Depinning exponents of the driven long-range elastic string

We perform a high-precision calculation of the critical exponents for the long-range elastic string driven through quenched disorder at the depinning transition, at zero temperature. Large-scale simulations are used to avoid finite-size effects and to enable high precision. The roughness, growth, and velocity exponents are calculated independently, and the dynamic and correlation length exponents are derived. The critical exponents satisfy known scaling relations and agree well with analytical predictions.Comment: 6 pages, 5 figure

Avalanches and Correlations in Driven Interface Depinning

We study the critical behavior of a driven interface in a medium with random pinning forces by analyzing spatial and temporal correlations in a lattice model recently proposed by Sneppen [Phys. Rev. Lett. {\bf 69}, 3539 (1992)]. The static and dynamic behavior of the model is related to the properties of directed percolation. We show that, due to the interplay of local and global growth rules, the usual method of dynamical scaling has to be modified. We separate the local from the global part of the dynamics by defining a train of causal growth events, or "avalanche", which can be ascribed a well-defined dynamical exponent $z_{loc} = 1 + \zeta_c \simeq 1.63$ where $\zeta_c$ is the roughness exponent of the interface. We observe that the avalanche size distribution obeys a power-law decay with an exponent $\kappa \simeq 1.25$.Comment: 7 pages, (5 figures available upon request), REVTeX, RUB-TP3-93-0

Directed Fixed Energy Sandpile Model

We numerically study the directed version of the fixed energy sandpile. On a closed square lattice, the dynamical evolution of a fixed density of sand grains is studied. The activity of the system shows a continuous phase transition around a critical density. While the deterministic version has the set of nontrivial exponents, the stochastic model is characterized by mean field like exponents.Comment: 5 pages, 6 figures, to be published in Phys. Rev.

Domain Dynamics of Magnetic Films with Perpendicular Anisotropy

We study the magnetic properties of nanoscale magnetic films with large perpendicular anisotropy comparing polarization microscopy measurements on Co_28Pt_72 alloy samples based on the magneto-optical Kerr effect with Monte Carlo simulations of a corresponding micromagnetic model. We focus on the understanding of the dynamics especially the temperature and field dependence of the magnetisation reversal process. The experimental and simulational results for hysteresis, the reversal mechanism, domain configurations during the reversal, and the time dependence of the magnetisation are in very good qualitative agreement. The results for the field and temperature dependence of the domain wall velocity suggest that for thin films the hysteresis can be described as a depinning transition of the domain walls rounded by thermal activation for finite temperatures.Comment: 7 pages Latex, Postscript figures included, accepted for publication in Phys.Rev.B, also availible at: http://www.thp.Uni-Duisburg.DE/Publikationen/Publist_Us_R.htm

Driven Depinning in Anisotropic Media

We show that the critical behavior of a driven interface, depinned from quenched random impurities, depends on the isotropy of the medium. In anisotropic media the interface is pinned by a bounding (conducting) surface characteristic of a model of mixed diodes and resistors. Different universality classes describe depinning along a hard and a generic direction. The exponents in the latter (tilted) case are highly anisotropic, and obtained exactly by a mapping to growing surfaces. Various scaling relations are proposed in the former case which explain a number of recent numerical observations.Comment: 4 pages with 2 postscript figures appended, REVTe

Theory of Hysteresis Loop in Ferromagnets

We consider three mechanisms of hysteresis phenomena in alternating magnetic field: the domain wall motion in a random medium, the nucleation and the retardation of magnetization due to slow (critical) fluctuations. We construct quantitative theory for all these processes. The hysteresis is characterized by two dynamic threshold fields, by coercive field and by the so-called reversal field. Their ratios to the static threshold field is shown to be function of two dimensionless variables constituted from the frequency and amplitude of the ac field as well as from some characteristics of the magnet. The area and the shape of the hysteresis loop are found. We consider different limiting cases in which power dependencies are valid. Numerical simulations show the domain wall formation and propagation and confirm the main theoretical predictions. Theory is compared with available experimental data.Comment: RevTex, 13 pages, 8 figures (PostScript), acknowledgements adde

Deterministic delivery of externally cold and precisely positioned single molecular ions

