A U(1) gauge-Higgs system with a radial degree of freedom

The phase diagram of a lattice U(1) gauge-Higgs model is derived without freezing the Higgs field length. For sufficienly small Higgs self-coupling strength, the “confinement” and “Higgs” phases are separated, in contrast to what is observed in the fixed length model.     

On the reconstruction of the conduction electron spectrum in metal-oxide superconductors owing to the interaction with coherent atomic displacements

A “pseudospin ferromagnet” model is proposed which describes the interaction of conduction electrons with coherent atomic displacements in metal-oxide high-T_c superconductors (HTSC). Non-quasiparticle states (“pseudospinons”) play an important role in this model. They make an appreciable contribution to thermodynamic and transport properties (e.g., to the linear term in specific heat), although not contributing to the density of states at E_F at T=0. In the superconducting phase, the pseudospinons give rise to gapless superconductivity at finite temperatures. For certain model parameter relations, a new energy scale (“Kondo temperature”) may occur in the electron spectrum near E_F. Using the results obtained, experimental data on the thermopower, nuclear spin-lattice relaxation rate and other properties of HTSC are discussed.     

Coloured-noise-induced transitions: Exact results for external dichotomous Markovian noise

A general method to calculate explicitly the stationary probability of nonlinear systems subjected to a special case of coloured noise is presented. For a simple model system the “phase diagram” for the various noise-induced transitions is determined.     

Exact solution of a massless scalar field with a relevant boundary interaction

We solve exactly the “boundary sine-Gordon” system of a massless scalar field with a potential at a boundary. This model has appeared in several contexts, including tunneling between quantum-Hall edge states and in dissipative quantum mechanics. For β² < 8π, this system exhibits a boundary renormalization-group flow from Neumann to Dirichlet boundary conditions. By taking the massless limit of the sine-Gordon model with boundary potential, we find the exact S-matrix for particles scattering off the boundary. Using the thermodynamic Bethe ansatz, we calculate the boundary entropy along the entire flow. We show how these particles correspond to wave packets in the classical Klein-Gordon equation, thus giving a more precise explanation of scattering in a massless theory.     

Interfacial waves with free-surface boundary conditions: an approach via a model equation

In a two-fluid system where the lower fluid is bounded below by a rigid bottom and the upper fluid is bounded above by a free surface, two kinds of solitary waves can propagate along the interface and the free surface: classical solitary waves characterized by a solitary pulse or generalized solitary waves with nondecaying oscillations in their tails in addition to the solitary pulse. The classical solitary waves move faster than the generalized solitary waves. The origin of the nonlocal solitary waves can be understood from a physical point of view. The dispersion relation for the above system shows that short waves can propagate at the same speed as a “slow” solitary wave. The interaction between the solitary wave and the short waves creates a nonlocal solitary wave. In this paper, the interfacial-wave problem is reduced to a system of ordinary differential equations by using a classical perturbation method, which takes into consideration the possible resonance between short waves and “slow” solitary waves. In the past, classical Korteweg–de Vries type models have been derived but cannot deal with the resonance. All solutions of the new system of model equations, including classical as well as generalized solitary waves, are constructed. The domain of validity of the model is discussed as well. It is also shown that fronts connecting two conjugate states cannot occur for “fast” waves. For “slow” waves, fronts exist but they have ripples in their tails.     

Core level binding energy shifts of K and Cs adlayers on Ru(001)

Using synchrotron radiation from the VUV ring at NSLS and vacuum ultraviolet radiation from a HeI resonance lamp, we have recorded high resolution photoemission spectra of K and Cs overlayers on Ru(001). It is found that for “thin” multilayer coverages ( 3 ML) the K3p and Cs5p core levels exhibit three sets of core levels which can be assigned to interface, “bulkrd and surface emission in increasing binding energy. The results are discussed in terms of the nature of electronic interaction and a thermodynamic model. The K3p core level spin-orbit splitting is also resolved in these measurements for K in the condensed phase, for the first time with photoemission spectroscopy.     

Estimation of nonlinear transfer functions for fully developed turbulence

A statistical method for modeling the linear and quadratically nonlinear relationship between fluctuations monitored at two points in space or time in a turbulent medium is presented. This relationship is described with the aid of linear and quadratic transfer functions and the concept of coherency is extended to quantify the goodness of the quadratic model. A unique feature of the approach described in this paper is that it is valid for non-Gaussian “input” and “output” signals. The validity of the approach is demonstrated with simulation data. The method is applied to experimental data taken in the turbulent edge plasma of the TEXT tokamak. The results indicate a three wave process with energy transfer to large scale fluctuations. The estimation of transfer functions is a first step in quantitatively measuring coupling coefficients and the energy transfer.     

