ferromagnetic semiconductor Cd_0.7Mn_0.3GeAs₂ at room temperature were investigated.     

Resonances and chaos in the collinear collision system (He,H 2 + ) and its isotopic variants

The collinear atom-diatom collision system provides one of the simplest instances of chaotic or irregular scattering. Classically, irregular scattering is manifest in the sensitive dependence of post-collision variables on initial conditions, and quantally, in the appearance of a dense spectrum of dynamical resonances. We examine the influence of kinematic factors on such dynamical resonances in collinear (He, H ₂ ⁺ ) collisions by computing the transition state spectra for collinear (He, HD⁺) and (He, DH⁺) collisions using the time-dependent quantum mechanical approach. The nearest neighbor spacing distributionP(s) and the spectral rigidity Δ₃(L) for these resonances suggest that the dynamics is predominantlyirregular for collinear (He, HD⁺) and predominantlyregular for collinear (He, DH⁺). These findings are reinforced by a significantly larger “correlation hole” in ensemble averaged survival probability ≪P(t)≫ values for collinear (He, HD⁺) than for collinear (He,DH⁺). In addition we have also examined measures of classical chaos through the dependence of the final vibrational action,n _f, on the initial vibrational phaseφ _i of the diatom, and Poincaré surfaces-of-section. They show that (He, HD⁺) collisions are partly chaotic over the entire energy range (0–2.78 eV) while (He, DH⁺) collisions, in contrast, are highly regular at collision energies below the classical threshold for reaction. Above the threshold, the scattering remains regular for initial vibrational statesv=0 and 1 of DH⁺.     

Interactions of charmed mesons with nucleons in the ¯<Emphasis Type="Italic">p</Emphasis><Emphasis Type="Italic">d</Emphasis> reaction

We study the possibility to measure the elastic ΦN (Φ≡J/ψ,ψ(2S), ψ(3770), χ_2c) scattering cross section in the reaction ˉp+d→Φ+n _sp and the elastic D(ˉD)N scattering cross section in the reaction ˉp+d→D ⁻ D ⁰ p _sp. Our studies indicate that the elastic scattering cross sections can be determined for Φ momenta about 4–6 GeV/c and D/ˉD momenta 2–5 GeV/c by selecting events with p _t≥ 0.4 GeV/c for Φ's and p _t(p _sp) ≥ 0.5 GeV/c for D/ˉD-meson production. Received: 8 November 1999     

Multichannel calculation of the very narrow D<Subscript>s0</Subscript><Superscript>*</Superscript>(2317) and the very broad D<Subscript>0</Subscript><Superscript>*</Superscript>(2300-2400)

The narrow D _s0 ^* (2317) and broad D ₀ ^* (2300-2400) charmed scalar mesons and their radial excitations are described in a coupled-channel quark model that also reproduces the properties of the light scalar nonet. All two-meson channels containing ground-state pseudoscalars and vectors are included. The parameters are chosen fixed at published values, except for the overall coupling constant λ, which is fine-tuned to reproduce the D _s0 ^* (2317) mass, and a damping constant α for subthreshold contributions. Variations of λ and D ₀ ^* (2300-2400) pole postions are studied for different α values. Calculated cross-sections for S-wave DK and Dπ scattering, as well as resonance pole positions, are given for the value of α that fits the light scalars. The thus predicted radially excited state D _s0 ^*′(2850), with a width of about 50MeV, seems to have been observed already.     

Analysis of supersonic flow around two bodies of revolution near a surface

The results of experimental and numerical investigations of the peculiarities of flow around two identical cylindrical bodies of revolution of diameter D = 50 mm and the body aspect ratio λ = 5 with conical forebodies whose apex angles are θ = 40° and 60°, which are located above a horizontal surface in parallel with one another and with the flow, are presented for the Mach numbers M_∞ = 4.03, Reynolds numbers Re₁ ≈ 55·10⁶ m⁻¹, fixed distance from the surface Y = Δy/D = 0.96, and the gaps between their axes Z = Δz/D = 1.06−2.4. The peculiarities of three-dimensional turbulent separated flows realizing on the bodies and on the plate as well as the possibilities of predicting the aerodynamic forces and moments acting on the bodies on the basis of numerical computations within the framework of the Euler equations are considered.     

