Kinetics of the long-range spherical model

The kinetic spherical model with long-range interactions is studied after a quench to $T < T_c$ or to $T = T_c$. For the two-time response and correlation functions of the order-parameter as well as for composite fields such as the energy density, the ageing exponents and the corresponding scaling functions are derived. The results are compared to the predictions which follow from local scale-invariance.Comment: added "fluctuation-dissipation ratios"; fixed typo

Local scale invariance as dynamical space-time symmetry in phase-ordering kinetics

The scaling of the spatio-temporal response of coarsening systems is studied through simulations of the 2D and 3D Ising model with Glauber dynamics. The scaling functions agree with the prediction of local scale invariance, extending dynamical scaling to a space-time dynamical symmetry.Comment: Latex, 4 pages, 4 figure

On the predictive power of Local Scale Invariance

Local Scale Invariance (LSI) is a theory for anisotropic critical phenomena designed in the spirit of conformal invariance. For a given representation of its generators it makes non-trivial predictions about the form of universal scaling functions. In the past decade several representations have been identified and the corresponding predictions were confirmed for various anisotropic critical systems. Such tests are usually based on a comparison of two-point quantities such as autocorrelation and response functions. The present work highlights a potential problem of the theory in the sense that it may predict any type of two-point function. More specifically, it is argued that for a given two-point correlator it is possible to construct a representation of the generators which exactly reproduces this particular correlator. This observation calls for a critical examination of the predictive content of the theory.Comment: 17 pages, 2 eps figure

Thermal effects in the magnetic Casimir-Polder interaction

We investigate the magnetic dipole coupling between a metallic surface and an atom in a thermal state, ground state and excited hyperine state. This interaction results in a repulsive correction and - unlike the electrical dipole contribution - depends sensitively on the Ohmic dissipation in the material

Two-time autocorrelation function in phase-ordering kinetics from local scale-invariance

The time-dependent scaling of the two-time autocorrelation function of spin systems without disorder undergoing phase-ordering kinetics is considered. Its form is shown to be determined by an extension of dynamical scaling to a local scale-invariance which turns out to be a new version of conformal invariance. The predicted autocorrelator is in agreement with Monte-Carlo data on the autocorrelation function of the 2D kinetic Ising model with Glauber dynamics quenched to a temperature below criticality.Comment: Latex2e, 7 pages with 2 figures, with epl macro, final from, to appear in EP

The first passage probability and control

First-passage probability used as measure of performance in stochastic control problem - dynamic programmin