Kramers problem for a multiwell potential

Fluctuational escape from a multiwell potential is shown to display new features, as compared to the conventional single-well case. The flux J may depend on friction gamma exponentially strongly, over an exponentially long period; for small enough temperatures, J(gamma) undergoes marked oscillations in the range of small gamma, and the time evolution of J changes drastically as gamma exceeds a critical value.     

Narrow-escape time problem: time needed for a particle to exit a confining domain through a small window

The time needed for a particle to exit a confining domain through a small window, called the narrow-escape time (NET), is a limiting factor of various processes, such as some biochemical reactions in cells. Obtaining an estimate of the mean NET for a given geometric environment is therefore a requisite step to quantify the reaction rate constant of such processes, which has raised a growing interest in the past few years. In this Letter, we determine explicitly the scaling dependence of the mean NET on both the volume of the confining domain and the starting point to aperture distance. We show that this analytical approach is applicable to a very wide range of stochastic processes, including anomalous diffusion or diffusion in the presence of an external force field, which cover situations of biological relevance.     

Controlling the nonlinear dynamics of the magnetization of a small ferromagnetic particle

A theoretical study was conducted of the excitation and control of the high-amplitude uniform precession of magnetization in small ferromagnetic particles by applying circularly and linearly polarized small-amplitude radio-frequency fields in the autoresonance mode while slowly varying the characteristics of external magnetic fields.     

Instanton paths for the problem of coherent quantum tunneling in small ferromagnetic particles

It is shown that the problem of instantons in ferromagnetic materials in a large-spin model is reduced to an exactly integrable dynamical system with a finite number of variables. For a rather wide class of models, there exists a continuum of instanton paths that form a one-parameter family of paths with essentially different shapes but with the same value of the Euclidean action. On the basis of the formalism developed, exact instanton solutions are constructed that describe macroscopic quantum tunneling for a small ferromagnetic particle with uniaxial or biaxial quadratic anisotropy in the presence of a magnetic field applied perpendicularly to the easy axis. These solutions are valid for any relations between the anisotropy parameters and for any magnitude of the magnetic field and its direction in the base plane. Based on the solutions obtained, the principles of macroscopic quantum tunneling in high-spin-molecule-type magnetic particles are described. Tunneling regimes of two types are obtained: (1) regimes that are characterized by destructive interference of instanton trajectories and oscillatory dependence of the transition probability on the magnitude of the magnetic field and (2) regimes in which all instantons have the same purely real value of the Euclidean action and there is no destructive interference.     

Structure of the mixed state induced in thin YBaCuO superconducting films by the field of a small ferromagnetic particle

The temperature dependence of the local energy barrier to formation of the mixed state in YBaCuO thin-film superconducting samples has been determined. The measurement technique is based on use of a small ferromagnetic particle as the magnetic field source. It is found that the energy barrier to creation of vortices (for the field oriented parallel to the CuO planes) is anomalously small while the dependence of the corresponding threshold current j _c(T) differs substantially from the temperature dependence of the pair-breaking current. The experimental results are interpreted in terms of the model of a Josephson medium. The observed temperature dependence of j _c points to a strong suppression of the superconducting order parameter at the intergrain boundaries, which for the most probable type of boundaries: superconductor-insulator-superconductor, is evidence of anisotropic pairing. Zh. éksp. Teor. Fiz. 116, 1735–1749 (November 1999)     

Short time scales in the Kramers problem: a stepwise growth of the escape flux

We prove rigorously and demonstrate in simulations that, for a potential system staying initially at the bottom of a well, the escape flux over the barrier grows on times of the order of a period of eigenoscillation in a stepwise manner, provided that friction is small or moderate. If the initial state is not at the bottom of the well, then, typically, some of the steps transform into oscillations. The stepwise/oscillatory evolution at short times appears to be a generic feature of a noise-induced flux.     

Secondary particle emission from a ferromagnetic binary compound

Secondary ion emission from an ion-bombarded binary compound in the ferro- and paramagnetic states has been studied using experimental methods and molecular dynamics simulations. The experiments were performed with a widely used NiPd binary compound, which was bombarded by obliquely incident 10-keV Ar ions. It is established that the intensity of Ni⁺ and Pd⁺ ion emission from a polycrystalline NiPd sample decreases significantly when it passes from the ferromagnetic to paramagnetic state. This effect is explained by a change in the surface binding energy and density of surface states at the Fermi level and by a cumulative process related to sputtering. The energies and directions of emission of secondary particles from poly- and single-crystalline NiPd samples in the ferromagnetic state have been jointly studied. It is established that the maximum of the polar angular distribution of secondary particles deviates toward the normal to the irradiated surface with a decrease in their energy. A difference in the azimuthal distribution of emitted Ni and Pd particles has been observed during the bombardment of a (001)NiPd crystal face and explained by specific features of correlated collisions. The best agreement of experimental data with the results of molecular dynamics simulations is obtained if the calculations are performed with allowance for an experimentally established modified composition of the three uppermost surface layers [39].     

