Phase nucleation in curved space

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The work carried so far has been focusing on developing a technique to compute quantum vacuum effects in stationary backgrounds and in theories with interactions, as these allow to consider phase transitions and bubble nucleation.We have developed such a method for a nonlinear quantum field theory for which we could exactly integrate the equation of motion and in turn quantize the theory at full nonlinear level, without resorting to a perturbative approach. Furthermore we have developed an original and very powerful numerical implementation of zeta-function regularization, based on the Weyl spectral theorem. We have tested this approach to compute the vacuum energy in a variety of cases (work published in Physical Review D) and we have just extended the approach to a non-relativistic Schrodinger quantum field theory (a paper is being written up and should be submitted before the summer).The problem we are currently engaged in has to do with the formation of bubbles, as outlined in the research proposal, in the context of a Bose binary mixture on a spherical surface. This part of the work is in progress: we have developed the necessary formalism to address this problem and we are in the process of developing its numerical implementation. We hope to finish a paper about this also before next summer.