New #preprint !
We study a stochastic PDE whose solutions want to be close to constant -1 or +1. But because it’s stochastic, the solutions occasionally jump between those two optima. How often, on average?
In technical terms, we study a certain nonlinear wave equation whose invariant measure is the
Joint work with my PhD advisor Nikolay Barashkov. #MathematicalPhysics #MathPhys
arXiv.orgEyring--Kramers law for the hyperbolic $ϕ^4$ modelWe study the expected transition frequency between the two metastable states of a stochastic wave equation with double-well potential. By transition state theory, the frequency factorizes into two components: one depends only on the invariant measure, given by the $ϕ^4_d$ quantum field theory, and the other takes the dynamics into account. We compute the first component with the variational approach to stochastic quantization when $d = 2, 3$. For the two-dimensional equation with random data but no stochastic forcing, we also compute the transmission coefficient.
