Disorder driven roughening transitions of elastic manifolds and periodic elastic media

The simultaneous effect of both disorder and crystal-lattice pinning on the equilibrium behavior of oriented elastic objects is studied using scaling arguments and a functional renormalization group technique. Our analysis applies to elastic manifolds, e.g., interfaces, as well as to periodic elastic media, e.g., charge-density waves or flux-line lattices. The competition between both pinning mechanisms leads to a continuous, disorder driven roughening transition between a flat state where the mean relative displacement saturates on large scales and a rough state with diverging relative displacement. The transition can be approached by changing the impurity concentration or, indirectly, by tuning the temperature since the pinning strengths of the random and crystal potential have in general a different temperature dependence. For D dimensional elastic manifolds interacting with either random-field or random-bond disorder a transition exists for 2<D<4, and the critical exponents are obtained to lowest order in . At the transition, the manifolds show a superuniversal logarithmic roughness. Dipolar interactions render lattice effects relevant also in the physical case of D=2. For periodic elastic media, a roughening transition exists only if the ratio p of the periodicities of the medium and the crystal lattice exceeds the critical value . For p<p _c the medium is always flat. Critical exponents are calculated in a double expansion in and and fulfill the scaling relations of random field models. Received 28 August 1998     

Energy landscapes, lowest gaps, and susceptibility of elastic manifolds at zero temperature

We study the effect of an external field on (1 + 1) and (2 + 1) dimensional elastic manifolds, at zero temperature and with random bond disorder. Due to the glassy energy landscape the configuration of a manifold changes often in abrupt, “first order”-type of large jumps when the field is applied. First the scaling behavior of the energy gap between the global energy minimum and the next lowest minimum of the manifold is considered, by employing exact ground state calculations and an extreme statistics argument. The scaling has a logarithmic prefactor originating from the number of the minima in the landscape, and reads ΔE ₁∼L ^θ[ln(L _z L ^{- ζ})]^-1/2, where ζ is the roughness exponent and θ is the energy fluctuation exponent of the manifold, L is the linear size of the manifold, and L_z is the system height. The gap scaling is extended to the case of a finite external field and yields for the susceptibility of the manifolds ∼L ^{2D + 1 - θ}[(1 - ζ)ln(L)]^1/2. We also present a mean field argument for the finite size scaling of the first jump field, h ₁∼L ^{d - θ}. The implications to wetting in random systems, to finite-temperature behavior and the relation to Kardar-Parisi-Zhang non-equilibrium surface growth are discussed. Received December 2000 and Received in final form April 2001     

Casimir amplitudes in a quantum spherical model with long-range interaction

A d-dimensional quantum model system confined to a general hypercubical geometry with linear spatial size L and “temporal size” 1/T ( T - temperature of the system) is considered in the spherical approximation under periodic boundary conditions. For a film geometry in different space dimensions , where is a parameter controlling the decay of the long-range interaction, the free energy and the Casimir amplitudes are given. We have proven that, if , the Casimir amplitude of the model, characterizing the leading temperature corrections to its ground state, is . The last implies that the universal constant of the model remains the same for both short, as well as long-range interactions, if one takes the normalization factor for the Gaussian model to be such that . This is a generalization to the case of long-range interaction of the well-known result due to Sachdev. That constant differs from the corresponding one characterizing the leading finite-size corrections at zero temperature which for is . Received 3 June 1999 and Received in final form 16 August 1999     

Conserved dynamics and interface roughening in spontaneous imbibition: A phase field model

The propagation and roughening of a fluid-gas interface through a disordered medium in the case of capillary driven spontaneous imbibition is considered. The system is described by a conserved (model B) phase-field model, with the structure of the disordered medium appearing as a quenched random field . The flow of liquid into the medium is obtained by imposing a non-equilibrium boundary condition on the chemical potential, which reproduces Washburn's equation for the slowing down motion of the average interface position H. The interface is found to be superrough, with global roughness exponent , indicating anomalous scaling. The spatial extent of the roughness is determined by a length scale arising from the conservation law. The interface advances by avalanche motion, which causes temporal multiscaling and qualitatively reproduces the experimental results of Horv'ath and Stanley (Phys. Rev. E 52, 5166 (1995)) on the temporal scaling of the interface. Received 24 November 1999     

