A novel stochastic approach of thermalization and symmetry breaking
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866917267038535680 |
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| author | Smii, Boubaker |
| author_facet | Smii, Boubaker |
| contents | We investigate thermalization and symmetry-breaking in a nonlinear stochastic Klein-Gordon equation on a spatial lattice, taking into account damping, nonlinear interaction, and stochastic forcing terms reduced by a perturbative solution based on retarded Green functions and the principle of Duhamel to establish a series expansion with the coupling constant. The obtained expressions have a visual representation in the form of rooted trees and Feynman-type diagrams, where their structural pattern will explain the combinatorial factors involved in the expansion. These representations offer a novel application and interpretation specifically tailored for the secondorder, damped Klein-Gordon setting, enabling more complex causal relationships to be explicitly modeled compared to first-order stochastic approaches, thus marking a technical innovation in diagrammatic expansions for such systems. The model takes into account both the initial data from a deterministic approach as well as stochastic sources, for instance, Gaussian noise. Simulations have been performed symmetry-breaking regime to show the relaxation towards stationary states and the symmetry-broken patterns. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_10563 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A novel stochastic approach of thermalization and symmetry breaking Smii, Boubaker Mathematical Physics 60 H10, 60H15, 35R60, 82C31 We investigate thermalization and symmetry-breaking in a nonlinear stochastic Klein-Gordon equation on a spatial lattice, taking into account damping, nonlinear interaction, and stochastic forcing terms reduced by a perturbative solution based on retarded Green functions and the principle of Duhamel to establish a series expansion with the coupling constant. The obtained expressions have a visual representation in the form of rooted trees and Feynman-type diagrams, where their structural pattern will explain the combinatorial factors involved in the expansion. These representations offer a novel application and interpretation specifically tailored for the secondorder, damped Klein-Gordon setting, enabling more complex causal relationships to be explicitly modeled compared to first-order stochastic approaches, thus marking a technical innovation in diagrammatic expansions for such systems. The model takes into account both the initial data from a deterministic approach as well as stochastic sources, for instance, Gaussian noise. Simulations have been performed symmetry-breaking regime to show the relaxation towards stationary states and the symmetry-broken patterns. |
| title | A novel stochastic approach of thermalization and symmetry breaking |
| topic | Mathematical Physics 60 H10, 60H15, 35R60, 82C31 |
| url | https://arxiv.org/abs/2602.10563 |