Effective nonlinear optical properties of shape distributed composite media

The effective linear and nonlinear optical properties of metal/dielectric composite media, in which ellipsoidal metal inclusions are distributed in shape, are investigated. The shape distribution function P(L _x, L _y) is assumed to be 2Δ^-2θ(L _x - 1/3 + Δ/3)θ(L _y - 1/3 + Δ/3)θ(2/3 + Δ/3 - L _x - L _y), where θ( ^{. . .} ) is the Heaviside function, Δ is the shape variance and L_i are the depolarization factors of the ellipsoidal inclusions along i-symmetric axes (i = x, y). Within the spectral representation, we adopt Maxwell-Garnett type approximation to study the effect of shape variance Δ on the effective nonlinear optical properties. Numerical results show that both the effective linear optical absorption α ∼ ωIm() and the modulus of the effective third-order optical nonlinearity enhancement |χ⁽³⁾ _e|/χ⁽³⁾ ₁ exhibit the nonmonotonic behavior with Δ. Moreover, with increasing Δ, the optical absorption and the nonlinearity enhancement bands become broad, accompanied with the decrease of their peaks. The adjustment of Δ from 0 to 1 allows us to examine the crossover behavior from no separation to large separation between optical absorption and nonlinearity enhancement peaks. As Δ → 0, i.e., the ellipsoidal shape deviates slightly from the spherical one, the dependence of |χ⁽³⁾ _e|/χ⁽³⁾ ₁ on Δ becomes strong first and then weak with increasing the imaginary part of inclusions' dielectric constant. In the dilute limit, the exact formula for the effective optical nonlinearity is derived, and the present approximation characterizes the exact results better than old mean field one does. Received 10 December 2002 Published online 4 June 2003 RID="a" ID="a"e-mail: lgaophys@pub.sz.jsinfo.net     

Adaptive Sub-sampling for Parametric Estimation of Gaussian Diffusions

We consider a Gaussian diffusion X _t (Ornstein-Uhlenbeck process) with drift coefficient γ and diffusion coefficient σ ², and an approximating process Y^e_tY^{\varepsilon}_{t} converging to X _t in L ₂ as ε→0. We study estimators [^(g)]_e\hat{\gamma}_{\varepsilon}, [^(s)]²_e\hat{\sigma}^{2}_{\varepsilon} which are asymptotically equivalent to the Maximum likelihood estimators of γ and σ ², respectively. We assume that the estimators are based on the available N=N(ε) observations extracted by sub-sampling only from the approximating process Y^e_tY^{\varepsilon}_{t} with time step Δ=Δ(ε). We characterize all such adaptive sub-sampling schemes for which [^(g)]_e\hat{\gamma}_{\varepsilon}, [^(s)]²_e\hat{\sigma}^{2}_{\varepsilon} are consistent and asymptotically efficient estimators of γ and σ ² as ε→0. The favorable adaptive sub-sampling schemes are identified by the conditions ε→0, Δ→0, (Δ/ε)→∞, and NΔ→∞, which implies that we sample from the process Y^e_tY^{\varepsilon}_{t} with a vanishing but coarse time step Δ(ε)≫ε. This study highlights the necessity to sub-sample at adequate rates when the observations are not generated by the underlying stochastic model whose parameters are being estimated. The adequate sub-sampling rates we identify seem to retain their validity in much wider contexts such as the additive triad application we briefly outline.     

