Petri Laarne🚨 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 \( \phi^4 \) #QuantumFieldTheory. The average transition time is called an Eyring–Kramers law, asymptotic in the low-temperature limit. It has already been derived for 2D stochastic heat equation and 1D wave; we extend it to 2D and 3D wave equations.
Joint work with my PhD advisor Nikolay Barashkov. #MathematicalPhysics #MathPhys
Eyring--Kramers law for the hyperbolic $Ï•^4$ model
We 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 $Ï•^4_d$ 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.
Guillermo Rubilar