Weak External Field Research Articles

Random Field Induced Order in Low Dimension I

Consider the classical XY model in a weak random external field pointing along the Y axis with strength \({\epsilon}\). We prove that the model defined on \({\mathbb{Z}^3}\) with nearest neighbor coupling exhibits residual magnetic order in the horizontal direction for arbitrarily weak random field strengths and, depending on field strength, sufficiently low temperature.

Domain wall motion in thin ferromagnetic nanotubes: Analytic results

Dynamics of magnetization domain walls (DWs) in thin ferromagnetic nanotubes subject to weak longitudinal external fields is addressed analytically in the regimes of strong and weak penalization. Exact solutions for the DW profiles and formulas for the DW propagation velocity are derived in both regimes. In particular, the DW speed is shown to depend nonlinearly on the nanotube radius.

Systematic effective field theory analysis of the D=2+1 quantum XY model at low temperatures

The low-temperature properties of the (2 + 1)-dimensional quantum XY model are studied within the framework of effective Lagrangians up to three-loop order. At zero temperature, the system is characterized by a spontaneously broken spin rotation symmetry, O(2) → 1, where the corresponding Goldstone bosons are the spin waves or magnons. Even though there is no spontaneously broken order at finite T, the low-temperature behavior of the system is still governed by the spin waves. The partition function is evaluated and various thermodynamic quantities, including the order parameter, are derived in the presence of a weak external field. In particular, we show that the spin-wave interaction is repulsive at low temperatures, its magnitude depending on the strength of the external field. We compare our results with those for the (2 + 1)-dimensional antiferromagnetic Heisenberg model, which, at T = 0, exhibits the spontaneously broken spin rotation symmetry O(3) → O(2).

Magnetic fields in a limb flare on July 19, 2012

The magnetic field intensity in the limb solar flare of July 19, 2012, was measured by the Zeeman bisector splitting in the Hα line. An average magnetic field is established to attain 200 G at a measurement error of ±100 G in the top of a radiant flare loop at a height of about 40 Mm. The confinement of a strong magnetic field in the high coronal arcade at a relatively weak external field of the corona (about 1–2 G) is considered using a model of a force-free magnetic flux rope with a fine magnetic structure at a scale of about 300 km.

Effects of boundaries on structure formation in low-dimensional colloid model systems near the liquid-solid-transition in equilibrium and in external fields and under shear

A brief review focusing on low-dimensional colloidal model systems is given describing both simulation studies and complementary experiments, elucidating the interplay between phase behavior, geometric structures, and transport phenomena. These studies address the response of these very soft colloidal systems to perturbations such as uniform or uniaxial compression, laser fields, randomly quenched disorder, and shear deformation caused by moving boundaries. Binary hard-disk mixtures are studied by Monte Carlo simulation, to investigate ordering on surfaces or in monolayers, modeling the effect of a substrate by an external potential. By weak external laser fields the miscibility of the mixture can be controlled, and the underlying mechanism (laser-induced demixing) is clarified. The stability of various space-filling structures is discussed only for the case where no laser fields are present.Hard spheres interacting with repulsive screened Coulomb or dipolar interaction confined in 2D and 3D narrow constrictions are investigated by Brownian Dynamics simulation. With respect to the structural behavior, it is found that layers or planes throughout the microchannel are formed. The arrangement of the particles is disturbed by diffusion, and can also be modified by an external driving force causing a density gradient along the channel. Then the number of layers or planes gets reduced, adjusting to the density gradient, and this self-organized change of order also shows up in the particle velocities. The experimental work that is reviewed here addresses dipolar colloidal particles confined by gravity on a solid substrate on which a set of pinning sites has been randomly distributed. The dynamics of the system is studied by tracking the trajectories of individual particles, and it is found that the mean square displacements of particles that are nearest neighbors of pinned particles are strongly affected by these defects. The influence of the pinning sites on the order and microscopic mechanism of phase transitions in two dimensions is investigated.