Weak nonleptonic decays of 3/2+ isobars in SU(3)

Weak transitions of decuplet isobars are expanded in terms of eigen-amplitudes of the direct channel in the framework of SU(3). Starting with the most general weak Hamiltonian and assuming intermediate states to be non-exotic, we obtain ΔI=1/2 rule for Ω⁻ decays. Invoking of the CP invariance forbids all thepv weak processesD(10)→D(10) +P(8). Decays of the charmed multiplets are also discussed in these dynamical considerations. We obtain triplet dominance of charm changing weak Hamiltonian for Ω*⁺⁺ ₃ decays.     

Photoproduction of baryons decaying into Nπ and Nη

A combined analysis of photoproduction data on γp↦ πN, ηN was performed including the data on KΛ and KΣ. The data are interpreted in an isobar model with s-channel baryon resonances and π, ρ (ω), K, and K ^* exchange in the t-channel. Three baryon resonances have a substantial coupling to ηN, the well-known N(1535)S ₁₁, N(1720)P ₁₃, and N(2070)D ₁₅. The inclusion of data with open strangeness reveals evidence for further new resonances, N(1840)P ₁₁, N(1875)D ₁₃ and, with weaker evidence, for N(2170)D ₁₃.     

Tails in harnesses

We consider space- and time-uniformd-dimensional random processes with linear local interaction, which we call harnesses and which may be used as discrete mathematical models of random interfaces. Their components are rea random variablesa _s ^t , wheres ∈ Z ^d andt=0, 1, 2.,... At every time step two events occur: first, every component turns into a linear combination of itsN neighbors, and second, a symmetric random i.i.d. “noise”v is added to every component. For any σ ∈Z _d ⁺ define Δ_σ a′ _s as follows. If σ=(0,...,0), σ=(0,...,0), Δ_σ a _s ^t =a _s ^t . Then by induction, wheree _i is thed-dimensional vector, whoseith component is one and other components are zeros. Denote |σ| the sum of components of σ. Call a real random variable ϕ symmetric if it is distributed as −ϕ. For any symmetric random variable ϕpower decay or P-decay is defined as the supremum of thoser for which therth absolute moment of ϕ is finite. Convergence a.s., in probability and in law whent→∞ is examined in terms of P-decay(v): Ifd=1, σ=0 ord=2, σ=(0,0), Δ_σ a _s ^t diverges. In all the other cases: If P-decay(v)<(d+2)/(d+|σ|), Δ_σ a _s ^t diverges; if P-decay(v)>(d+2)/(d+|σ|), Δ_σ a _s ^t , converges and P-decay(ν) For any symmetric random variable ϕexponential decay or E-decay is defined as the supremum of thoser for which the expectation of exp(|x|^r) is finite. Let E-decay(v)>0. Whenever Δ_σ a _s ^t converges (that is, ifd>2 or |σ|>0: Ifd>2, E-decay(lima _s ^t )=min(E-decay(v),d+2/2); if |σ|=1, E-decay (lim Δ_σ a _s ^t )=min(E-decay(ν),d+2); if |σ| ⩾, E-decay (lim Δ_σ a _s ^t )=E-decay(ν).     

Search for the NN → 6q phase transition in the np-polarized measurements at T kin = 1–6 GeV

The measurements of np-spin observables at 0° have been performed for the first time on the Delta-Sigma experimental facility of LHE JINR up to P _n = 4.5 GeV/c using the monochromatic neutron beam. They include detailed measurements of the Δσ _L(np) spin differences and the study of the np → pn elastic charge-exchange process. In the Δσ _L(np) and −Δσ _L(I = 0) energy dependencies over the energy region T_kin = 1.2–3.7 GeV the peculiarity at 1.8 GeV was observed. Such energy behavior was predicted by the QCD approach as a signal of the NN → 6q phase transition. For the exhaustive investigation of this effect it is necessary to measure the energy dependence of the complete set of np observables with both longitudinal (L) and transverse (T) polarizations of the neutron beam and proton target. This will allow Direct Reconstruction of all three NN forward Scattering Amplitudes (DRSA) to be performed, and the observed peculiarity to be checked around T_kin = 1.8 GeV and at the higher energies using the Argand diagrams method.     