Spontaneous breaking of scale invariance in a supersymmetric model

The phase structure of a large N, O(N) supersymmetric model in three dimensions is studied. Of special interest is the spontaneous breaking of scale invariance which occurs at a fixed value of the coupling constant, λ₀=λ_c=4π. In this phase the bosons and fermions acquire a mass while a Goldstone boson (dilaton) and Goldstone fermion (“dilatino”) are dynamically generated as massless bound states. The absence of renormalization of the dimensionless coupling constant λ₀ leaves these Goldstone particles massless.     

Coherent noise, scale invariance and intermittency in large systems

We introduce a new class of models in which a large number of “agents” organize under the influence of an externally imposed coherent noise. The model shows reorganization events whose size distribution closely follows a power law over many decades, even in the case where the agents do not interact with each other. In addition, the system displays “aftershock” events in which large disturbances are followed by a string of others at times which are distributed according to a t⁻¹ law. We also find that the lifetimes of the agents in the system possess a power-law distribution. We explain all these results using an approximate analytic treatment of the dynamics and discuss a number of variations on the basic model relevant to the study of particular physical systems.     

Structure and reactivity of environmental interfaces: Application of grazing angle X-ray spectroscopy and long-period X-ray standing waves

Chemical processes occurring at environmental interfaces (e.g. mineral–fluid, mineral–organic matter and mineral–biofilm interfaces) have a profound impact on the environmental fate and bioavailability of aqueous metals and other contaminant species. However, the direct analysis of molecular scale structure and properties of environmental interfaces, particularly under “high-pressure” or “wet” conditions is highly challenging. Synchrotron based X-ray scattering and spectroscopic approaches offer numerous advantages, such as the high penetrating power and molecular scale information inherent to X-ray techniques. Yet, the ability to localize information content to environmental interfaces requires challenging experimental configurations. Here, the application of grazing angle X-ray fluorescence techniques is reviewed, including the presentation of a model formalism that allows for quantitative analysis of fluorescent yield profiles and discussion of the experimental setup. Illustrative examples are discussed, particularly in the context of combining results of GI measurements with the results of other complementary interface probes such as crystal truncation rod diffraction and X-ray microprobe spectroscopic studies.     

Length scale competition in nonlinear Klein-Gordon models: a collective coordinate approach

Working within the framework of nonlinear Klein-Gordon models as a paradigmatic example, we show that length scale competition, an instability of solitons subjected to perturbations of an specific length, can be understood by means of a collective coordinate approach in terms of soliton position and width. As a consequence, we provide a natural explanation of the phenomenon in much simpler terms than any previous treatment of the problem. Our technique allows us to study the existence of length scale competition in most soliton bearing nonlinear models and can be extended to coherent structures with more degrees of freedom.     

The Hadron to quark-gluon transition in relativistic heavy-ion collisions

In this paper we construct a scenario for the QCD transition from the hadron phase to the quark/gluon phase using physical models for these phases. The hadron phase is modeled by a spectrum of hadrons with masses which drop (with a common scaling factor) towards zero at chiral symmetry restoration. The number of hadronic effective degrees of freedom is limited by the number of microscopic degrees of freedom in the quark/gluon phase. This limitation can be imposed either by fiat or through the introduction of a temperature-dependent excluded volume. Given that the number of degrees of freedom in hadrons and in quarks and gluons are roughly equal, the QCD phase transition is inhibited by the bag constant. The only phase transition seen in lattice-gauge calculations, once low-mass quarks are included, is the restoration of chiral symmetry which occurs at the relatively low temperature of ˜ 150 MeV. At present, lattice gauge calculations do not have the resolution to determine the properties of the higher hadronic states accurately. They do, however, demonstrate that chiral restoration takes place in the (ρ. a₁), ( +)), ( −)) and (π, σ) systems by yielding “screening masses” for chiral partners which are distinct for T < T _xSR and identical for T>T _xSR. Further, within numerical accuracy, these “screening masses” are consistent with pure thermal energies and show no evidence of remaining bare masses once chiral symmetry is restored. These, and other lattice-gauge results, will be discussed in the light of our scenario. We shall also consider the consequences of our picture for relativistic heavy-ion experiments.     

Completeness of “good” Bethe ansatz solutions of a quantum-group-invariant Heisenberg model

The sl_q(2) quantum-group-invariant Heisenberg model with open boundary conditions is investigated by means of the Bethe ansatz. As is well known, quantum groups for q equal to a root of unity possess a finite number of “good” representations with non-zero q-dimension and “bad” ones with vanishing q-dimension. Correspondingly, the state space of an invariant Heisenberg chain decomposes into “good” and “bad” states. A “good” state may be described by a path of only “good” representations. It is shown that the “good” states are given by all “good” Bethe ansatz solutions with roots restricted to the first periodicity strip, i.e. only positive-parity strings (in the language of Takahashi) are allowed. Applying Bethe's string-counting technique completeness of the “good” Bethe states is proven, i.e. the same number of states is found as the number of all restricted paths on the sl_q(2) Bratteli diagram. It is the first time that a “completeness” proof for an anisotropic quantum-invariant reduced Heisenberg model is performed.     

