Multi-channel Bethe-Salpeter equation

A general form of multi-channel Bethe-Salpeter equation is considered. In contradistinction to the hitherto applied approaches, our coupled system of equations leads to the simultaneous solutions for all relativistic four-point Green functions (elastic and inelastic) appearing in a given theory. A set of relations which may be helpful in approximate treatments is given. An example of extracting useful information from the equations is discussed: we consider the most general trilinear coupling of N different scalar fields and obtain - in the ladder approximation - closed expressions for the Regge trajectories and their couplings to different channels in the vicinity of l = -1. Sum rules and an example containing non-obvious symmetry are discussed.Comment: 16 pages. Extended version published in JHEP. Uses JHEP.cls (included

Barkhausen noise in the Random Field Ising Magnet Nd2_2Fe14_{14}B

With sintered needles aligned and a magnetic field applied transverse to its easy axis, the rare-earth ferromagnet Nd$_2$Fe$_{14}$B becomes a room-temperature realization of the Random Field Ising Model. The transverse field tunes the pinning potential of the magnetic domains in a continuous fashion. We study the magnetic domain reversal and avalanche dynamics between liquid helium and room temperatures at a series of transverse fields using a Barkhausen noise technique. The avalanche size and energy distributions follow power-law behavior with a cutoff dependent on the pinning strength dialed in by the transverse field, consistent with theoretical predictions for Barkhausen avalanches in disordered materials. A scaling analysis reveals two regimes of behavior: one at low temperature and high transverse field, where the dynamics are governed by the randomness, and the second at high temperature and low transverse field where thermal fluctuations dominate the dynamics.Comment: 16 pages, 7 figures. Under review at Phys. Rev.

Space Representation of Stochastic Processes with Delay

We show that a time series $x_t$ evolving by a non-local update rule $x_t = f (x_{t-n},x_{t-k})$ with two different delays $k<n$ can be mapped onto a local process in two dimensions with special time-delayed boundary conditions provided that $n$ and $k$ are coprime. For certain stochastic update rules exhibiting a non-equilibrium phase transition this mapping implies that the critical behavior does not depend on the short delay $k$. In these cases, the autocorrelation function of the time series is related to the critical properties of directed percolation.Comment: 6 pages, 8 figure

Accuracy controlled data assimilation for parabolic problems

This paper is concerned with the recovery of (approximate) solutions to parabolic problems from incomplete and possibly inconsistent observational data, given on a time-space cylinder that is a strict subset of the computational domain under consideration. Unlike previous approaches to this and related problems our starting point is a regularized least squares formulation in a continuous infinite-dimensional setting that is based on stable variational time-space formulations of the parabolic PDE. This allows us to derive a priori as well as a posteriori error bounds for the recovered states with respect to a certain reference solution. In these bounds the regularization parameter is disentangled from the underlying discretization. An important ingredient for the derivation of a posteriori bounds is the construction of suitable Fortin operators which allow us to control oscillation errors stemming from the discretization of dual norms. Moreover, the variational framework allows us to contrive preconditioners for the discrete problems whose application can be performed in linear time, and for which the condition numbers of the preconditioned systems are uniformly proportional to that of the regularized continuous problem. In particular, we provide suitable stopping criteria for the iterative solvers based on the a posteriori error bounds. The presented numerical experiments quantify the theoretical findings and demonstrate the performance of the numerical scheme in relation with the underlying discretization and regularization

Magnetic hysteresis in Ising-like dipole-dipole model

Using zero temperature Monte Carlo simulations we have studied the magnetic hysteresis in a three-dimensional Ising model with nearest neighbor exchange and dipolar interaction. The average magnetization of spins located inside a sphere on a cubic lattice is determined as a function of magnetic field varied periodically. The simulations have justified the appearance of hysteresis and allowed us to have a deeper insight into the series of metastable states developed during this process.Comment: REVTEX, 10 pages including 4 figure

Static Versus Dynamic Friction: The Role of Coherence

A simple model for solid friction is analyzed. It is based on tangential springs representing interlocked asperities of the surfaces in contact. Each spring is given a maximal strain according to a probability distribution. At their maximal strain the springs break irreversibly. Initially all springs are assumed to have zero strain, because at static contact local elastic stresses are expected to relax. Relative tangential motion of the two solids leads to a loss of coherence of the initial state: The springs get out of phase due to differences in their sizes. This mechanism alone is shown to lead to a difference between static and dynamic friction forces already. We find that in this case the ratio of the static and dynamic coefficients decreases with increasing relative width of the probability distribution, and has a lower bound of 1 and an upper bound of 2.Comment: 10 pages, 2 figures, revtex

Long-range epidemic spreading with immunization

We study the phase transition between survival and extinction in an epidemic process with long-range interactions and immunization. This model can be viewed as the well-known general epidemic process (GEP) in which nearest-neighbor interactions are replaced by Levy flights over distances r which are distributed as P(r) ~ r^(-d-sigma). By extensive numerical simulations we confirm previous field-theoretical results obtained by Janssen et al. [Eur. Phys. J. B7, 137 (1999)].Comment: LaTeX, 14 pages, 4 eps figure