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 leads to the nonequilibrium equation of motion of the coordinate that describes small departures from the critical bubble and allows us to extract the growth rate consistently in a weak coupling expansion and in the thin wall limit. Viscosity effects arise from the interaction of this coordinate with the 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 depends 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 approximation that transcend a particular model. These are long-wavelength hydrodynamic 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 - 0.003 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 Langevin equation for the radial coordinate and derive the generalized fluctuation dissipation relation. The noise is correlated on time scales Omega(-1) as a result of the coupling to the slow hydrodynamic modes. We discuss the applicability of our results to describe the growth rate of hadron bubbles in a quark-hadron first order transition. [S0556-2821(99)07120-9].