Electromagnetic properties of massive neutrinos

The vertex function for a virtual massive neutrino is calculated in the limit of soft real photons. A method based on employing the neutrino self-energy operator in a weak external electromagnetic field in the approximation linear in the field is developed in order to render this calculation of the vertex function convenient. It is shown that the electric charge and the electric dipole moment of the real neutrino are zero; only the magnetic moment is nonzero for massive neutrinos. A fourth-generation heavy neutrino of mass not less than half of the Z-boson mass is considered as a massive neutrino.

How does degree heterogeneity affect nucleation on complex networks?

Nucleation is an initiating process of a stable phase from a metastable phase in a first-order phase transition. Taking the Ising model as a paradigm, we investigate the dynamics of nucleation on complex networks and focus on the role played by the heterogeneity of degree distribution on nucleation rate. Using Monte Carlo simulation combined with forward flux sampling, we find that for a weak external field the nucleation rate decreases monotonically as degree heterogeneity increases. Interestingly, for a relatively strong external field the nucleation rate exhibits a nonmonotonic dependence on degree heterogeneity, in which there exists a maximal nucleation rate at an intermediate level of degree heterogeneity. Furthermore, we develop a heterogeneous mean-field theory for evaluating the free-energy barrier of nucleation. The theoretical estimations are qualitatively consistent with the simulation results. Our study suggests that degree heterogeneity plays a nontrivial role in the dynamics of phase transitions in networked Ising systems.

Classical spin glass system in external field with taking into account relaxation effects

We study statistical properties of disordered spin systems under the influence of an external field with taking into account relaxation effects. For description of system the spatial 1D Heisenberg spin-glass Hamiltonian is used. In addition, we suppose that interactions occur between nearest-neighboring spins and they are random. Exact solutions which define angular configuration of the spin in nodes were obtained from the equations of stationary points of Hamiltonian and the corresponding conditions for the energy local minimum. On the basis of these recurrent solutions an effective parallel algorithm is developed for simulation of stabile spin-chains of an arbitrary length. It is shown that by way of an independent order of N2 numerical simulations (where N is number of spin in each chain) it is possible to generate ensemble of spin-chains, which is completely ergodic which is equivalent to full self-averaging of spin-chains’ vector polarization. Distributions of different parameters (energy, average polarization by coordinates, and spin-spin interaction constant) of unperturbed system are calculated. In particular, analytically is proved and numerically is shown, that for the Heisenberg nearest-neighboring Hamiltonian model, the distribution of spin-spin interaction constants as opposed to widely used Gauss-Edwards-Anderson distribution satisfies Levy alpha-stable distribution law. This distribution is nonanalytic function and does not have variance. In the work we have in detail studied critical properties of an ensemble depending on value of external field parameters (from amplitude and frequency) and have shown that even at weak external fields the spin-glass systemis strongly frustrated. It is shown that frustrations have fractal behavior, they are selfsimilar and do not disappear at scale decreasing of area. By the numerical computation is shown that the average polarization of spin-glass on a different coordinates can have values which can lead to catastrophes in the equation ofClausius-Mossotti for dielectric constant. In other words, for some values of external field parameter, a critical phenomenon occurs in the system which is impossible to describe by the real-valued Heisenberg spin-glass Hamiltonian. For the solution of this problem at first the complex-valued disordered Hamiltonian is used. Physically this type of extension of Hamiltonian allows to consider relaxation effects which occur in the system under the influence of an external field. On the basis of developed approach an effective parallel algorithm is developed for simulation of statistic parameters of spin-glass system under the influence of an external field.