Attractive forces between anisotropic inclusions in the membrane of a vesicle

The fluctuation-induced interaction between two rod-like, rigid inclusions in a fluid vesicle is studied by means of canonical ensemble Monte-Carlo simulations. The vesicle membrane is represented by a triangulated network of hard spheres. Five rigidly connected hard spheres form rod-like inclusions that can leap between sites of the triangular network. Their effective interaction potential is computed as a function of mutual distance and angle of the inclusions. On account of the hard-core potential among these, the nature of the potential is purely entropic. Special precaution is taken to reduce lattice artifacts and the influence of finite-size effects due to the spherical geometry. Our results show that the effective potential is attractive and short-range compared with the rod length L. Its well depth is of the order of , where is the bending modulus. Received 5 February 1999 and Received in final form 14 May 1999     

Heat transport through a quantum dot with one-dimensional interacting leads under Coulomb blockade regime

The peculiarities of a low temperature heat transfer through a ballistic quantum dot (a double potential barrier) with interacting leads due to a long-range Coulomb interaction (in the geometrical capacitance approach) are considered. It is found that the thermal conductance K shows periodic peaks as a function of the electrostatic potential of a dot at low temperatures. At the peak maximum it is whereas near the minimum it is . Near the peak maximum the dependence K(T) is essentially nonmonotonic at the temperatures correspondent to the level spacing in the quantum dot. Received 20 October 1999 and Received in final form 20 January 2000     

Momentum transport and torque scaling in Taylor-Couette flow from an analogy with turbulent convection

We generalize an analogy between rotating and stratified shear flows. This analogy is summarized in Table 1. We use this analogy in the unstable case (centrifugally unstable flow vs. convection) to compute the torque in Taylor-Couette configuration, as a function of the Reynolds number. At low Reynolds numbers, when most of the dissipation comes from the mean flow, we predict that the non-dimensional torque G = T/ν² L, where L is the cylinder length, scales with Reynolds number R and gap width η, G = 1.46η^3/2(1 - η)^-7/4 R ^3/2. At larger Reynolds number, velocity fluctuations become non-negligible in the dissipation. In these regimes, there is no exact power law dependence the torque versus Reynolds. Instead, we obtain logarithmic corrections to the classical ultra-hard (exponent 2) regimes: G = 0.50 . These predictions are found to be in excellent agreement with avail-able experimental data. Predictions for scaling of velocity fluctuations are also provided. Received 7 June 2001 and Received in final form 7 December 2001     

Nonmonotonic external field dependence of the magnetization in a finite Ising model: Theory and MC simulation

Using field theory and Monte Carlo (MC) simulation we investigate the finite-size effects of the magnetization M for the three-dimensional Ising model in a finite cubic geometry with periodic boundary conditions. The field theory with infinite cutoff gives a scaling form of the equation of state where is the reduced temperature, h is the external field and L is the size of system. Below and at the theory predicts a nonmonotonic dependence of f(x,y) with respect to at fixed and a crossover from nonmonotonic to monotonic behaviour when y is further increased. These results are confirmed by MC simulation. The scaling function f(x,y) obtained from the field theory is in good quantitative agreement with the finite-size MC data. Good agreement is also found for the bulk value at . Received 20 July 1999 and Received in final form 11 November 1999     

Violation of finite-size scaling in three dimensions

We reexamine the range of validity of finite-size scaling in the lattice model and the field theory below four dimensions. We show that general renormalization-group arguments based on the renormalizability of the theory do not rule out the possibility of a violation of finite-size scaling due to a finite lattice constant and a finite cutoff. For a confined geometry of linear size L with periodic boundary conditions we analyze the approach towards bulk critical behavior as at fixed for where is the bulk correlation length. We show that for this analysis ordinary renormalized perturbation theory is sufficient. On the basis of one-loop results and of exact results in the spherical limit we find that finite-size scaling is violated for both the lattice model and the field theory in the region . The non-scaling effects in the field theory and in the lattice model differ significantly from each other. Received 5 February 1999     

A theoretical spectroscopic study of single ammonia molecules adsorbed on the surface of fcc-type argon clusters. Surface effects on the ν 2 vibration-inversion mode

Ammonia monomers have been adsorbed on argon clusters at low temperature K by Rohmund and Huisken [#!frfh97!#] using the pick-up technique. They measured the spectrum of the NH₃ molecules in the region of the umbrella mode. Two broad bands centered around 970 and 1000 cm^-1 with finer details were observed. The authors attempted to interpret the obtained spectrum on the basis of the free rotation motions of the molecules. In this paper semi-empirical atom-atom potential energy calculations are performed for the ammonia monomer adsorbed on a rigid face-centered-cubic (fcc)-type surface of the argon cluster. In the equilibrium position of the rigid molecule on the cluster surface the orientational potential energy surface exhibits two quasi-equivalent minima separated by a potential barrier of about 100 cm^-1. The symmetry of the molecular vibration-inversion double-well potential is destroyed; the inversion motion is then forbidden in the ground state. On the basis of the two adsorption orientations, the vibrational frequency shifts are calculated and the obtained infrared bar-spectrum agrees with the experimental one. Received 6 April 1999 and Received in final form 19 July 1999     

