Nuclei colliding at very high energy create a strong, quasi-classical gluon field during the initial phase of their interaction. We present an analytic calculation of the initial space-time evolution of this field in the limit of very high energies using a formal recursive solution of the Yang-Mills equations. We provide analytic expressions for the initial chromo-electric and chromo-magnetic fields and for their energy-momentum tensor. In particular, we discuss event-averaged results for energy density and energy flow as well as for longitudinal and transverse pressure of this system. For example, we find that the ratio of longitudinal to transverse pressure very early in the system behaves as pL/pT = −[1 − 3 2awhere τ is the longitudinal proper time, Q is related to the saturation scales Qs of the two nuclei, and a = ln(Q 2 /m 2 ) withm a scale to be defined later. Our results are generally applicable if τ 1/Q. As already discussed in a previous paper, the transverse energy flow S i of the gluon field exhibits hydrodynamic-like contributions that follow transverse gradients of the energy density ∇ i ε. In addition, a rapidity-odd energy flow also emerges from the non-abelian analog of Gauss' Law and generates non-vanishing angular momentum of the field. We will discuss the space-time picture that emerges from our analysis and its implications for observables in heavy ion collisions.

We discuss a model for the energy distribution and the early space-time evolution of a heavy ion collision. We estimate the gluon field generated in the wake of hard processes and through primordial fluctuations of the color charges in the nuclei. Without specifying the dynamical mechanism of thermalization we calculate the energy momentum tensor of the following plasma phase. The results of this model can be used as initial conditions for a further hydrodynamic evolution.Comment: Contribution to Quark Matter 2005; 4 pages, 4 figure

We apply a large-scale computational technique, known as topology optimization, to the inverse design of photonic Dirac cones. In particular, we report on a variety of photonic crystal geometries, realizable in simple isotropic dielectric materials, which exhibit dual-polarization Dirac cones. We present photonic crystals of different symmetry types, such as four-fold and six-fold rotational symmetries, with Dirac cones at different points within the Brillouin zone. The demonstrated and related optimization techniques open new avenues to bandstructure engineering and manipulating the propagation of light in periodic media, with possible applications to exotic optical phenomena such as effective zero-index media and topological photonics.

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