Nonequilibrium stationary state of a current-carrying thermostated system

We find an explicit expression for the long time evolution and stationary speed distribution of N point particles in 2D moving under the action of a weak external field E, and undergoing elastic collisions with either a fixed periodic array of convex scatterers, or with virtual random scatterers. The total kinetic energy of the N-particles is kept fixed by a Gaussian thermostat which induces an interaction between the particles. We show analytically and numerically that for weak fields this distribution is universal, i.e., independent of the position or shape of the obstacles, as far as they form a dispersing billiard with finite horizon, or the nature of the stochastic scattering. Our results are nonperturbative. They exploit the existence of two time scales; the velocity directions become uniformized in times of order unity while the speeds change only on a time scale of O(|E|−2).

Large deviation principles for nongradient weakly asymmetric stochastic lattice gases

We consider a lattice gas on the discrete d-dimensional torus $(\mathbb{Z}/N\mathbb{Z})^d$ with a generic translation invariant, finite range interaction satisfying a uniform strong mixing condition. The lattice gas performs a Kawasaki dynamics in the presence of a weak external field E/N. We show that, under diffusive rescaling, the hydrodynamic behavior of the lattice gas is described by a nonlinear driven diffusion equation. We then prove the associated dynamical large deviation principle. Under suitable assumptions on the external field (e.g., E constant), we finally analyze the variational problem defining the quasi-potential and characterize the optimal exit trajectory. From these results we deduce the asymptotic behavior of the stationary measures of the stochastic lattice gas, which are not explicitly known. In particular, when the external field E is constant, we prove a stationary large deviation principle for the empirical density and show that the rate function does not depend on E.

Ultrafast heating and magnetic switching with weak external magnetic field

The TbFeCo magneto-optical media with the coercivity of bigger than 1.0 kOe are used for the investigation of ultrafast heating and magnetic switching with the weak external magnetic field. It has been found that the laser-induced active region becomes larger with an external magnetic field because the boundary of the active region is magnetized with the assistance of the external field during the ultrafast heating. According to this physical phenomenon, the so called “mark expansion method” has been proposed for visual observation of ultrafast switching marks. Using this method, the ultrafast magnetic switching in TbFeCo media has been studied using 40 fs laser pulse with linear polarization. The result shows that the ultrafast magnetic switching can be implemented by the laser pulse with assistance of the weak external field of about 0.7 kOe. Further studies show that the area percentage of the magnetic mark expansion relative to its thermal mark decreases with the increasing of the laser pulse energy. There exists the threshold pulse energy that the active region is fully magnetized. The theoretical analysis of electron, spin, and lattice temperatures has been conducted to the active region of the media where the maximum spin temperature is close to the Curie temperature of the media. The result indicates that the media become active at 4.137 ps and the ultrafast heating plays a key role for the ultrafast magnetic switching. The weak external magnetic field provides sufficient driving force to control the magnetization direction in the media.

Magnetic Microstructures for Control of Brownian Motion and Microparticle Transport

A platform of microscopic magnetic wires and discrete bits of disks patterned on a surface offers dynamic control over the motion of fluid borne magnetic particles. The energy landscape associated with the local domain wall field originating from zigzag wire vertices is tuned by weak external fields to vary Brownian trajectories between strong confinements and delocalized spatial excursions. The corresponding spatial coverage of single particle trajectories allows the energy profile of such a magnetic trap to be mapped. Remote manipulation and guided transport of these objects across various opaque and transparent rigid surfaces as well as flexible films supporting discrete magnetic disks is presented.

Effects of confinement and external fields on structure and transport in colloidal dispersions in reduced dimensionality

