Smoothening of a random surface as it results from the edwards-wilkinson kinetic equation

The time evolution of a random surfacez=h(r, t) (r=x, y) formed by a deposition process of the Edwards-Wilkinson type is discussed. The discussion is based on the author’s former derivation of the autocorrelation functionA _h(|r − r′|,t, t′)=〈h(r,t)h(r′,t′)〉 of the height functionh(r,t) under the assumption of a stochastic initial condition [V. Bezák: Acta Physica Univ. Comenianae39 (1998) 135]. Under the assumption of a steady (non-zero) deposition rate, the varianceσ _h ² (t)=〈[h(r,t)]²〉 increases logarithmically in time whilst the correlation lengthl _h(t) of the height functionh(r,t) increases as ∼t ^1/2. Therefore, the ratioσ _h(t)/l _h (t) tends to zero and the surfacez=h(r,t) does always tend towards a smoothened appearance. This work has been supported by the Slovak Grant Agency VEGA under contract No. 1/4319/97.     

Exact Analysis of Level-Crossing Statistics for (d+1)-Dimensional Fluctuating Surfaces

We carry out an exact analysis of the average frequency ν⁺ _αxi in the direction x _i of positiveslope crossing of a given level α such that, h(x, t) − = α, of growing surfaces in spatial dimension d. Here, h(x, t) is the surface height at time t, and is its mean value. We analyze the problem when the surface growth dynamics is governed by the Kardar-Parisi-Zhang (KPZ) equation without surface tension, in the time regime prior to appearance of cusp singularities (sharp valleys), as well as in the random deposition (RD) model. The total number N ⁺ of such level-crossings with positive slope in all the directions is then shown to scale with time as t ^d/2 for both the KPZ equation and the RD model. PACS number(s): 52.75.Rx, 68.35.Ct     

Coarsening process in one-dimensional surface growth models

Surface growth models may give rise to instabilities with mound formation whose typical linear size L increases with time (coarsening process). In one dimensional systems coarsening is generally driven by an attractive interaction between domain walls or kinks. This picture applies to growth models for which the largest surface slope remains constant in time (corresponding to model B of dynamics): coarsening is known to be logarithmic in the absence of noise ( L(t) ∼ ln t) and to follow a power law ( L(t) ∼t ^1/3) when noise is present. If the surface slope increases indefinitely, the deterministic equation looks like a modified Cahn-Hilliard equation: here we study the late stages of coarsening through a linear stability analysis of the stationary periodic configurations and through a direct numerical integration. Analytical and numerical results agree with regard to the conclusion that steepening of mounds makes deterministic coarsening faster : if α is the exponent describing the steepening of the maximal slope M of mounds ( M ^α∼L) we find that L(t) ∼t ⁿ: n is equal to for 1≤α≤2 and it decreases from to for α≥2, according to n = α/(5α - 2). On the other side, the numerical solution of the corresponding stochastic equation clearly shows that in the presence of shot noise steepening of mounds makes coarsening slower than in model B: L(t) ∼t ^1/4, irrespectively of α. Finally, the presence of a symmetry breaking term is shown not to modify the coarsening law of model α = 1, both in the absence and in the presence of noise. Received 28 September 2001 and Received in final form 21 November 2001     

The Variational Principle for a Class of Asymptotically Abelian C*-Algebras

Let (A,α) be a C^*-dynamical system. We introduce the notion of pressure P _α(H) of the automorphism α at a self-adjoint operator H∈A. Then we consider the class of AF-systems satisfying the following condition: there exists a dense α-invariant *-subalgebra ? of A such that for all pairs a,b∈? the C^*-algebra they generate is finite dimensional, and there is p=p(a,b)∈ℕ such that [α ^j (a),b]= 0 for |j|≥p. For systems in this class we prove the variational principle, i.e. show that P _α(H) is the supremum of the quantities h _φ(α) −φ(H), where h _φ(α) is the Connes–Narnhofer–Thirring dynamical entropy of α with respect to the α-invariant state φ. If H∈A, and P _α(H) is finite, we show that any state on which the supremum is attained is a KMS-state with respect to a one-parameter automorphism group naturally associated with H. In particular, Voiculescu's topological entropy is equal to the supremum of h _φ(α), and any state of finite maximal entropy is a trace. Received: 19 April 2000 / Accepted: 14 June 2000     

The productions of the top-pions and top-Higgs associated with the charm quark at the hadron colliders