Temperature and size dependence of the optical response of small Ag clusters

The absorption spectra of small Ag ⁺ n clusters are calculated at finite vibrational temperature by using a microscopic tight-binding RPA method. We consider free clusters with sizes between n = 3 and n =13 and take into account explicitly the degrees of freedom corresponding to the 4 d-electrons. We analyze the optical absorption as a function of the cluster size. We show that the contribution of the d-electrons has an important influence on the size dependence of the energy of the Mie plasmon. We also perform ensemble averages to obtain the absorption spectra for different vibrational temperatures. We obtain relatively good agreement with experiment for a temperature . The dynamics of the 4 d-electrons, which shows in small clusters an incipient delocalized character for n >7, yields an important contribution to the absorption spectrum already for n =13. We find that the strength of this contribution can be controlled by varying the vibrational temperature. Received: 4 January 1999 / Received in final form: 12 May 1999     

Chain length dependence of anomalous swelling in multilamellar lipid vesicles

Using small-angle X-ray scattering, the repeat distance vs. temperature is measured for a homologous series of multilamellar vesicles of lecithins with varying acyl chain length in excess water condition around the lipid main transition. A systematic chain length dependence is found which is in accordance with a bending rigidity renormalization and critical unbinding of the lamellae close to the transition, as previously suggested in H?nger et al. [Phys. Rev. Lett. 72, 3911 (1994)]. Received 13 January 1999 and Received in final form 6 September 1999     

Scaling relationship between effective critical exponents throughout the crossover region in thin Ising films

The Monte Carlo (MC) approach is used to check the validity of the scaling relationship for the effective critical exponents in thin Ising films. We investigate this relationship not just in the critical region but throughout the crossover to the expected two-dimensional behavior. Our results indicate that this scaling relationship is very well-fulfilled throughout the entire crossover temperature region, as predicted by a previous renormalization group analysis. The two-dimensional universality class of Ising films is confirmed by means of data collapsing plots for plates with increasing L, up to L=100. The evolution of the maximum value of the effective critical exponents with film thickness is discussed. Received 22 April 1999     

Atomic Rayleigh scattering cross-sections and the associated anomalous dispersion in the X-ray regions

Elastic scattering cross-sections for Pd, Ag, Cd, In, Sn, Sb, Pt, Au and Pb are measured at an angle of 90 in the X-ray region 5.41 keV. These energies fall between the high-energy side of the L- and M-shell absorption edges of the atoms considered. The present atomic region is significant for solid X-rays to assess the contribution of resonance and solid-state environmental effects. Also it is the anomalous scattering region for many of the atoms of the periodic table. Experimental results are compared with theoretical calculations based on form factor formalisms including the anomalous corrections and available recent S-matrix values. Based on the experimental evidence, the present results indicate the influence of solid-state environmental effects, the importance of anomalous corrections nearer to absorption edges, the correctness of revised high-energy limit values, the superiority of S-matrix predictions over form factor values on measured elastic scattering cross-sections in the X-ray regime and also show the resonance behavior around K, L and M absorption edges. Received: 27 January 1998 / Received in final form: 4 January 1999     

Interaction induced delocalization of two particles: large system size calculations and dependence on interaction strength

The localization length L₂ of two interacting particles in a one-dimensional disordered system is studied for very large system sizes by an efficient and accurate variant of the Green function method. The numerical results (at the band center) can be well described by the functional form L ₂ =L ₁ [0.5+c(U) L ₁ ] where L₁ is the one-particle localization length and the coefficient depends on the strength U of the on-site Hubbard interaction. The Breit-Wigner width or equivalently the (inverse) life time of non-interacting pair states is analytically calculated for small disorder and taking into account the energy dependence of the one-particle localization length. This provides a consistent theoretical explanation of the numerically found U-dependence of c(U). Received 16 September 1998     

Dynamic exponent in extremal models of pinning

The depinning transition of a front moving in a time-independent random potential is studied. The temporal development of the overall roughness w(L,t) of an initially flat front, , is the classical means to have access to the dynamic exponent. However, in the case of front propagation in quenched disorder via extremal dynamics, we show that the initial increase in front roughness implies an extra dependence over the system size which comes from the fact that the activity is essentially localized in a narrow region of space. We propose an analytic expression for the exponent and confirm this for different models (crack front propagation, Edwards-Wilkinson model in a quenched noise etc.). Received 27 August 1999