Parametric Resonance For Complex Fields

Recently, there have been studies of parametric resonance decay of oscillating real homogeneous cosmological scalar fields, in both the narrow-band and broad-band case, primarily within the context of inflaton decay and (p)reheating. However, many realistic models of particle cosmology, such as supersymmetric ones, inherently involve complex scalar fields. In the oscillations of complex scalars, a relative phase between the oscillations in the real and imaginary components may prevent the violations of adiabaticity that have been argued to underly broad-band parametric resonance. In this paper, we give a treatment of parametric resonance for the decay of homogeneous complex scalar fields, analyzing properties of the resonance in the presence of out of phase oscillations of the real and imaginary components. For phase-invariant coupling of the driving parameter field to the decay field, and Mathieu type resonance, we give an explicit mapping from the complex resonance case to an equivalent real case with shifted resonance parameters. In addition, we consider the consequences of the complex field case as they apply to ``instant preheating,'' the explosive decay of non-convex potentials, and resonance in an expanding FRW universe. Applications of our considerations to supersymmetric cosmological models will be presented elsewhere.Comment: 20 pages, 2 figure

Unloaded Speed of Shortening in Voltage-Clamped Intact Skeletal Muscle Fibers from wt, mdx, and Transgenic Minidystrophin Mice Using a Novel High-Speed Acquisition System

Skeletal muscle unloaded shortening has been indirectly determined in the past. Here, we present a novel high-speed optical tracking technique that allows recording of unloaded shortening in single intact, voltage-clamped mammalian skeletal muscle fibers with 2-ms time resolution. L-type Ca2+ currents were simultaneously recorded. The time course of shortening was biexponential: a fast initial phase, τ1, and a slower successive phase, τ2, with activation energies of 59 kJ/mol and 47 kJ/mol. Maximum unloaded shortening speed, vu,max, was faster than that derived using other techniques, e.g., ∼14.0 L0 s−1 at 30°C. Our technique also allowed direct determination of shortening acceleration. We applied our technique to single fibers from C57 wild-type, dystrophic mdx, and minidystrophin-expressing mice to test whether unloaded shortening was affected in the pathophysiological mechanism of Duchenne muscular dystrophy. vu,max and au,max values were not significantly different in the three strains, whereas τ1 and τ2 were increased in mdx fibers. The results were complemented by myosin heavy and light chain (MLC) determinations that showed the same myosin heavy chain IIA profiles in the interossei muscles from the different strains. In mdx muscle, MLC-1f was significantly increased and MLC-2f and MLC-3f somewhat reduced. Fast initial active shortening seems almost unaffected in mdx muscle