Map Lattices Coupled by Collisions: Hitting Time Statistics and Collisions Per Lattice Unit
Map Lattices Coupled by Collisions: Hitting Time Statistics and Collisions Per Lattice Unit
复制标题
由碰撞耦合的地图晶格：每个晶格单元的命中时间统计和碰撞
DOI：
10.1007/s00023-022-01164-2
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发表时间：
2022
期刊：
影响因子：
--
通讯作者：
Bahsoun W
中科院分区：
文献类型：
--
作者：
Bahsoun W
We study map lattices coupled by collision and show how perturbations of transfer operators associated with the spatially periodic approximation of the model can be used to extract information about collisions per lattice unit. More precisely, we study a map on a finite box ofLsites with periodic boundary conditions, coupled by collision. We derive, via a non-trivial first-order approximation for the leading eigenvalue of the rare event transfer operator, a formula for thefirst collision rateand a correspondingfirst hitting time law. For the former we show that the formula scales at the order of, whereis the coupling strength, and for the latter, by tracking theLdependency in our arguments, we show that the error in the law is of order \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$O\left( C(L)\frac{L\varepsilon ^2}{\zeta (L)}\cdot \left| \ln \frac{L\varepsilon ^2}{\zeta (L)}\right| \right) $$\end{document}, whereis given in terms of the spectral gap of the rare event transfer operator, andC(L) has an explicit expression. Finally, we derive anexplicit formulafor the first collision rateper lattice unit.
We study map lattices coupled by collision and show how perturbations of transfer operators associated with the spatially periodic approximation of the model can be used to extract information about collisions per lattice unit. More precisely, we study a map on a finite box ofLsites with periodic boundary conditions, coupled by collision. We derive, via a non-trivial first-order approximation for the leading eigenvalue of the rare event transfer operator, a formula for thefirst collision rateand a correspondingfirst hitting time law. For the former we show that the formula scales at the order of, whereis the coupling strength, and for the latter, by tracking theLdependency in our arguments, we show that the error in the law is of order \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$O\left( C(L)\frac{L\varepsilon ^2}{\zeta (L)}\cdot \left| \ln \frac{L\varepsilon ^2}{\zeta (L)}\right| \right) $$\end{document}, whereis given in terms of the spectral gap of the rare event transfer operator, andC(L) has an explicit expression. Finally, we derive anexplicit formulafor the first collision rateper lattice unit.
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