{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/probabilistic-description-of-dissipative","title":"Probabilistic description of dissipative chaotic scattering","arxiv_id":"2308.13555","date":"2023-08-24","proceeding":null,"authors":["Lachlan Burton","Holger Dullin","Eduardo G. Altmann"],"abstract":"We investigate the extent to which the probabilistic properties of a chaotic scattering system with dissipation can be understood from the properties of the dissipation-free system. For large energies $E$, a fully chaotic scattering leads to an exponential decay of the survival probability $P(t) \\sim e^{-\\kappa t}$ with an escape rate $\\kappa$ that decreases with $E$. Dissipation $\\gamma>0$ leads to the appearance of different finite-time regimes in $P(t)$. We show how these different regimes can be understood for small $\\gamma\\ll 1$ and $t\\gg 1/\\kappa_0$ from the effective escape rate $\\kappa_\\gamma(t)=\\kappa_0(E(t))$ (including the non-hyperbolic regime) until the energy reaches a critical value $E_c$ at which no escape is possible. More generally, we argue that for small dissipation $\\gamma$ and long times $t$ the surviving trajectories in the dissipative system are distributed according to the conditionally invariant measure of the conservative system at the corresponding energy $E(t)<E(0)$. Quantitative predictions of our general theory are compared with numerical simulations in the Henon-Heiles model.","url_abs":"https://arxiv.org/abs/2308.13555v1","url_pdf":"https://arxiv.org/pdf/2308.13555v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"probabilistic-description-of-dissipative","repo_url":"https://github.com/LnBn/DissipativeScattering","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}