Decay of Magnetic Fields in the Early Universe

We study the evolution of a stochastic helical magnetic field generated in the early Universe after the electroweak phase transition, using standard magnetohydrodynamics (MHD). We find how the coherence length xi, magnetic energy E_M and magnetic helicity H evolve with time. We show that the self-similarity of the magnetic power spectrum alone implies that xi ~ t^{1/2}. This in turn implies that magnetic helicity decays as H ~ t^{-2s}, and that the magnetic energy decays as E_M ~ t^{-0.5-2s}, where s is inversely proportional to the magnetic Reynolds number Re_M. These laws improve on several previous estimates.Comment: 5pp LaTeX + World Sci procs class, 3 eps figs. Talk given at Strong and Electroweak Matter, Oct 2-5 2002, Heidelber

Metastability of persistent currents in trapped gases of atoms

We examine the conditions that give rise to metastable, persistent currents in a trapped Bose-Einstein condensate. A necessary condition for the stability of persistent currents is that the trapping potential is not a monotonically increasing function of the distance from the trap center. Persistent currents also require that the interatomic interactions are sufficiently strong and repulsive. Finally, any off-center vortex state is shown to be unstable, while a driven gas shows hysteresis.Comment: 7 pages, RevTex, 5 figure

Real-time Chern-Simons term for hypermagnetic fields

If non-vanishing chemical potentials are assigned to chiral fermions, then a Chern-Simons term is induced for the corresponding gauge fields. In thermal equilibrium anomalous processes adjust the chemical potentials such that the coefficient of the Chern-Simons term vanishes, but it has been argued that there are non-equilibrium epochs in cosmology where this is not the case and that, consequently, certain fermionic number densities and large-scale (hypermagnetic) field strengths get coupled to each other. We generalise the Chern-Simons term to a real-time situation relevant for dynamical considerations, by deriving the anomalous Hard Thermal Loop effective action for the hypermagnetic fields, write down the corresponding equations of motion, and discuss some exponentially growing solutions thereof.Comment: 13 page

The Cosmic Microwave Background and Helical Magnetic Fields: the tensor mode

We study the effect of a possible helicity component of a primordial magnetic field on the tensor part of the cosmic microwave background temperature anisotropies and polarization. We give analytical approximations for the tensor contributions induced by helicity, discussing their amplitude and spectral index in dependence of the power spectrum of the primordial magnetic field. We find that an helical magnetic field creates a parity odd component of gravity waves inducing parity odd polarization signals. However, only if the magnetic field is close to scale invariant and if its helical part is close to maximal, the effect is sufficiently large to be observable. We also discuss the implications of causality on the magnetic field spectrum.Comment: We have corrected a normalisation error which was pointed out to us by Antony Lewis. It enhances our limits on the magnetic fields by (2\pi)^{3/4} ~