In this work, we focus on low-dimensional colloidal model systems, via simulation studies and also some complementary experiments, in order to elucidate the interplay between phase behavior, geometric structures and transport properties. In particular, we try to investigate the (nonlinear!) response of these very soft colloidal systems to various perturbations: uniform and uniaxial pressure, laser fields, shear due to moving boundaries and randomly quenched disorder. We study ordering phenomena on surfaces or in monolayers by Monte Carlo computer simulations of binary hard-disk mixtures, the influence of a substrate being modeled by an external potential. Weak external fields allow a controlled tuning of the miscibility of the mixture. We discuss the laser induced de-mixing for the three different possible couplings to the external potential. The structural behavior of hard spheres interacting with repulsive screened Coulomb or dipolar interaction in 2D and 3D narrow constrictions is investigated using Brownian dynamics simulations. Due to misfits between multiples of the lattice parameter and the channel widths, a variety of ordered and disordered lattice structures have been observed. The resulting local lattice structures and defect probabilities are studied for various cross sections. The influence of a self-organized order within the system is reflected in the velocity of the particles and their diffusive behavior. Additionally, in an experimental system of dipolar colloidal particles confined by gravity on a solid substrate we investigate the effect of pinning on the dynamics of a two-dimensional colloidal liquid. This work contains sections reviewing previous work by the authors as well as new, unpublished results. Among the latter are detailed studies of the phase boundaries of the de-mixing regime in binary systems in external light fields, configurations for shear induced effects at structured walls, studies on the effect of confinement on the structures and defect densities in three-dimensional systems, the effect of confinement and barriers on two-dimensional flow and diffusion, and the effect of pinning sites on the diffusion.

A new parallel algorithm for simulation of spin glasses on scales of space-time periods of external fields with consideration of relaxation effects

We have investigated the statistical properties of an ensemble of disordered 1D spatial spin chains (SSCs) of finite length, placed in an external field, with consideration of relaxation effects. The short-range interaction complex-classical Hamiltonian was first used for solving this problem. A system of recurrent equations is obtained on the nodes of the spin-chain lattice. An efficient mathematical algorithm is developed on the basis of these equations with consideration of advanced Sylvester conditions which allows one to step by step construct a huge number of stable spin chains in parallel. The distribution functions of different parameters of spin glass system are constructed from first principles by analyzing the calculation results of the 1D SSCs ensemble. It is shown that the behaviors of different distributions parameters are quite different even at weak external fields. The ensemble energy and constants of spin-spin interactions are being changed smoothly depending on the external field in the limit of statistical equilibrium, while some of them such as the mean value of polarizations of the ensemble and parameters of its orderings are frustrated. We have also studied some critical properties of the ensemble such as catastrophes in the Clausius-Mossotti equation depending on the value of the external field. We have shown that the generalized complex-classical approach excludes these catastrophes, which allows one to organize continuous parallel computing on the whole region of values of the external field including critical points. A new representation of the partition function is suggested based on these investigations. Being opposite to the usual definition, it is a complex function and its derivatives are everywhere defined, including at critical points.

Particle motion in weak relativistic gravitational fields

We derive the geodesic equation of motion in the presence of weak gravitational fields produced by relativistic sources such as cosmic strings, decomposed into scalar, vector and tensor parts. To test the result, we perform the first N-body simulations with relativistic weak gravitational external fields. Our test case is a moving straight string, for which we recover the well-known result for the impulse on nonrelativistic particles. We find that the vector (gravito-magnetic) force is an essential contributor. Our results mean that it is now possible to incorporate straightforwardly into N-body simulations all weak relativistic sources, including networks of cosmic defects.

Open field equilibrium current and cross-field passing electrons as an initiator of a closed flux surface in EC-heated toroidal plasmas

A model for the non-inductive initiation of a closed flux surface observed in electron cyclotron (EC) heated toroidal plasmas is presented. First, a pressure-driven equilibrium toroidal current develops under a weak external vertical field so as to counter balance the pressure-ballooning and current-hoop forces. When the self-field from the current almost cancels out the external vertical field, a forward energetic part of electrons in the velocity space begins to make cross-field passing (CFP) orbits. The CFP electrons are generated by the EC heating of bulk electrons and subsequent pitch-angle scattering, which is analyzed using the Fokker–Planck equation. They provide an additional current that closes the field lines. The model is examined for experiments in the small low aspect ratio device of LATE and in the large conventional device of JT-60U with a search for appropriate modes of EC heating. Simultaneous coincidence of the model with these two experiments is obtained in terms of microwave power and driven current. The results predict that initiation of a closed flux surface requires more and more EC power as the plasma major radius increases. In particular, careful injection of high N‖ EC waves is needed for large devices, both for initiation of a closed flux surface and for subsequent enlargement of the flux surface by the usual EC current drive onto the closed flux area.