Photoproduction of neutral pion pairs from the proton

Double neutral pion photoproduction from the proton has been measured at MAMI for photon energies between threshold and 820 MeV. The reaction was identified by an invariant mass and missing mass analysis. From threshold up to 370 MeV the total cross-section does not exceed 30 nb. For higher energies it shows a smooth rise until it reaches a maximum of about 10 μb at E _γ = 740 MeV. Dalitz plots of m ²(π⁰π⁰) versus m ²(p,π⁰) for seven bins of incident photon energy have been analysed. For E _γ > 610 MeV, a strong contribution of a sequential decay is observed with the Δ(1232)-resonance as intermediate state. A comparison to model calculations shows that these sequential decays presumably originate from the D ₁₃(1520) and also the P ₁₁(1440)-resonance. Received: 6 June 2000 / Accepted: 18 August 2000     

The newly observed open-charm states in quark model

Comparing the measured properties of the newly observed open-charm states D(2550), D(2600), D(2750), D(2760), D _s1(2710), D _sJ (2860), and D _sJ (3040) with our predicted spectroscopy and strong decays in a constituent quark model, we find that (1) the D(2 ¹ S ₀) assignment to D(2550) remains open for its too broad width determined by experiment; (2) the D(2600) and D _s1(2710) can be identified as the 2 ³ S ₁–1 ³ D ₁ mixtures; (3) if the D(2760) and D(2750) are indeed the same resonance, they would be the D(1 ³ D ₃); otherwise, they could be assigned as the D(1 ³ D ₃) and D^￠₂(1D)D^{\prime}_{2}(1D), respectively; (4) the D _sJ (2860) could be either the D _s1(2710)’s partner or the D _s (1 ³ D ₃); and (5) both the D _s1(2P) and D^￠_s1(2P)D^{\prime}_{s1}(2P) interpretations for the D _sJ (3040) seem likely. The E1 and M1 radiative decays of these sates are also studied. Further experimental efforts are needed to test the present quarkonium assignments for these new open-charm states.     

From independent particle towards collective motion for two polarized electrons on a square lattice

The two dimensional crossover from independent particle towards collective motion is studied using 2 polarized electrons (spinless fermions) interacting via a U/r Coulomb repulsion in a L×L square lattice with periodic boundary conditions and nearest neighbor hopping t. Three regimes characterize the ground state when U/t increases. Firstly, when the fluctuation Δr of the spacing r between the two particles is larger than the lattice spacing a, there is a scaling length L ₀ = π²(t/U) such that the relative fluctuation Δr/〈r〉 is a universal function of the dimensionless ratio L/L ₀, up to finite size corrections of order L^-2. L < L ₀ and L > L ₀ are respectively the limits of the free particle Fermi motion and of the correlated motion of a Wigner molecule. Secondly, when U/t exceeds a threshold U ^*(L)/t, Δr becomes smaller than a, giving rise to a correlated lattice regime where the previous scaling breaks down and analytical expansions in powers of t/U become valid. A weak random potential reduces the scaling length and favors the correlated motion. Received 28 March 2002 Published online 19 November 2002     

Dissociation of molecular hydrogen ions by an IR laser pulse

Dissociation dynamics of the simplest molecular systems, such as H₂ ⁺, D₂ ⁺ and HD⁺ ions, in an intense IR laser field has been investigated by numerical modeling. An n-term approximation has been developed to describe the molecular system dynamics in an intense electromagnetic field. Calculations by the n-term approximation have been compared to an accurate numerical solution of the two-particle problem. The dissociation probability as a function of the frequency and intensity of radiation for different isotopes in a molecular hydrogen ion is discussed. A quasistatic model of molecule dissociation in an IR field has been suggested, and limits of its applicability have been determined. Zh. éksp. Teor. Fiz. 113, 128–143 (January 1998)