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     

Transport theory of multiterminal hybrid structures

We derive a microscopic transport theory of multiterminal hybrid structures in which a superconductor is connected to several spin-polarized electrodes. We discuss the non-perturbative physics of extended contacts, and show that such contacts can be well represented by averaging out the phase of the electronic wave function. The intercontact Andreev reflection and elastic cotunneling conductances are identical if the phase can be averaged out, namely in the presence of at least one extended contact. The maximal conductance of a two-channel contact is proportional to (e ²/h)(a ₀/D)²exp[-D/ξ(ω^*)], where D is the distance between the contacts, a₀ the lattice spacing, ξ(ω) is the superconducting coherence length, and ω^* is the cross-over frequency between a perturbative regime ( ω < ω^*) and a non perturbative regime ( ω^* < ω < Δ). Received 18 June 2001 and Received in final form 17 January 2002     

Annihilation of nematic point defects: Pre-collision and post-collision evolution

The annihilation of the nematic hedgehog and anti-hedgehog within an infinite cylinder of radius R is studied. The semi-microscopic lattice-type model and Brownian molecular dynamics are used. We distinguish among the i) early pre-collision, ii) late pre-collision, iii) early post-collision, and iv) late post-collision stages. In the pre-collision stage our results agree qualitatively with the existing experimental observations and also continuum-type simulations. The core of each defect exhibits a ring-like structure, where the ring axis is set perpendicular to the cylinder symmetry axis. For ξ⁽⁰⁾_d/(2R) > 1 the interaction between defects is negligible, where ξ⁽⁰⁾_d describes the initial separation of defects. Consequently, the defects annihilate within the simulation time window for ξ⁽⁰⁾_d/(2R) < 1. For close enough defects their separation scales as ξ_d (t_c - t)^0.4±0.1, where t_c stands for the collision time. In elastically anisotropic medium the hedgehog is faster than the anti-hedgehog. In the early pre-collision stage the defects can be treated as point-like particles, possessing inherent core structure, that interact via the nematic director field. In the late pre-collision stage the cores reflect the interaction between defects. After the collision a charge-less ring structure is first formed. In the early post-collision stage the ring adopts an essentially untwisted circular structure of the radius ξ_r. In the late post-collision stage we observe two qualitatively different scenarios. For μ = ξ_r/R < μ_c ∼ 0.25 the ring collapses leading to the escaped radial equilibrium structure. For μ > μ_c the chargeless ring triggers the nucleation growth into the planar polar structure with line defects.     

Vortex pinning in YBa2Cu3O7?x films

Evidence that pinning on linear or planar defects dominates the vortex dynamics in YBa₂Cu₃O_7−x (YBCO) films is provided by complex impedance measurements at temperature 8 K<T<T _c and magnetic field 0<B<6 T. Below the vortex lattice melting transition B_g(T) but above a threshold field B_p≈8(1-T/T _c ) T, the inductance of vortices increases as B², much less rapidly than predicted for collective pinning of vortices by point defects. Above the vortex melting line, critical scaling persists over the region B_g(T<B<B^*(T) where the vortex correlation length ξ exceeds a characteristic length scale ξ^*≡ξ(B=B^*)≈450?. The value of ξ^* is not sensitive to Al-doping in the Cu sites in the lattice and is close to the size of twin domains in the film. The nature of the observed crossovers is discussed in terms of available theoretical models for a glass-liquid transition at B_g.     

Dynamics of a Peierls system in a light field

Equations describing the temporal dynamics of the order parameter ξ(t) of a metal-semiconductor phase transition and the density n(t) of electron-hole pairs in a Peierls system in a light field are obtained on the basis of the Lagrange equation for the phonon mode and the Liouville equation for the density matrix of the electronic subsystem. The equations obtained are analyzed for a stationary state (with adiabatically slow variation of the light intensity I) and for a transient process near the initial and final states of dynamic equilibrium (with the light field switched on abruptly). It is shown that for adiabatically slow growth of the intensity I up to a certain critical value I _c the band gap of the electronic spectrum decreases but the semiconductor phase of the Peierls system remains stable. For I>I _c the stationary semiconductor state (ξ≠0) becomes unstable. When the light is switched on abruptly, the deviation of the system parameters from the initial values is described by an exponential law with a characteristic reciprocal of the rise time of the process linearly dependent on the irradiation intensity I. As a new position of equilibrium is approached, three qualitatively different regimes of behavior of the order parameter ξ and density n are possible. For low intensities I(I< I ₁) a purely relaxational aperiodic process occurs. For intermediate intensities I(I ₁<I<I _c) damped oscillations of ξ and n are observed near a new stationary semiconductor state with a smaller band gap. For I>I _c the stationary semiconductor state with ξ≠0 is absent. The experimental data on the irradiation of a vanadium dioxide film with a powerful laser pulse is interpreted on the basis of the theory developed. Zh. éksp. Teor. Fiz. 116, 2154–2175 (December 1999)     

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.     

