Quantum theory of spin waves in finite chiral spin chains

We calculate the effect of spin waves on the properties of finite-size spin chains with a chiral spin ground state observed on biatomic Fe chains deposited on iridium(001). The system is described with a Heisenberg model supplemented with a Dzyaloshinskii-Moriya coupling and a uniaxial single ion anisotropy that presents a chiral spin ground state. Spin waves are studied using the Holstein-Primakoff boson representation of spin operators. Both the renormalized ground state and the elementary excitations are found by means of Bogoliubov transformation, as a function of the two variables that can be controlled experimentally, the applied magnetic field and the chain length. Three main results are found. First, because of the noncollinear nature of the classical ground state, there is a significant zero-point reduction of the ground-state magnetization of the spin spiral. Second, there is a critical external field from which the ground state changes from chiral spin ground state to collinear ferromagnetic order. The character of the two lowest-energy spin waves changes from edge modes to confined bulk modes over this critical field. Third, in the spin-spiral state, the spin-wave spectrum exhibits oscillatory behavior as function of the chain length with the same period of the spin helix.

Application of density functional theory to analysis of energetic heterogeneity and pore size distribution of activated carbons

A new approach based on the nonlocal density functional theory to determine pore size distribution (PSD) of activated carbons and energetic heterogeneity of the pore wall is proposed. The energetic heterogeneity is modeled with an energy distribution function (EDF), describing the distribution of solid-fluid potential well depth (this distribution is a Dirac delta function for an energetic homogeneous surface). The approach allows simultaneous determining of the PSD (assuming slit shape) and EDF from nitrogen or argon isotherms at their respective boiling points by using a set of local isotherms calculated for a range of pore widths and solid-fluid potential well depths. It is found that the structure of the pore wall surface significantly differs from that of graphitized carbon black. This could be attributed to defects in the crystalline structure of the surface, active oxide centers, finite size of the pore walls (in either wall thickness or pore length), and so forth. Those factors depend on the precursor and the process of carbonization and activation and hence provide a fingerprint for each adsorbent. The approach allows very accurate correlation of the experimental adsorption isotherm and leads to PSDs that are simpler and more realistic than those obtained with the original nonlocal density functional theory.

Effects of graphene layer size on the adsorption of fluids on graphitized thermal carbon black. A computer simulation study

The adsorption of Lennard-Jones fluids (argon and nitrogen) onto a graphitized thermal carbon black surface was studied with a Grand Canonical Monte Carlo Simulation (GCMC). The surface was assumed to be finite in length and composed of three graphene layers. When the GCMC simulation was used to describe adsorption on a graphite surface, an over-prediction of the isotherm was consistently observed in the pressure regions where the first and second layers are formed. To remove this over-prediction, surface mediation was accounted for to reduce the fluid-fluid interaction. Do and co-workers have introduced the so-called surface-mediation damping factor to correct the over-prediction for the case of a graphite surface of infinite extent, and this approach has yielded a good description of the adsorption isotherm. In this paper, the effects of the finite size of the graphene layer on the adsorption isotherm and how these would affect the extent of the surface mediation were studied. It was found that this finite-surface model provides a better description of the experimental data for graphitized thermal carbon black of high surface area (i.e. small crystallite size) while the infinite- surface model describes data for carbon black of very low surface area (i.e. large crystallite size).

Self-organized criticality in dynamics without branching

We demonstrate the phenomenon of self-organized criticality (SOC) in a simple random walk model described by a random walk of a myopic ant, i.e., a walker who can see only nearest neighbors. The ant acts on the underlying lattice aiming at uniform digging, i.e., reduction of the height profile of the surface but is unaffected by the underlying lattice. In one, two, and three dimensions we have explored this model and have obtained power laws in the time intervals between consecutive events of "digging." Being a simple random walk, the power laws in space translate to power laws in time. We also study the finite size scaling of asymptotic scale invariant process as well as dynamic scaling in this system. This model differs qualitatively from the cascade models of SOC.

Universality in the fast orientational relaxation near isotropic-nematic transition

Detailed molecular dynamics simulations of Lennard-Jones ellipsoids have been carried out to investigate the emergence of criticality in the single-particle orientational relaxation near the isotropic-nematic (IN) phase transition. The simulations show a sudden appearance of a power-law behavior in the decay of the second-rank orientational relaxation as the IN transition is approached. The simulated value of the power-law exponent is 0.56, which is larger than the mean-field value (0.5) but less than the observed value (0.63) and may be due to the finite size of the simulated system. The decay of the first-rank orientational time correlation function, on the other hand, is nearly exponential but its decay becomes very slow near the isotropic-nematic transition, The zero-frequency rotational friction, calculated from the simulated angular Velocity correlation function, shows a marked increase near the IN transition.

