AI 中文总结
该研究证明可逆且幂有界的有限线性端点可实现自主GKSL开放量子动力学，并将其应用于D2Q9多弛豫时间格子玻尔兹曼方法，构建出重现经典卡勒曼轨迹的GKSL演化。
AI 中文摘要
卡勒曼升维将非线性多项式动力学转化为有限线性系统，但所得截断通常是非幺正的，且不一定对应物理量子演化。我们证明，若有限线性端点可逆且幂有界，则其可在真空相干态上实现自主的戈里尼-科萨科夫斯基-苏达山-林德布拉德（GKSL）实现，反之亦然。该构造是显式的，直接将非幺正映射实现为开放系统动力学，无需端点后选择，且在重复时间步中各有一次编码与解码。我们将该结果应用于完整D2Q9多弛豫时间格子玻尔兹曼（LB）时间步，通过将碰撞与周期流编译为单个卡勒曼端点。所得GKSL演化在多个时间步上重现经典卡勒曼轨迹，而与非线性LB动力学的剩余偏差为预期的卡勒曼截断误差。该结果为有限非幺正动力学的自主开放量子实现建立了通用准则，卡勒曼-LB动力学则为具体示例。
英文摘要
Carleman lifting converts nonlinear polynomial dynamics into finite linear systems, but the resulting truncations are generally nonunitary and need not correspond to physical quantum evolution. We prove that a finite linear endpoint admits an autonomous Gorini--Kossakowski--Sudarshan--Lindblad (GKSL) realization on vacuum coherences if and only if it is invertible and power bounded. The construction is explicit and realizes the nonunitary map directly as open-system dynamics, with no endpoint postselection and with one encoding and one decoding over repeated timesteps. We apply the result to the complete D2Q9 multiple-relaxation-time lattice Boltzmann (LB) timestep by compiling collision and periodic streaming into a single Carleman endpoint. The resulting GKSL evolution reproduces the classical Carleman trajectory over multiple timesteps, while the remaining discrepancy from nonlinear LB dynamics is the expected Carleman truncation error. The result establishes a general criterion for autonomous open-quantum realization of finite nonunitary dynamics, with Carleman--LB dynamics as a concrete example.
Comments10 pages, 2 figures