In the topcolor-assisted technicolor (TC2) model, the typical physical particles, top-pions and top-Higgs, are predicted and the existence of these particles could be regarded as robust evidence for the model. These particles are accessible at the Tevatron and LHC, and furthermore the flavor-changing (FC) feature of the TC2 model may provide us with a unique opportunity to probe them. In this paper, we study some interesting FC production processes of top-pions and top-Higgs particles at the Tevatron and LHC, i.e., cΠ_t ^- and cΠ_t ⁰(h_t ⁰) productions. We find that the light charged top-pions are not favorable by the Tevatron experiments, and the Tevatron has little capability to probe the neutral top-pion and top-Higgs particles via these FC production processes. At LHC, however, the cross section can reach the level of 10–100 pb for cΠ_t ^- production and 10–100 fb for cΠ_t ⁰(h_t ⁰) production. So one can expect that enough signals could be produced at the LHC experiments. Furthermore, the SM backgrounds should be clean due to the FC feature of the processes, and the FC decay modes Π_t ^-→bc̄, Π_t ⁰(h_t ⁰)→tc̄ can provide us with the signal typical for the detection of the top-pions and top-Higgs particles. Therefore, one may have hope to find the signal of top-pions and top-Higgs particles with the running of LHC via these FC processes. PACS 12.60.Nz; 14.80.Mz; 12.15.LK; 14.65.Ha     

Lattice Dislocations in a 1-Dimensional Model

The spectral properties of the Schr?dinger operator T(t)=−d ²/dx ²+q(x,t) in L ²(ℝ) are studied, where the potential q is defined by q=p(x+t), x>0, and q=p(x), x<0; p is a 1-periodic potential and t∈ℝ is the dislocation parameter. For each t the absolutely continuous spectrum σ _ac (T(t))=σ _ac (T(0)) consists of intervals, which are separated by the gaps γ _n (T(t))=γ _n (T(0))=(α _n ⁻,α _n ⁺), n≥1. We prove: in each gap γ _n ≠?, n≥ 1 there exist two unique “states” (an eigenvalue and a resonance) λ _n ^±(t) of the dislocation operator, such that λ _n ^±(0)=α _n ^± and the point λ _n ^±(t) runs clockwise around the gap γ _n changing the energy sheet whenever it hits α _n ^±, making n/2 complete revolutions in unit time. On the first sheet λ _n ^±(t) is an eigenvalue and on the second sheet λ _n ^±(t) is a resonance. In general, these motions are not monotonic. There exists a unique state λ₀(t) in the basic gap γ₀(T(t))=γ₀(T(0))=(−∞ ,α₀ ⁺). The asymptotics of λ _n ^±(t) as n→∞ is determined. Received: 5 April 1999 / Accepted: 3 March 2000     

A Construction of Blow up Solutions for Co-rotational Wave Maps

The existence of co-rotational finite time blow up solutions to the wave map problem from ${\mathbb{R}^{2+1} \to N}The existence of co-rotational finite time blow up solutions to the wave map problem from \mathbbR²⁺¹ ? N{\mathbb{R}^{2+1} \to N} , where N is a surface of revolution with metric d ρ ² + g(ρ)² dθ², g an entire function, is proven. These are of the form u(t,r)=Q(l(t)t)+R(t,r){u(t,r)=Q(\lambda(t)t)+\mathcal{R}(t,r)} , where Q is a time independent solution of the co-rotational wave map equation −u _tt  + u _rr  + r ⁻¹ u _r  = r ⁻² g(u)g′(u), λ(t) = t ^−1-ν, ν > 1/2 is arbitrary, and R{\mathcal{R}} is a term whose local energy goes to zero as t → 0.     

Emission of light nuclei (<Emphasis Type="Italic">p,d, t</Emphasis>, α) in the process of annihilation of slow antiprotons in nuclear emulsion

The annihilation of slow (∼7 MeV) antiprotons in nuclear emulsion has been studied. The yields and energy spectra of p, d, t, and α particles in the evaporation region have been measured. The shape of the spectra of p, d, and t is in agreement with the Maxwell distribution and the excitation energy of a nucleus is consistent with a theoretical estimate for evaporation from the equilibrium state. The probability of the absorption of antiprotons inside the nucleus estimated from the multiplicity of h particles is ɛ = (2.0 ± 0.6) × 10⁻². The relative d/p yield coincides with a similar ratio appearing in the capture of slow π⁻ mesons by nuclei in the nuclear emulsion. The yields of t and α particles in the process of the annihilation of antiprotons are much higher than those in a similar process for pions. To identify g particles (0.29 < β < 0.70), energy losses dE/dx on ionization and multiple scattering have been measured. In this velocity region, the yields of p, d, t, and pions have been observed. The ratios (n _d /n _p ) _g , (n _d /n _p ) _b , and n _d /n _p measured in the capture of π⁻ mesons are almost the same. In this velocity range (g particles), α particles have not been observed.     

