We investigate the process of phase conversion in a thermally-driven {\it weakly} first-order quark-hadron transition. This scenario is physically appealing even if the nature of this transition in equilibrium proves to be a smooth crossover for vanishing baryonic chemical potential. We construct an effective potential by combining the equation of state obtained within Lattice QCD for the partonic sector with that of a gas of resonances in the hadronic phase, and present numerical results on bubble profiles, nucleation rates and time evolution, including the effects from reheating on the dynamics for different expansion scenarios. Our findings confirm the standard picture of a cosmological first-order transition, in which the process of phase conversion is entirely dominated by nucleation, also in the case of a weakly first-order transition. On the other hand, we show that, even for expansion rates much lower than those expected in high-energy heavy ion collisions, nucleation is very unlikely, indicating that the main mechanism of phase conversion is spinodal decomposition. Our results are compared to those obtained for a strongly first-order transition, as the one provided by the MIT bag model.Comment: 12 pages, 10 figures; v2: 1 reference added, minor modifications, matches published versio

We present a systematic semiclassical procedure to compute the partition function for scalar field theories at finite temperature. The central objects in our scheme are the solutions of the classical equations of motion in imaginary time, with spatially independent boundary conditions. Field fluctuations -both field deviations around these classical solutions, and fluctuations of the boundary value of the fields -are resummed in a Gaussian approximation. In our final expression for the partition function, this resummation is reduced to solving certain ordinary differential equations. Moreover, we show that it is renormalizable with the usual 1-loop counterterms.

We show that the one-loop effective action at finite temperature for a scalar field with quartic interaction has the same renormalized expression as at zero temperature if written in terms of a certain classical field φc, and if we trade free propagators at zero temperature for their finitetemperature counterparts. The result follows if we write the partition function as an integral over field eigenstates (boundary fields) of the density matrix element in the functional Schrödinger fieldrepresentation, and perform a semiclassical expansion in two steps: first, we integrate around the saddle-point for fixed boundary fields, which is the classical field φc, a functional of the boundary fields; then, we perform a saddle-point integration over the boundary fields, whose correlations characterize the thermal properties of the system. This procedure provides a dimensionally-reduced effective theory for the thermal system. We calculate the two-point correlation as an example. * abessa@ect.ufrn.br †

We present a unified formulation for quantum statistical physics based on the representation of the density matrix as a functional integral. For quantum statistical ͑thermal͒ field theory, the stochastic variable of the statistical theory is a boundary field configuration. We explore the properties of an effective theory for such boundary configurations and apply it to the computation of the partition function of an interacting onedimensional quantum-mechanical system at finite temperature. Plots of free energy and specific heat show excellent agreement with more involved semiclassical results. The method of calculation provides an alternative to the usual sum over periodic trajectories: it sums over paths with coincident end points and includes nonvanishing boundary terms. An appropriately modified expansion into modified Matsubara modes is presented.