We consider a Brownian particle that switches between two different diffusion states ( D 0 , D 1 ) according to a two-state Markov chain. We further assume that the particle’s position is reset to an initial value X r at a Poisson rate r , and that the discrete diffusion state is simultaneously reset according to the stationary distribution ρ n , n = 0, 1, of the Markov chain. We derive an explicit expression for the non-equilibrium steady state (NESS) on ##IMG## [http://ej.iop.org/images/1751-8121/53/27/275003/aab97e0ieqn1.gif] {$\mathbb{R}$} , which is given by the sum of two decaying exponentials. In the fast switching limit the NESS reduces to the exponential distribution of pure diffusion with stochastic resetting. The effective diffusivity is given by the mean ##IMG## [http://ej.io...] {$\overline{D}={\rho }_{0}{D}_{0}+{\rho }_{1}{D}_{1}$}

中文翻译：

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切换扩散和随机重置

我们考虑一个布朗粒子，它根据一个二态马尔可夫链在两个不同的扩散状态（D 0，D 1）之间切换。我们进一步假设粒子的位置以泊松比r重置为初始值X r，并且离散扩散状态根据马尔可夫链的静态分布ρn，n = 0，1同时重置。我们在## IMG ## [http://ej.iop.org/images/1751-8121/53/27/275003/aab97e0ieqn1.gif] {$上得出了非平衡稳态（NESS）的显式表达式。 \ mathbb {R} $}，它由两个衰减指数的总和给出。在快速切换极限中，NESS减少为具有随机重置的纯扩散的指数分布。有效扩散系数由平均值## IMG ## [http：//ej.io ...] {$ \ overline {D} = {\ rho __ {0} {D} _ {0} + { \ rho} _ {1} {D} _ {1} $}