元胞自动机(cellular automata)是定义在格点上的离散动力系统,其中每个格点携带有限状态集,并依据局域确定性规则随时间演化。元胞自动机的重要应用之一是流体的格气模型(lattice gas models),该框架为流体的流体力学行为提供了基于粒子的微观描述。宏观流体方程通过对大量格点与时间步长进行粗粒化(coarse-graining)而涌现,从而提供了一条自下而上的流体力学推导路径。一个著名范例是Frisch-Hasslacher-Pomeau(FHP)模型:一种定义在二维三角格点上的元胞自动机,其粗粒化后可导出二维Navier-Stokes方程。本文通过两项修改构建了FHP模型的宇称破缺推广:引入手性两体碰撞规则,并系统地旋转粒子速度以模拟背景磁场效应。我们证明该元胞自动机导出的流体力学模型具有奇粘度(odd viscosity)——一种表征奇流体(odd fluids)的横向输运系数。我们通过对手性FHP元胞自动机的泊肃叶流(Poiseuille-flow)模拟验证了所解析得到的输运系数。结果表明,本文所提出的手性元胞自动机为微观宇称破缺散射过程与宏观奇流体流体力学之间建立了桥梁。
Cellular automata are discrete dynamical systems defined on a lattice, in which each site carries a finite set of states that evolve in time according to local deterministic rules. An important application of cellular automata is in lattice gas models of fluids, where the cellular automaton framework provides a particle-based microscopic description of hydrodynamic behavior. The macroscopic fluid equations emerge after coarse-graining over many lattice sites and time steps, offering a bottom-up route to hydrodynamics. A celebrated example is the Frisch-Hasslacher-Pomeau (FHP) model, an automaton defined on a two-dimensional triangular lattice that yields the two-dimensional Navier-Stokes equations upon coarse-graining. In this work, we construct a parity-breaking generalization of the FHP model through two modifications: introducing chiral two-body collision rules and systematically rotating particle velocities to mimic the effect of a background magnetic field. We show that this automaton yields a hydrodynamic model with odd viscosity, a transverse transport coefficient that is a hallmark of odd fluids. We verify the analytical transport coefficients using Poiseuille-flow simulations of the chiral FHP automaton. Our results demonstrate that the chiral automaton introduced here provides a bridge between microscopic parity-breaking scattering processes and macroscopic odd-fluid hydrodynamics.