Generalized Fokker-Planck equation for a class of stochastic dynamical systems driven by additive Gaussian and Poissonian fractional white noises of order <Emphasis Type="Italic">α</Emphasis>

In a first stage, the paper deals with the derivation and the solution of the equation of the probability density function of a stochastic system driven simultaneously by a fractional Gaussian white noise and a fractional Poissonian white noise both of the same order. The key is the Taylor’s series of fractional order f(x + h) = E _α(h^αD _x ^α)f(x) where E _α() denotes the Mittag-Leffler function, and D _x ^α is the so-called modified Riemann-Liouville fractional derivative which removes the effects of the non-zero initial value of the function under consideration. The corresponding fractional linear partial differential equation is solved by using a suitable extension of the Lagrange’s technique involving an auxiliary set of fractional differential equations. As an example, one considers a half-oscillator of fractional order driven by a fractional Poissonian noise.      

Existence and Modulation of Uniform Sliding States in Driven and Overdamped Particle Chains

In this paper we are mainly concerned with existence and modulation of uniform sliding states for particle chains with damping γ and external driving force F. If the on-site potential vanishes, then for each F > 0 there exist trivial uniform sliding states x _n (t) = n ω + ν t + α for which the particles are uniformly spaced with spacing ω > 0, the sliding velocity of each particle is ν = F/γ, and the phase α is arbitrary. If the particle chain with convex interaction potential is placed in a periodic on-site potential, we show under some conditions the existence of modulated uniform sliding states of the form

Weak chaos and metastability in a symplectic system of many long-range-coupled standard maps

We introduce, and numerically study, a system of N symplectically and globally coupled standard maps localized in a d=1 lattice array. The global coupling is modulated through a factor r^-α, being r the distance between maps. Thus, interactions are long-range (nonintegrable) when 0≤α≤1, and short-range (integrable) when α>1. We verify that the largest Lyapunov exponent λ_M scales as λ_M ∝ N^-κ(α), where κ(α) is positive when interactions are long-range, yielding weak chaos in the thermodynamic limit N↦∞ (hence λ_M→0). In the short-range case, κ(α) appears to vanish, and the behaviour corresponds to strong chaos. We show that, for certain values of the control parameters of the system, long-lasting metastable states can be present. Their duration t_c scales as t_c ∝N^β(α), where β(α) appears to be numerically in agreement with the following behavior: β>0 for 0 ≤α< 1, and zero for α≥1. These results are consistent with features typically found in nonextensive statistical mechanics. Moreover, they exhibit strong similarity between the present discrete-time system, and the α-XY Hamiltonian ferromagnetic model.     

Production of the charged top-pions from TC2 model at the TeV energy e<Superscript>-</Superscript>γ colliders

The top-pions (Π_t ^0,±) and the top-Higgs (h_t ⁰) are the typical particles predicted by the topcolor-assisted technicolor (TC2) model and the observation of these particles can be regarded as direct evidence of the TC2 model. In this paper, we study three pair production processes of these new particles at the next generation eγ colliders, i.e., e^-γ→e^-Π_t ⁺Π_t ^-, e^-γ→ν_eΠ_t ^-Π_t ⁰ and e^-γ→ν_eΠ_t ^-h_t ⁰. The results show that the production rates can reach the level 10⁰–10¹ fb with reasonable parameter values. So one can expect that enough signals could be produced in future high- energy linear collider experiments. Furthermore, the flavor-changing (FC) decay modes Π_t ^-→bc̄, Π_t ⁰(h_t ⁰)→tc̄ can provide us with the typical signal to detect these new particles. PACS 12.60Nz; 14.80.Mz; 12.15.LK; 14.65.Ha     

Conserved Noise Restricted Curvature Model

A restricted curvature model with conservation of total number of particles is introduced. The surface width W of the model grows as t ^β at the beginning with β≈0.25 and becomes saturated at L ^α for t≫L ^z with α≈1.5, where L is the system size. The conservation law leads to a new universality class following sixth-order linear equation with conservative noise. The relation between our model and the equation is discussed.     

