Dynamical viscosity of nucleating bubbles - art. no. 125003

We study the viscosity corrections to the growth rate of nucleating bubbles in a slightly supercooled first order phase transition in (1+1)- and (3+1) -dimensional scalar field theory. We proposed microscopic approach that lea ds to the nonequilibrium equation of motion of the coordinate that describe s small departures from the critical bubble and allows us to extract the gr owth rate consistently in a weak coupling expansion and in the thin wall li mit. Viscosity effects arise from the interaction of this coordinate with t he stable quantum and thermal fluctuations around a critical hubble. In the case of 1 + 1 dimensions we provide an estimate for the growth rate that d epends on the details of the free energy functional. In 3 + 1 dimensions we recognize robust features that are a direct consequence of the thin wall a pproximation that transcend a particular model. These are long-wavelength h ydrodynamic fluctuations that describe surface waves. We identify these low energy modes with quasi Goldstone modes which are related to surface waves on interfaces in phase ordered Ising-like systems. In the thin wall limit the coupling of this coordinate to these hydrodynamic modes results in the largest contribution to the viscosity corrections to the growth rate. For a phi(4) scalar field theory at temperature T<T-c, the growth rate to lowest order in the quartic self-coupling lambda is Omega = (root 2/R-c) [1 - 0.0 03 lambda T xi(R-c/xi(2)] with R-c, xi the critical radius and the width of the bubble wall, respectively. We obtain the effective non-Markovian Lange vin equation for the radial coordinate and derive the generalized fluctuati on dissipation relation. The noise is correlated on time scales Omega(-1) a s a result of the coupling to the slow hydrodynamic modes. We discuss the a pplicability of our results to describe the growth rate of hadron bubbles i n a quark-hadron first order transition. [S0556-2821(99)07120-9].