Phase nucleation in curved space

到目前为止，所进行的工作主要集中在开发一种技术来计算固定背景和相互作用理论中的量子真空效应，因为这些技术允许考虑相变和气泡成核。我们已经为非线性量子场论开发了这样一种方法，我们可以精确地对运动方程进行积分，并在完全非线性水平上对理论进行量子化，而无需诉诸摄动方法。此外，我们已经开发了一个原始的和非常强大的ζ函数正则化的数值实现，基于Weyl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（发表在《物理评论D》上），我们刚刚将这种方法扩展到非相对论性薛定谔量子场论（一篇论文正在撰写中，应该在夏天之前提交）。我们目前正在研究的问题与气泡的形成有关，正如研究计划中概述的那样，在球面上的玻色二元混合物的背景下。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执行的过程中。我们希望在明年夏天之前完成一篇关于这个的论文。

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.