BARYON NUMBER DIFFUSION AND SHAPE INSTABILITIES IN THE QUARK-HADRON PHASE-TRANSITION FOR HEAVY-ION COLLISIONS AND COSMOLOGY

If the quark-hadron transition is first order, hadron bubbles nucleate with a radius R(nuc) and grow into the quark sea. Baryon number prefe rs to reside in the quark phase and must diffuse away from the interfa ce in order for the phase transition to proceed. This slowly diffusing excess baryon number that forms on the surface of the bubble wall may drive a shape instability of the bubble wall. This instability to non -spherical structure occurs when the bubbles have grown to a critical size of (7-1000)R(nuc), a much shorter length scale than the instabili ties studied previously; this effect can thus be important for heavy-i on collisions. The stability of the bubbles depends very sensitively o n the ratio epsilon = n(h)/n(q) of baryon number in the two phases (in local thermodynamic equilibrium). For the expected values of the para meters, bubbles of the hadronic phase are likely to be stable in the e arly Universe and unstable in heavy-ion collisions. The phenomenology of heavy-ion collisions could be altered by the instability of the had ron bubbles, although future work that takes into account mutual heati ng effects of the bubbles and the expansion of the hot underlying plas ma will be required to confirm this.