Eyring--Kramers law for the hyperbolic \(\phi^4\) 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 \(\phi^4_d\) quantum field theory,...

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Veröffentlicht in:arXiv.org 2024-10
Hauptverfasser: Barashkov, Nikolay, Laarne, Petri
Format: Artikel
Sprache:eng
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Zusammenfassung: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 \(\phi^4_d\) 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.
ISSN:2331-8422