Eyring--Kramers law for the hyperbolic $ϕ^4$ model
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866909985107083264 |
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| author | Barashkov, Nikolay Laarne, Petri |
| author_facet | Barashkov, Nikolay Laarne, Petri |
| contents | 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 $ϕ^4_d$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_03495 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Eyring--Kramers law for the hyperbolic $ϕ^4$ model Barashkov, Nikolay Laarne, Petri Analysis of PDEs Mathematical Physics Probability 60H30, 81S20 (Primary), 35L71, 81T08 (Secondary) 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 $ϕ^4_d$ 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. |
| title | Eyring--Kramers law for the hyperbolic $ϕ^4$ model |
| topic | Analysis of PDEs Mathematical Physics Probability 60H30, 81S20 (Primary), 35L71, 81T08 (Secondary) |
| url | https://arxiv.org/abs/2410.03495 |