Metastability of cubic nonlinear wave equation

Consider a nonlinear wave equation with a double-well potential and stochastic forcing. How often does the field jump from one potential well to the other? We answer this question for a cubic equation and random initial data sampled from its invariant measure, the phi^4 quantum field theory. This low-temperature asymptotic behaviour is known as an Eyring--Kramers law.

In the talk, we outline how this question of dynamics can be reduced to computing some partition functions. We also briefly discuss two different notions of metastable transitions. This presentation relates to joint work (still unpublished) with Nikolay Barashkov.