Internal waves in a compressible two-layer model atmosphere: Hamiltonian description

We consider slow, compared to the speed of sound, motions of an ideal compressible fluid (gas) in a gravitational field in the presence of two isentropic layers with a small specific-entropy difference between them. Assuming the flow to be potential in each of the layers (v _{1, 2} = ▿ϕ_{1, 2}) and neglecting the acoustic degrees of freedom (div($ \bar \rho $ \bar \rho (z)▿ϕ_{1, 2}) ≈ 0, where $ \bar \rho $ \bar \rho (z) is the average equilibrium density), we derive the equations of motion for the boundary in terms of the shape of the surface z = η(x, y, t) itself and the difference between the boundary values of the two velocity field potentials: ψ(x, y, t) = ψ₁ − ψ₂. We prove the Hamilto nian structure of the derived equations specified by a Lagrangian of the form ℒ = ∫$ \bar \rho $ \bar \rho (η)η _t ψdxdy − ℋ{η, ψ}. The system under consideration is the simplest theoretical model for studying internal waves in a sharply stratified atmosphere in which the decrease in equilibrium gas density due to gas compressibility with increasing height is essentially taken into account. For plane flows, we make a generalization to the case where each of the layers has its own constant potential vorticity. We investigate a system with a model dependence $ \bar \rho $ \bar \rho (z) ∝ e ^−2αz with which the Hamiltonian ℋ{η, ψ} can be represented explicitly. We consider a long-wavelength dynamic regime with dispersion corrections and derive an approximate nonlinear equation of the form u _t + auu _x − b[−$ \hat \partial _x^2 $ \hat \partial _x^2 + α²]^1/2 u _x = 0 (Smith’s equation) for the slow evolution of a traveling wave.     

Reacting polymers with highly correlated initial conditions

We propose and theoretically study an experiment designed to measure short-time polymer reaction kinetics in melts or dilute solutions. The photolysis of groups centrally located along chain backbones, one group per chain, creates pairs of spatially highly correlated macroradicals. We calculate time-dependent rate coefficients κ(t) governing their first-order recombination kinetics, which are novel on account of the far-from-equilibrium initial conditions. In dilute solutions (good solvents) reaction kinetics are intrinsically weak, despite the highly reactive radical groups involved. This leads to a generalised mean-field kinetics in which the rate of radical density decay - ∼S(t), where S(t) ∼t ^{- (1 + g/3)} is the equilibrium return probability for 2 reactive groups, given initial contact. Here g≈ 0.27 is the correlation hole exponent for self-avoiding chain ends. For times beyond the longest coil relaxation time τ, - ∼S(t) remains true, but center of gravity coil diffusion takes over with rms displacement of reactive groups x(t) ∼t ^1/2 and S(t) ∼ 1/x ³(t). At the shortest times ( t 10^-6s), recombination is inhibited due to spin selection rules and we find ∼tS(t). In melts, kinetics are intrinsically diffusion-controlled, leading to entirely different rate laws. During the regime limited by spin selection rules, the density of radicals decays linearly, n(0) - n(t) ∼t. At longer times the standard result - ∼d ³(t)/d (for randomly distributed ends) is replaced by ∼d2x ³(t)/d ² for these correlated initial conditions. The long-time behavior, t > τ, has the same scaling form in time as for dilute solutions. Received 18 May 2000     

Two-point correlation function in systems with van der Waals type interaction

The behavior of the bulk two-point correlation function G(;T| d ) in d-dimensional system with van der Waals type interactions is investigated and its consequences on the finite-size scaling properties of the susceptibility in such finite systems with periodic boundary conditions is discussed within mean-spherical model which is an example of Ornstein and Zernike type theory. The interaction is supposed to decay at large distances r as r ^{- (d + σ)}, with 2 < d < 4, 2 < σ < 4 and d + σ≤6. It is shown that G(;T| d ) decays as r ^{- (d - 2)} for 1 ≪r≪ξ, exponentially for ξ≪r≪r ^*, where r ^* = (σ - 2)ξlnξ, and again in a power law as r ^{- (d + σ)} for r≫r ^*. The analytical form of the leading-order scaling function of G(;T| d ) in any of these regimes is derived. Received 28 May 2001     