Kramers Kronig analysis of the optical properties of small silver particles

In order to complete a preceding paper the dielectric constant? of the particle material of small silver particles with diameters between 210 and 25 Å is computed in the wavelength region 365≦λ≦455 nm from the measured spectra of thesmall particle plasma reasonance absorption. For this purpose a properKramers Kronig relation is derived, and is checked by applying to particles with Drude free electron gas. The results, concerning the silver particles, are that the real part of? changes slightly, whereas the imaginary part is markedly enhanced (up to the ten-fold of the bulk values) if the particle size decreases. This size dependence of? can quantitatively be described with thefree path effect within the accuracy of the measured values. Conversely, thebulk dielectric constant of silver is obtained by applying the free path effect to the measured dielectric constant of the small particles.     

Activated tunneling decay of metastable state: Solution of the Kramers problem

At sufficiently low friction the Fokker-Planck equation for Brownian motion in a potential well is reduced to an integral equation for the energy variable. The basic small parameter of the problem is the ratio of the temperature T to the depth U₀ of the well. Quantum tunneling effects are naturally incorporated into the calculations. An explicit solution for Kramers' problem of the lifetime of the Brownian particle in the potential well is given.     

Dynamical solution to the problem of a small cosmological constant and late-time cosmic acceleration

Increasing evidence suggests that most of the energy density of the universe consists of a dark energy component with negative pressure that causes the cosmic expansion to accelerate. We address why this component comes to dominate the universe only recently. We present a class of theories based on an evolving scalar field where the explanation is based entirely on internal dynamical properties of the solutions. In the theories we consider, the dynamics causes the scalar field to lock automatically into a negative pressure state at the onset of matter domination such that the present epoch is the earliest possible time consistent with nucleosynthesis restrictions when it can start to dominate.     

The DORT solution in acoustic inverse scattering problem of a small elastic scatterer

The DORT (French acronym for Décomposition de l’Opérateur de Retournement Temporel) method is a novel approach for active detection and focusing of acoustic waves on the targets in the scattering medium. This technique involves the determination of the invariant of the time-reversal operator obtained by measurement of the scattering data in a pulse-echo mode. In this paper, a proposed approach based on the DORT method is developed to solve the acoustic inverse scattering problem of a small metallic scatterer. The proposed approach not only estimates the position of the scatterer, but also determines the physical properties of an unknown metallic scatterer such as the shape (cylinder or sphere), the material (density), and the size (radius) in an anisotropic scattering case. Theoretical and numerical simulation results are also studied and investigated to show that the proposed approach can simultaneously characterize all those properties of an unknown metallic scatterer. Moreover, the advantage of the proposed approach is to avoid the complex iterative scheme in solving the direct scattering problem and results in smaller computational load and faster implementation.     

Solution of the exit problem in Brans-Dicke theory

We consider a general scalar field driving inflation in Brans-Dicke theory and use the Brans-Dicke scalar field itself in the decaying factor so as to get a “graceful exit” from the inflationary scenario.     

Switching magnetization of a nanoscale ferromagnetic particle using nonlocal spin injection

We have performed nonlocal spin injection into a nanoscale ferromagnetic particle configured in a lateral spin-valve structure to switch its magnetization only by spin current. The nonlocal spin injection aligns the magnetization of the particle parallel to the magnetization of the spin injector. The spin current responsible for switching is estimated from the experiment to be about 200 microA, which is reasonable compared with the values obtained for conventional pillar structures. Interestingly, the switching always occurs from antiparallel to parallel in the particle-injector magnetic configurations, where no opposite switching is observed. Possible reasons for this discrepancy are discussed.     

Conductivity of a small metallic particle

The size-dependent ac-conductivity of a small metallic particle is studied for electrons enclosed in a box with random impurities. The exact wave functions and energies are calculated numerically up to 500 electrons, then the Kubo-formula is evaluated, and an ensemble average is performed. A strong size- and frequency dependence of the conductivity is found which is in good agreement with random matrix results. The size dependence of the dc-conductivity agrees qualitatively with microwave absorption measurements on submicron particles.     

Asymptotic solution of the anti-plane problem for a two-dimensional lattice

Propagation of unsteady waves under the effect of a step point load on a square lattice of springconnected masses is investigated. The problem is solved by two methods. Asymptotic solutions at large time intervals, which describe the behavior of long-wave perturbations, are derived analytically. The solution over the whole time interval for the waves of the entire spectral range is derived by the finite difference method. These solutions are compared, and their good agreement is shown.