We present the preparation and deterministic delivery of a selectable number of externally cold molecular ions. A laser cooled ensemble of Mg^+ ions subsequently confined in several linear Paul traps inter-connected via a quadrupole guide serves as a cold bath for a single or up to a few hundred molecular ions. Sympathetic cooling embeds the molecular ions in the crystalline structure. MgH^+ ions, that serve as a model system for a large variety of other possible molecular ions, are cooled down close to the Doppler limit and are positioned with an accuracy of one micrometer. After the production process, severely compromising the vacuum conditions, the molecular ion is efficiently transfered into nearly background-free environment. The transfer of a molecular ion between different traps as well as the control of the molecular ions in the traps is demonstrated. Schemes, optimized for the transfer of a specific number of ions, are realized and their efficiencies are evaluated. This versatile source applicable for broad charge-to-mass ratios of externally cold and precisely positioned molecular ions can serve as a container-free target preparation device well suited for diffraction or spectroscopic measurements on individual molecular ions at high repetition rates (kHz).Comment: 11 pages, 8 figure

Efficient photoionization for barium ion trapping using a dipole-allowed resonant two-photon transition

Two efficient and isotope-selective resonant two-photon ionization techniques for loading barium ions into radio-frequency (RF)-traps are demonstrated. The scheme of using a strong dipole-allowed transition at \lambda=553 nm as a first step towards ionization is compared to the established technique of using a weak intercombination line (\lambda=413 nm). An increase of two orders of magnitude in the ionization efficiency is found favoring the transition at 553 nm. This technique can be implemented using commercial all-solid-state laser systems and is expected to be advantageous compared to other narrowband photoionization schemes of barium in cases where highest efficiency and isotope-selectivity are required.Comment: 8 pages, 5 figure

Scaling properties of driven interfaces in disordered media

We perform a systematic study of several models that have been proposed for the purpose of understanding the motion of driven interfaces in disordered media. We identify two distinct universality classes: (i) One of these, referred to as directed percolation depinning (DPD), can be described by a Langevin equation similar to the Kardar-Parisi-Zhang equation, but with quenched disorder. (ii) The other, referred to as quenched Edwards-Wilkinson (QEW), can be described by a Langevin equation similar to the Edwards-Wilkinson equation but with quenched disorder. We find that for the DPD universality class the coefficient $\lambda$ of the nonlinear term diverges at the depinning transition, while for the QEW universality class either $\lambda = 0$ or $\lambda \to 0$ as the depinning transition is approached. The identification of the two universality classes allows us to better understand many of the results previously obtained experimentally and numerically. However, we find that some results cannot be understood in terms of the exponents obtained for the two universality classes {\it at\/} the depinning transition. In order to understand these remaining disagreements, we investigate the scaling properties of models in each of the two universality classes {\it above\/} the depinning transition. For the DPD universality class, we find for the roughness exponent $\alpha_P = 0.63 \pm 0.03$ for the pinned phase, and $\alpha_M = 0.75 \pm 0.05$ for the moving phase. For the growth exponent, we find $\beta_P = 0.67 \pm 0.05$ for the pinned phase, and $\beta_M = 0.74 \pm 0.06$ for the moving phase. Furthermore, we find an anomalous scaling of the prefactor of the width on the driving force. A new exponent $\varphi_M = -0.12 \pm 0.06$, characterizing the scaling of this prefactor, is shown to relate the values of the roughnessComment: Latex manuscript, Revtex 3.0, 15 pages, and 15 figures also available via anonymous ftp from ftp://jhilad.bu.edu/pub/abms/ (128.197.42.52

Interface Scaling in the Contact Process

Scaling properties of an interface representation of the critical contact process are studied in dimensions 1 - 3. Simulations confirm the scaling relation beta_W = 1 - theta between the interface-width growth exponent beta_W and the exponent theta governing the decay of the order parameter. A scaling property of the height distribution, which serves as the basis for this relation, is also verified. The height-height correlation function shows clear signs of anomalous scaling, in accord with Lopez' analysis [Phys. Rev. Lett. 83, 4594 (1999)], but no evidence of multiscaling.Comment: 10 pages, 9 figure