Non-linear scission/recombination kinetics of living polymerization

Living polymers are formed by reversible association of primary units (unimers). Generally the chain statistical weight involves a factor σ < 1 suppressing short chains in comparison with free unimers. Living polymerization is a sharp thermodynamic transition for σ ≪ 1 which is typically the case. We show that this sharpness has an important effect on the kinetics of living polymerization (one-dimensional association). The kinetic model involves i) the unimer activation step (a transition to an assembly-competent state); ii) the scission/recombination processes providing growth of polymer chains and relaxation of their length distribution. Analyzing the polymerization with no chains but unimers at t = 0 , with initial concentration of unimers M ≳ M ^* (M^* is the critical polymerization concentration), we determine the time evolution of the chain length distribution and find that: 1) for M ^* ≪ M ≪ M ^*/σ the kinetics is characterized by 5 distinct time stages demarcated by 4 characteristic times t₁, t₂, t₃ and t^*; 2) there are transient regimes (t ₁ ≲ t ≲ t ₃) when the molecular-weight distribution is strongly non-exponential; 3) the chain scissions are negligible at times shorter than t₂. The chain growth is auto-accelerated for t ₁ ≲ t ≲ t ₂ : the cut-off chain length (= polymerization degree 〈n〉_w N ₁ ∝ t ² in this regime. 4) For t ₂ < t < t ₃ the length distribution is characterized by essentially 2 non-linear modes; the shorter cut-off length N₁ is decreasing with time in this regime, while the length scale N₂ of the second mode is increasing. (5) The terminal relaxation time of the polymer length distribution, t^*, shows a sharp maximum in the vicinity of M^*; the effective exponent is as high as ∼ σ^-1/3 just above M^*.     

Construction of Fredholm representations and a modification of the Higson-Roe corona

The Fredholm representation theory is well adapted to the construction of homotopy invariants of non-simply-connected manifolds by means of the generalized Hirzebruch formula [σ(M)] = 〈L(M)ch _A f*ξ, [M]〉 ∈ K _A ⁰(pt) ⊗ Q, where A = C*[π] is the C*-algebra of the group π, π = π ₁(M). The bundle ξ ∈ K _A ⁰(Bπ) is the canonical A-bundle generated by the natural representation π → A. Recently, the first author constructed a natural family of Fredholm representations that lead to a symmetric vector bundle on the completion of the fundamental group with a modification of the Higson-Roe corona, provided that the completion is a closed manifold.     

Relationships between a microscopic parameter and the stochastic equations for interface's evolution of two growth models

The relationship between a microscopic parameter p, that is related to the probability of choosing a mechanism of deposition, and the stochastic equation for the interface's evolution is studied for two different models. It is found that in one model, that is similar to ballistic deposition, the corresponding stochastic equation can be represented by a Kardar-Parisi-Zhang (KPZ) equation where both λ and ν depend on p in the following way: ν(p) = νp and λ(p) = λp ^3/2. Furthermore, in the other studied model, which is similar to random deposition with relaxation, the stochastic equation can be represented by an Edwards-Wilkinson (EW) equation where ν depends on p according to ν(p) = νp ². It is expected that these results will help to find a framework for the development of stochastic equations starting from microscopic details of growth models. Received 26 August 2002 / Received in final form 20 November 2002 Published online 6 March 2003 RID="a" ID="a"e-mail: ealbano@inifta.unlp.edu.ar     

High frequency sound and the boson peak in amorphous silica

We present the results of extensive molecular dynamics computer simulations in which the high frequency dynamics of silica, i.e. for frequencies ν > 0.5 THz, is investigated in the viscous liquid state as well as in the glass state. We characterize the properties of high frequency sound modes by analyzing J _l(q,ν) and J _t(q,ν), the longitudinal and transverse current correlation function, respectively. For wave-vectors q > 0.4 ?^-1 the spectra are sitting on top of a flat background. The dynamic structure factor S(q,ν) exhibits for q > 0.23 ?^-1 a boson peak which is located nearly independent of q around 1.7 THz and for which the intensity scales approximately linearly with temperature. We show that the low frequency part of the boson peak is mainly due to the elastic scattering of transverse acoustic modes with frequencies around 1 THz. The strength of this scattering depends on q and is largest around q = 1.7 ?^-1, the location of the first sharp diffraction peak in the static structure factor. By studying S(q,ν) for different system sizes we show that strong finite size effects are present in the low frequency part of the boson peak in that for small systems part of its intensity is missing. We discuss the consequences of these finite size effects for the structural relaxation. Received 27 June 2000 and Received in final form 9 January 2001     