Growing length and time scales in glass-forming liquids

The glass transition, whereby liquids transform into amorphous solids at low temperatures, is a subject of intense research despite decades of investigation. Explaining the enormous increase in relaxation times of a liquid upon supercooling is essential for understanding the glass transition. Although many theories, such as the Adam-Gibbs theory, have sought to relate growing relaxation times to length scales associated with spatial correlations in liquid structure or motion of molecules, the role of length scales in glassy dynamics is not well established. Recent studies of spatially correlated rearrangements of molecules leading to structural relaxation, termed ``spatially heterogeneous dynamics,'' provide fresh impetus in this direction. A powerful approach to extract length scales in critical phenomena is finite-size scaling, wherein a system is studied for sizes traversing the length scales of interest. We perform finite-size scaling for a realistic glass-former, using computer simulations, to evaluate the length scale associated with spatially heterogeneous dynamics, which grows as temperature decreases. However, relaxation times that also grow with decreasing temperature do not exhibit standard finite-size scaling with this length. We show that relaxation times are instead determined, for all studied system sizes and temperatures, by configurational entropy, in accordance with the Adam-Gibbs relation, but in disagreement with theoretical expectations based on spin-glass models that configurational entropy is not relevant at temperatures substantially above the critical temperature of mode-coupling theory. Our results provide new insights into the dynamics of glass-forming liquids and pose serious challenges to existing theoretical descriptions.

Electron-electron interactions in polyacetylene

Experimental evidence for strong electron-electron interactions in polyacetylene is presented. These include (i) observation of a dipole forbidden state below the optical gap, (ii) observation of negative spin densities at sites at which noninteracting models predict zero spin density (iii) vanishing optical gap, in the infinite chain limit, in the closely related symmetrical linear cyanine dyes. To correctly explain these features it is necessary to solve correlated model Hamiltonians. Using diagrammatic valence bond method model exact solutions of correlated models of finite-size systems can be obtained and various physical properties of the low-lying states can be computed. These properties, when extrapolated to the infinite chain limit explain many of the experimental features observed in polyacetylene.

Supersolid and solitonic phases in the one-dimensional extended Bose-Hubbard model

We report our findings on the quantum phase transitions in cold bosonic atoms in a one-dimensional optical lattice using the finite-size density-matrix renormalization-group method in the framework of the extended Bose-Hubbard model. We consider wide ranges of values for the filling factors and the nearest-neighbor interactions. At commensurate fillings, we obtain two different types of charge-density wave phases and a Mott insulator phase. However, departure from commensurate fillings yields the exotic supersolid phase where both the crystalline and the superfluid orders coexist. In addition, we obtain the signatures for the solitary waves and the superfluid phase.

Bond-order wave phase, spin solitons, and thermodynamics of a frustrated linear spin-1/2 Heisenberg antiferromagnet

The linear spin-1/2 Heisenberg antiferromagnet with exchanges J(1) and J(2) between first and second neighbors has a bond-order wave (BOW) phase that starts at the fluid-dimer transition at J(2)/J(1)=0.2411 and is particularly simple at J(2)/J(1)=1/2. The BOW phase has a doubly degenerate singlet ground state, broken inversion symmetry, and a finite-energy gap E-m to the lowest-triplet state. The interval 0.4 < J(2)/J(1) < 1.0 has large E-m and small finite-size corrections. Exact solutions are presented up to N = 28 spins with either periodic or open boundary conditions and for thermodynamics up to N = 18. The elementary excitations of the BOW phase with large E-m are topological spin-1/2 solitons that separate BOWs with opposite phase in a regular array of spins. The molar spin susceptibility chi(M)(T) is exponentially small for T << E-m and increases nearly linearly with T to a broad maximum. J(1) and J(2) spin chains approximate the magnetic properties of the BOW phase of Hubbard-type models and provide a starting point for modeling alkali-tetracyanoquinodimethane salts.

Dust Deposition on Single Cylinders

The inertial impaction of Lycopodium spores on single wires lying transverse to the direction of flow has been studied. The equations of particle motion in a potential flow field have been modified for the case when Stokes' law is inapplicable. Solutions to the above equations have been obtained by digital computation. Rec, the Reynolds number based on cylinder diameter, varied from 4 to 240; particle trajectories in a flow field at Rec = 10 have been determined for inertia parameter K = 1, 2, 4, 6, and 10. Ten trajectories were developed for the above cases by the numerical stepwise method. Experiments were performed by depositing Lycopodium spores on adhesive-coated wires of various diameters and at different velocities. The weight of dust deposited was determined with a microbalance. The experimental conditions were:. Wire diameters: 345, 457, 1500 μ. Particle diameter: 35 μ. Air velocities: 20-250 cm/sec. Inertia parameter: 1-60. The particle was considered as a point mass in the theoretical analysis. But in the experiments the ratio of particle size to wire size was not negligible (rp/rc = 0·1) and hence the effect of finite size of particle on collection efficiency due to the direct interception effect has been estimated. The effect of particle size distribution on collection efficiency has also been estimated. The experimental efficiencies obtained compare well with the calculated efficiencies at Rec = 10 when direct interception is taken into account.

Analysis of Dynamic Heterogeneity in a Glass Former from the Spatial Correlations of Mobility

The growth of characteristic length scales associated with dynamic heterogeneity in glass-forming liquids is investigated in an extensive computational study of a four-point, time-dependent structure factor defined from spatial correlations of mobility, for a model liquid for system sizes extending up to 351 232 particles, in constant-energy and constant-temperature ensembles. Our estimates for dynamic correlation lengths and susceptibilities are consistent with previous results from finite size scaling. We find scaling exponents that are inconsistent with predictions from inhomogeneous mode coupling theory and a recent simulation confirmation of these predictions.