Super-Diffusivity in a Shear Flow Model¶from Perpetual Homogenization

This paper is concerned with the asymptotic behavior solutions of stochastic differential equations dy _t =dω _t −∇Γ(y _t ) dt, y ₀=0 and d=2. Γ is a 2 &\times; 2 skew-symmetric matrix associated to a shear flow characterized by an infinite number of spatial scales Γ₁₂=−Γ₂₁=h(x ₁), with h(x ₁)=∑ _{n =0} ^∞γ _n h ⁿ (x ₁/R _n ), where h ⁿ are smooth functions of period 1, h ⁿ (0)=0, γ _n and R _n grow exponentially fast with n. We can show that y ^t has an anomalous fast behavior (?[|y ^t |²]∼t ^1+ν with ν > 0) and obtain quantitative estimates on the anomaly using and developing the tools of homogenization. Received: 1 June 2001 / Accepted: 11 January 2002     

On the Energy Growth of Some Periodically Driven Quantum Systems with Shrinking Gaps in the Spectrum

We consider quantum Hamiltonians of the form H(t)=H+V(t) where the spectrum of H is semibounded and discrete, and the eigenvalues behave as E _n ∼n ^α , with 0<α<1. In particular, the gaps between successive eigenvalues decay as n ^α−1. V(t) is supposed to be periodic, bounded, continuously differentiable in the strong sense and such that the matrix entries with respect to the spectral decomposition of H obey the estimate ‖V(t) _m,n ‖≤ε|m−n|^−p max {m,n}^−2γ for m≠n, where ε>0, p≥1 and γ=(1−α)/2. We show that the energy diffusion exponent can be arbitrarily small provided p is sufficiently large and ε is small enough. More precisely, for any initial condition Ψ∈Dom(H ^1/2), the diffusion of energy is bounded from above as 〈H〉 _Ψ (t)=O(t ^σ ), where . As an application we consider the Hamiltonian H(t)=|p| ^α +ε v(θ,t) on L ²(S ¹,dθ) which was discussed earlier in the literature by Howland.     

Statistical model of fluorescence blinking

Blinking of single molecules and nanocrystals is modeled as a two-state renewal process with on (fluorescent) and off (non-fluorescent) states. The on and off-times may have power-law or exponential distributions. A fractional generalization of the exponential function is used to develop a unified treatment of the blinking statistics for both types of distributions. In the framework of the two-state model, an equation for the probability density p(t _on|t) of the total on-time is derived. As applied to power-law blinking, the equation contains derivatives of fractional orders α and β equal to the exponents of the on and off-time power-law distributions, respectively. In the limit case of α = β = 1, the distributions become exponential and the fractional differential equation reduces to an integer order differential equation. Solutions to these equations are expressed in terms of fractional stable distributions. The Poisson transform of p(t _on|t) is the photon number distribution that determines the photon counting statistics. It is shown that the long-time asymptotic behavior of Mandel’s Q parameter follows a power law: M(t) ∝ t ^γ . The function γ(α, β) is defined on the (α, β) plane. An analysis of the relative variance of the total on-time shows that it decays only when α = β = 1 or α < β. Otherwise, relative fluctuations either exhibit asymptotic power-law growth or approach a constant level. Analytical calculations are in good agreement with the results of Monte Carlo simulations.     

Growth and Roughness of the Interface for Ballistic Deposition

In ballistic deposition (BD), (d+1)-dimensional particles fall sequentially at random towards an initially flat, large but bounded d-dimensional surface, and each particle sticks to the first point of contact. For both lattice and continuum BD, a law of large numbers in the thermodynamic limit establishes convergence of the mean height and surface width (sample standard deviation of the height) of the interface to constants h(t) and w(t), respectively, depending on time t. We show that h(t) is asymptotically linear in t, while (w(t))² grows at least logarithmically in t when d=1. We use duality results showing that w(t) can be interpreted as the standard deviation of the height for deposition onto a surface growing from a single point.     

Dual analytic model of generalized parton distributions

A model for generalized parton distributions (GPDs) in the form of ∼(x/g ₀)^{(1−x)ᾶ(t)}, where ᾶ(t) = α(t) − α(0) is the nonlinear part of the Regge trajectory and g ₀ is a parameter, g ₀ > 1, is presented. For linear trajectories, it reduces to earlier proposals. We compare the calculated moments of these GPDs with the experimental data on form factors and find that the effects from the nonlinearity of Regge trajectories are large. By Fourier transforming the obtained GPDs, we access the spatial distribution of protons in the transverse plane. The relation between dual amplitudes with Mandelstam analyticity and composite models in the infinite-momentum frame is discussed, the integration variable in dual models being associated with the quark longitudinal-momentum fraction x in the nucleon. The text was submitted by the authors in English.     

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.