Large-scale amplification of a magnetic field by turbulent helicity fluctuations

In this paper the procedure of large-scale averaging of the magnetic-field diffusion equation with the α-term curlα(r,t)B(r,t) is used to show that a nonuniform distribution of the turbulent helicity fluctuations (more precisely, the fluctuations of the coefficient α) with a zero average value gives rise to large-scale amplification of the initial magnetic field. A detailed study is carried out of the dependence of the resulting large-scale α effect on the characteristics of the correlator 〈〈α(r, t)α(r″,t″)〉〉 in a rotating medium with a nonuniform distribution of the angular velocity ω=ω(ρ,z) (ρ is the distance for the rotation axis z). The effect of helicity fluctuations and the diffusion coefficient on the turbulent diffusion process is also investigated. Zh. éksp. Teor. Fiz. 116, 85–104 (July 1999)     

Possible Loss and Recovery of Gibbsianness¶During the Stochastic Evolution of Gibbs Measures

We consider Ising-spin systems starting from an initial Gibbs measure ν and evolving under a spin-flip dynamics towards a reversible Gibbs measure μ≠ν. Both ν and μ are assumed to have a translation-invariant finite-range interaction. We study the Gibbsian character of the measure νS(t) at time t and show the following: (1) For all ν and μ, νS(t) is Gibbs for small t. (2) If both ν and μ have a high or infinite temperature, then νS(t) is Gibbs for all t > 0. (3) If ν has a low non-zero temperature and a zero magnetic field and μ has a high or infinite temperature, then νS(t) is Gibbs for small t and non-Gibbs for large t. (4) If ν has a low non-zero temperature and a non-zero magnetic field and μ has a high or infinite temperature, then νS(t) is Gibbs for small t, non-Gibbs for intermediate t, and Gibbs for large t. The regime where μ has a low or zero temperature and t is not small remains open. This regime presumably allows for many different scenarios. Received: 26 April 2001 / Accepted: 10 October 2001     

Renormalization group analysis of polymer cyclization with non-equilibrium initial conditions

We develop a renormalization group approach for cyclizing polymers for the case when chain ends are initially close together (ring initial conditions). We analyze the behavior at times much shorter than the longest polymer relaxation time. In agreement with our previous work (Europhys. Lett. 73, 621 (2006)) we find that the leading time dependence of the reaction rate k(t) for ring initial conditions and equilibrium initial conditions are related, namely k _ring(t) ∝ t ^-δ and k _eq(t) ∝ t ^1-δ for times less than the longest polymer relaxation time. Here δ is an effective exponent which approaches δ = 5/4 for very long Rouse chains. Our present analysis also suggests a “sub-leading” term proportional to (ln t)/t which should be particularly significant for smaller values of the renormalized reaction rate and early times. For Zimm dynamics, our RG analysis indicates that the leading time dependence for the reaction rate is k(t) ∼ 1/t for very long chains. The leading term is again consistent with the expected relation between ring and equilibrium initial conditions. We also find a logarithmic correction term which we “exponentiate” to a logarithmic form with a Landau pole. The presence of the logarithm is particularly important for smaller chains and, in the Zimm case, large values of the reaction rate.     

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.     

Exact Analytical Solution of the Schrödinger Equation for an N-Identical Body-Force System

A mathematical method is presented for solving the Schr?dinger equation for a system of identical body forces. The N-body forces are more easily introduced and treated within the hyperspherical harmonics. The problem of the N-body potential has been used at the level of both classical and quantum mechanics. The hypercentral interacting potential is assumed to depend on the hyperradius x = (ξ₁² + ξ₂² + ⋯ + ξ_N−1²)^1/2 only, where ξ₁,ξ₂,…,ξ_N−1 are Jacobi relative coordinates which are functions of N-particle relative positions r₁₂,r₂₃,…,r_N1. The problem of the harmonic oscillator and the Coulomb-type potential has been widely studied in different contexts. Using the N-body potential V(x) = ax² + bx − (c/x) as an example, and assuming an ansatz for the eigenfunction, an exact analytical solution of the Schr?dinger equation for an N-body system in three dimensions is obtained. This method is also applicable to some other types of potentials for N-identical interacting particles.     

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     

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.