Parametrically forced pattern formation

Pattern formation in a nonlinear damped Mathieu-type partial differential equation defined on one space variable is analyzed. A bifurcation analysis of an averaged equation is performed and compared to full numerical simulations. Parametric resonance leads to periodically varying patterns whose spatial structure is determined by amplitude and detuning of the periodic forcing. At onset, patterns appear subcritically and attractor crowding is observed for large detuning. The evolution of patterns under the increase of the forcing amplitude is studied. It is found that spatially homogeneous and temporally periodic solutions occur for all detuning at a certain amplitude of the forcing. Although the system is dissipative, spatial solitons are found representing domain walls creating a phase jump of the solutions. Qualitative comparisons with experiments in vertically vibrating granular media are made. (c) 2001 American Institute of Physics.     

Collective sea-gull effect in πp interactions at 250 GeV/c

A collective “sea-gull” effect is observed for a system of fast hadrons produced in the fragmentation regions of nondiffractive π⁺p-interactions at 250 GeV/c. The effect is not reproduced by the FRITIOF fragmentation model in its details. It is demonstrated that hard-like processes, both in the collision phase and in the fragmentation phase, are not properly treated in the model.     

Monte Carlo simulations on a rigid-rod model for a langmuir monolayer

A monolayer of amphiphilic molecules on water surface (Langmuir monolayer) at the so-called “solid” phase is studied using Monte Carlo simulations. Each molecule is considered to be a rigid rod, one end (the hydrophilic “head”) of which is assumed to be fixed on a two-dimensional lattice, while the other end (the hydrophobic “tail”) interacts with its nearest and next-nearest neighbours through the Lennard-Jones potential. With increase in temperature, the system undergoes a first-order transition from a low-tilt to a high-tilt phase. With increase in tail-length, the two-phase coexistence region decreases and the transition becomes sharper.     

On the low-frequency limit of the Schönfeld pulse 1/f law

On the basis of propositions of the common fluctuation theory, peculiarities of small fluctuations in real physical systems with limited sizes are analyzed. It is established that small fluctuations should necessarily be divided into two types of fluctuations: “small” and “very small”. It is shown that the damping process of “small” fluctuations has relaxation character, while the damping process of “very small” fluctuations is of random character, i.e., it represents a random rectangular signal. The probability density of “very small” fluctuations is shown to be Gaussian. The agreement of the obtained results with experimental data acquired from semiconductor-based devices is analyzed. A relation between the generation–recombination noise and phonon number fluctuations in semiconductors is studied. On the basis of this consideration it is shown that the Schönfeld pulse spectrum preserves its well-known 1/f form only in the range of intermediate frequencies; at lower frequencies the spectrum gets saturated. An expression for the low-frequency limit of Schönfeld pulse 1/f law is obtained.     

The short-range van Hemmen model in a simple Kikuchi approximation: Comparison with the mean-field model and with spin-glasses

A simple first-order Kikuchi approximation is studied for the short-range (nearest-neighbour) version of the van Hemmen mean-field model originally proposed for spin-glasses. Although the approximation is very similar to the mean-field treatment, the phase diagrams from the two methods are drastically different. Previously reported results are reviewed and extended. The “reentrant” ferromagnetic to “spin-glass” transition found in zero magnetic field persists in small fields. The equilibrium magnetization displays a maximum as a function of temperature in the reentrance region. The characteristic S-shape of the magnetization versus field in the “spin-glass” region and magnetic hysteresis are observed. In addition, some exact results concerning the problem of the lower critical dimension of the short-range model are derived.     

Market mill dependence pattern in the stock market: Multiscale conditional dynamics

Market Mill is a complex dependence pattern leading to nonlinear correlations and predictability in intraday dynamics of stock prices. The present paper puts together previous efforts to build a dynamical model reflecting the market mill asymmetries. We show that certain properties of the conditional dynamics at a single time scale such as a characteristic shape of an asymmetry-generating component of the conditional probability distribution result in the “elementary” market mill pattern. This asymmetry-generating component matches the empirical distribution obtained from the market data. Multiple time scale considerations make the resulting “composite” mill similar to the empirical market mill patterns. Multiscale model also reflects a multi-agent nature of the market. Interpretation of variations of asymmetry patterns of individual stocks in terms of specific deformations of the fundamental market mill asymmetry patterns is described.