关于两种粒子的可逆元胞自动机
On two reversible cellular automata with two particle species
摘要：
我们介绍了一对时间可逆模型定义的离散时空晶格上的3个国家，每个网站，具体来说，一个空缺和两个味道（物种）的粒子。局部更新规则再现规则54可逆元胞自动机时，只有一个物种的粒子是存在的，并满足味道交换（C），空间反转（P），和时间反转（T）对称性的要求。我们发现封闭形式的表达式为三个本地保守的费用，并提供了一个明确的矩阵乘积形式的巨正则吉布斯状态，这是相同的两种模式。对于其中一个模型，这个吉布斯态家族似乎是平衡态（即空间和时间平移不变）的完整表征，而对于另一个模型，我们凭经验发现了一个局部保守电荷序列，每个支持大小大于2，暗示其代数可积性。最后，我们数值研究的时空关联函数的电荷密度的行为，并测试流体动力学预测模型正好有三个本地电荷。令人惊讶的是，数值观察到的“声速”与流体动力学值不匹配。的偏差是显着的，或者他们衰减非常缓慢的模拟时间，这给我们留下了一个悬而未决的问题，这种玻璃行为的机制，在一个确定性的局部相互作用系统。
英文摘要：
We introduce a pair of time-reversible models defined on the discrete space-time lattice with 3 states per site, specifically, a vacancy and a particle of two flavours (species). The local update rules reproduce the rule 54 reversible cellular automaton when only a single species of particles is present, and satisfy the requirements of flavour exchange (C), space-reversal (P), and time-reversal (T) symmetries. We find closed-form expressions for three local conserved charges and provide an explicit matrix product form of the grand canonical Gibbs states, which are identical for both models. For one of the models this family of Gibbs states seems to be a complete characterisation of equilibrium (i.e. space and time translation invariant) states, while for the other model we empirically find a sequence of local conserved charges, one for each support size larger than 2, hinting to its algebraic integrability. Finally, we numerically investigate the behaviour of spatio-temporal correlation functions of charge densities, and test the hydrodynamic prediction for the model with exactly three local charges. Surprisingly, the numerically observed 'sound velocity' does not match the hydrodynamic value. The deviations are either significant, or they decay extremely slowly with the simulation time, which leaves us with an open question for the mechanism of such a glassy behaviour in a deterministic locally interacting system.
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