1999/04/30 by S. M. Alamoudi, D. G. Barci, Daniel G. Barci +7 · 17 citations
Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Condensed matter physics #Coupling (piping) #Geometry #Lambda #Materials science #Mathematical physics #Physics #Quantum mechanics #Quantum, superfluid, helium dynamics #Scalar (mathematics) #Theoretical and Computational Physics #Thermodynamics #cond-mat #hep-ph #nucl-th
paper · pdf · doi:10.1103/physrevd.60.125003
published in Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields 60(12) (American Physical Society) · 40 pages, 4 figures, revtex, minor changes, to be published in Phys. Rev. D
arxiv created 1999/08/22 · openalex publication_date 1999/11/01 · arxiv updated 2016/08/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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 propose a 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 bubble. 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 \ensuremathφ4 scalar field theory at temperature T<Tc, the growth rate to lowest order in the quartic self-coupling \ensuremathλ is \ensuremathΩ=(√(2)/Rc)[1\ensuremath-0.003\ensuremathλT\ensuremathξ(Rc/\ensuremathξ)2] with Rc,\ensuremathξ 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 \ensuremathΩ^\ensuremath-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.