Phase nucleation in curved space

迄今为止，我们的工作主要集中在发展一种技术来计算静态背景和相互作用理论中的量子真空效应，因为这允许考虑相变和气泡成核。我们已经发展了一种非线性量子场论的方法，我们可以精确地积分运动方程，从而在完全非线性水平上对理论进行重新计算。而不是采取一种令人不安的方法。此外，我们已经开发了一个原始的和非常强大的数值实现zeta函数正则化，基于外尔谱定理。我们已经在各种情况下测试了这种方法来计算真空能量（工作发表在物理评论D），我们刚刚扩展了非相对论薛定谔量子场论的方法（一篇论文正在撰写中，应该会在夏天之前提交）。我们目前正在研究的问题与泡沫的形成有关，正如研究提案中所概述的那样，在玻色二元混合物的背景下，在球面上。这部分工作正在进行中：我们已经制定了解决这一问题的必要形式，我们正在制定其数字实施。我们希望在明年夏天之前完成一篇关于这方面的论文。

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.