Exploring initial correlations in a Gibbs state by application of external field

We demonstrate that local application of a weak external field increases distinguishability between states with and without initial correlations. We consider the case where a two-level system linearly and adiabatically interacts with an infinite number of bosons. We evaluate the trace distance (or, equivalently, the Hilbert-Schmidt distance) between the quantum states which evolve from two kinds of initial states; the correlated Gibbs state and its uncorrelated marginal state. We find that the trace distance increases above its initial value for any and all parameter settings. This indicates that we can explore the existence of initial system-environment correlations with applying a local external field, which causes the breakdown of the contractivity.

Environment-assisted metrology with spin qubits

We investigate the sensitivity of a recently proposed method for precision measurement [Phys. Rev. Lett. 106, 140502 (2011)], focusing on an implementation based on solid-state spin systems. The scheme amplifies a quantum sensor response to weak external fields by exploiting its coupling to spin impurities in the environment. We analyze the limits to the sensitivity due to decoherence and propose dynamical decoupling schemes to increase the spin coherence time. The sensitivity is also limited by the environment spin polarization; therefore, we discuss strategies to polarize the environment spins and present a method to extend the scheme to the case of zero polarization. The coherence time and polarization determine a figure of merit for the environment's ability to enhance the sensitivity compared to echo-based sensing schemes. This figure of merit can be used to engineer optimized samples for high-sensitivity nanoscale magnetic sensing, such as diamond nanocrystals with controlled impurity density.

Vector-axial vector correlators in weak electric field and the holographic dynamics of the chiral condensate

Abstract The transverse part of the vector-axial vector flavor current correlator in the presence of weak external electric field is studied using holography. The correlator is calculated using a bottom-up model proposed recently, that includes both contributions of higher string states and the non-linear dynamics of the chiral condensate. It is shown that for low momenta the result agrees with the relation proposed by Son and Yamamoto motivated by a simpler holographic model. This suggests that the Son-Yamamoto relation is generically valid in the IR of models with the proper chiral symmetry breaking pattern.

Efficient Adsorption and Combined Heterogeneous/Homogeneous Fenton Oxidation of Amaranth Using Supported Nano-FeOOH As Cathodic Catalysts

Iron oxyhydroxide (FeOOH) as heterogeneous catalyst has been widely used in Fenton-like advanced oxidation processes due to its attractive properties such as wide-operating pH range and controllable iron leaching into solution. However, little is known about the Fe3+/Fe2+ transformation of supported FeOOH catalyst under the external electrical field condition, which is of the essence in electro-Fenton-like oxidation reactions. In this study, activated carbon-supported nano-FeOOH (FeOOH/AC) catalysts were prepared by the air oxidation of ferrous hydroxide suspension method. The as-prepared catalyst was characterized with various characterization techniques and identified as goethite and lepidocrocite mixed crystals. Adsorption and electrochemically assisted oxidation of amaranth with the FeOOH/AC heterogeneous catalysts were investigated at pH 4.0 using graphite felt as cathode. Under weak acidic and external electric field conditions, the supported nano-FeOOH catalyst undergoes proton-promoted dissolution and electrochemical reductive dissolution processes, which facilitates Fe3+/Fe2+ transformation and produces a beneficial enhancement of the heterogeneous/homogeneous electro-Fenton reaction rates. Experimental results demonstrated that the FeOOH/AC heterogeneous catalyst possesses admirable adsorbability, and the electrochemically assisted oxidation of amaranth takes place not only through the heterogeneous Fenton reaction on catalyst/solution interface but also through the homogeneous Fenton reaction in bulk solution due to iron liberation from the supported nano-FeOOH. In addition, a possible electrochemically assisted oxidation mechanism is also proposed.