Triangular Ising antiferromagnet in a staggered field

We study the equilibrium properties of the nearest-neighbor Ising antiferromagnet on a triangular lattice in the presence of a staggered field conjugate to one of the degenerate ground states. Using a mapping of the ground states of the model without the staggered field to dimer coverings on the dual lattice, we classify the ground states into sectors specified by the number of "strings." We show that the effect of the staggered field is to generate long-range interactions between strings. In the limiting case of the antiferromagnetic coupling constant J becoming infinitely large, we prove the existence of a phase transition in this system and obtain a finite lower bound for the transition temperature. For finite J, we study the equilibrium properties of the system using Monte Carlo simulations with three different dynamics. We find that in all the three cases, equilibration times for low-field values increase rapidly with system size at low temperatures. Due to this difficulty in equilibrating sufficiently large systems at low temperatures, our finite-size scaling analysis of the numerical results does not permit a definite conclusion about the existence of st phase transition for finite values of J. A surprising feature in the system is the fact that unlike usual glassy systems; a zero-temperature quench almost always leads to the ground state, while a slow cooling does not.

Dynamical cluster approximation: Nonlocal dynamics of correlated electron systems

We recently introduced the dynamical cluster approximation (DCA), a technique that includes short-ranged dynamical correlations in addition to the local dynamics of the dynamical mean-field approximation while preserving causality. The technique is based on an iterative self-consistency scheme on a finite-size periodic cluster. The dynamical mean-field approximation (exact result) is obtained by taking the cluster to a single site (the thermodynamic limit). Here, we provide details of our method, explicitly show that it is causal, systematic, Phi derivable, and that it becomes conserving as the cluster size increases. We demonstrate the DCA by applying it to a quantum Monte Carlo and exact enumeration study of the two-dimensional Falicov-Kimball model. The resulting spectral functions preserve causality, and the spectra and the charge-density-wave transition temperature converge quickly and systematically to the thermodynamic limit as the cluster size increases.

Light scattering in random media with wavelength-scale structures : astronomical and industrial applications

Light scattering, or scattering and absorption of electromagnetic waves, is an important tool in all remote-sensing observations. In astronomy, the light scattered or absorbed by a distant object can be the only source of information. In Solar-system studies, the light-scattering methods are employed when interpreting observations of atmosphereless bodies such as asteroids, atmospheres of planets, and cometary or interplanetary dust. Our Earth is constantly monitored from artificial satellites at different wavelengths. With remote sensing of Earth the light-scattering methods are not the only source of information: there is always the possibility to make in situ measurements. The satellite-based remote sensing is, however, superior in the sense of speed and coverage if only the scattered signal can be reliably interpreted. The optical properties of many industrial products play a key role in their quality. Especially for products such as paint and paper, the ability to obscure the background and to reflect light is of utmost importance. High-grade papers are evaluated based on their brightness, opacity, color, and gloss. In product development, there is a need for computer-based simulation methods that could predict the optical properties and, therefore, could be used in optimizing the quality while reducing the material costs. With paper, for instance, pilot experiments with an actual paper machine can be very time- and resource-consuming. The light-scattering methods presented in this thesis solve rigorously the interaction of light and material with wavelength-scale structures. These methods are computationally demanding, thus the speed and accuracy of the methods play a key role. Different implementations of the discrete-dipole approximation are compared in the thesis and the results provide practical guidelines in choosing a suitable code. In addition, a novel method is presented for the numerical computations of orientation-averaged light-scattering properties of a particle, and the method is compared against existing techniques. Simulation of light scattering for various targets and the possible problems arising from the finite size of the model target are discussed in the thesis. Scattering by single particles and small clusters is considered, as well as scattering in particulate media, and scattering in continuous media with porosity or surface roughness. Various techniques for modeling the scattering media are presented and the results are applied to optimizing the structure of paper. However, the same methods can be applied in light-scattering studies of Solar-system regoliths or cometary dust, or in any remote-sensing problem involving light scattering in random media with wavelength-scale structures.

Interfacial shear rheology of highly confined glassy polymers

We present results on interfacial shear rheology measurements on Langmuir monolayers of two different polymers, poly(vinyl acetate) and poly(methyl methacrylate) as a function of surface concentration and temperature. While for the high glass transition poly(methyl methacrylate) polymer we find a systematic transition from a viscous dominated regime to an elastic dominated regime as surface concentration is increased, monolayers of the low glass transition polymer, poly(vinyl acetate), remain viscous even at very high surface concentrations. We further interpret the results in terms of the soft glassy rheology model of Sollich et al. P. Sollich, F. C. Lequeux, P. Hebraud and M. E. Cates, Phys. Rev. Lett., 1997, 78, 2020-2023] and provide evidence of possible reduction in glass transition temperatures in both poly(methyl methacrylate) and poly(vinyl acetate) monolayers due to finite size effects.