AI 中文总结
本文以量子朗之万动力学为例，研究相干演化与耗散如何塑造亚稳态，通过两态与多态模型推导谱分离判据，并证明调节耗散可加速接近目标状态，数值实验验证了改进效果。
AI 中文摘要
亚稳态将表观平衡与真实收敛区分开来：动力系统在达到其稳态之前，可以在一个中间状态附近停留很长时间。在用于优化的量子动力学中，这样的平台期会延迟向集中于非凸势全局极小值附近的目标状态的进展。本文中，我们以量子朗之万动力学（QLD）作为具体示例[CLW+25]，开创性地研究相干演化与耗散塑造亚稳态的一般机制，其中目标函数编码在势中，阱之间的相干转移与可调耗散相互作用。为量化这种相互作用，我们精确求解了一个两态模型，并推导出基于隧穿频率、耗散强度和阻尼不平衡的谱分离判据。将分析扩展到多态模型，我们证明阱间足够弱的隧穿可以将慢速的群体转移与阱内的快速弛豫分离开来。此外，我们建立了改变耗散结构可缩短接近预定目标状态所需时间的条件。在双阱和多阱势上的数值实验证明了这些改进，同时保持目标和精度不变，并计入了控制所花费的时间。
英文摘要
Metastability separates apparent equilibration from true convergence: a dynamical system can remain near an intermediate state long before reaching its stationary state. In quantum dynamics used for optimization, such a plateau can delay progress toward a target concentrated near the global minimizers of a nonconvex potential. In this paper, we initiate the study of the general mechanisms by which coherent evolution and dissipation shape metastability, using quantum Langevin dynamics (QLD) as a concrete example [CLW+25], where the objective function is encoded in the potential and coherent transfer between wells interacts with tunable dissipation. To quantify this interaction, we solve a two-state model precisely and derive a spectral-separation criterion in terms of tunneling frequency, dissipation strength, and damping imbalance. Extending the analysis to multi-state models, we show that sufficiently weak tunneling between wells can separate slow population transfer from fast relaxation within each well. In addition, we establish conditions under which changing the structure of dissipation shortens the time needed to approach a prescribed target state. Numerical experiments on double-well and multi-well potentials demonstrate these improvements while keeping the target and accuracy fixed and accounting for the time spent on control.
Comments64 pages, 12 figures
