标题： 确定性细胞自动机在随机边界驱动下的可积性 显示英文标题

标题： Integrability of a deterministic cellular automaton driven by stochastic boundaries

摘要： 我们提出一个相互作用的多体时空离散马尔可夫链模型，该模型由一个可积的确定性和可逆的细胞自动机（[Bobenko等, CMP 158, 127 (1993)]中的规则54）组成，在有限的一维格子Z_2^n上，并且在两个格子边界处有局部随机马尔可夫链，为吸收或发射孤子提供化学浴。 对于浴参数的通用值，证明了这个多体马尔可夫链的遍历性和混合性，意味着存在一个唯一的非平衡稳态。 后者通过一种特别简单的矩阵乘积假设形式——称为补丁假设——被精确且显式地构造出来。 这使得能够在稳态中显式计算可观测量和$k$-点关联，以及构造一组非平凡的局部守恒定律。 也提出了对马尔可夫矩阵的完整谱和特征向量（衰减模式）进行精确解的可行性。 我们猜想，我们的想法可以为经典确定性格子系统的边界驱动可积性理论铺平道路。 显示英文摘要

摘要： We propose an interacting many-body space-time-discrete Markov chain model, which is composed of an integrable deterministic and reversible cellular automaton (the rule 54 of [Bobenko et al, CMP 158, 127 (1993)]) on a finite one-dimensional lattice Z_2^n, and local stochastic Markov chains at the two lattice boundaries which provide chemical baths for absorbing or emitting the solitons. Ergodicity and mixing of this many-body Markov chain is proven for generic values of bath parameters, implying existence of a unique non-equilibrium steady state. The latter is constructed exactly and explicitly in terms of a particularly simple form of matrix product ansatz which is termed a patch ansatz. This gives rise to an explicit computation of observables and $k$-point correlations in the steady state as well as the construction of a nontrivial set of local conservation laws. Feasibility of an exact solution for the full spectrum and eigenvectors (decay modes) of the Markov matrix is suggested as well. We conjecture that our ideas can pave the road towards a theory of integrability of boundary driven classical deterministic lattice systems.