Metastable transition times of the 1D dynamical sine-Gordon model

2025/09/17 by Petri Laarne, Laarne, Petri
Mathematics · Physics and Astronomy · #60H15 (Primary) #60J45 #60J60 #81S20 #82C44 (Secondary) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR) #Stochastic processes and statistical mechanics #Theoretical and Computational Physics #stochastic dynamics and bifurcation

paper · pdf · doi:10.48550/arxiv.2509.13806

openalex publication_date 2025/09/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the dynamics of a stochastic heat equation with γsin(βu) nonlinearity on one-dimensional torus. We show an Eyring--Kramers law for the jump rate between potential wells in the small-noise limit, and that the transition state undergoes a bifurcation at γβ= 1. The argument follows the potential-theoretic approach of Berglund and Gentz [Electron. J. Probab. 2013].

Citations

• Eyring-Kramers Law for the Underdamped Langevin Process
• A simple construction of the sine-Gordon model via stochastic quantization
• Global well-posedness of the dynamical sine-Gordon model up to 6π
• Geometric Characterization of the Eyring-Kramers Formula
• On the two-dimensional hyperbolic stochastic sine-Gordon equation
• Exponential loss of memory for the 2-dimensional Allen-Cahn equation\n with small noise
• The dynamical sine-Gordon model in the full subcritical regime
• Sharp asymptotics of the first exit point density
• Effects of weak spatiotemporal noise on a bistable one-dimensional system
• The Activated Complex in Chemical Reactions

Related

• Eyring--Kramers law for the hyperbolic ϕ⁴ model
• Metastability of one-dimensional, non-reversible diffusions with periodic boundary conditions
• Sharp asymptotics of metastable transition times for one dimensional SPDEs
• Exponential ergodicity for the stochastic hyperbolic sine-Gordon equation on the circle
• Stochastic metastability by spontaneous localization