Understanding the ultimate rate at which information propagates is a pivotal issue in nonequilibrium physics. Nevertheless, the task of elucidating the propagation speed inherent in quantum bosonic systems presents challenges due to the unbounded nature of their interactions. In this study, we tackle the problem of macroscopic particle transport in a long-range generalization of the lattice Bose-Hubbard model through the lens of the quantum speed limit. By developing a unified approach based on optimal transport theory, we rigorously prove that the minimum time required for macroscopic particle transport is always bounded by the distance between the source and target regions, while retaining its significance even in the thermodynamic limit. Furthermore, we derive an upper bound for the probability of observing a specific number of bosons inside the target region, thereby providing additional insights into the dynamics of particle transport. Our results hold true for arbitrary initial states under both long-range hopping and long-range interactions, thus resolving an open problem of particle transport in generic bosonic systems.

中文翻译：

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远程系统中宏观粒子传输的最佳光锥：量子速度限制方法


了解信息传播的最终速率是非平衡物理学的一个关键问题。然而，由于量子玻色子系统相互作用的无限性质，阐明量子玻色子系统固有的传播速度的任务面临着挑战。在这项研究中，我们通过量子速度极限的透镜解决了晶格玻色-哈伯德模型的长程推广中的宏观粒子输运问题。通过开发基于最优输运理论的统一方法，我们严格证明了宏观粒子输运所需的最短时间始终受源区域和目标区域之间的距离限制，同时即使在热力学极限下也保留其重要性。此外，我们得出了在目标区域内观察到特定数量玻色子的概率的上限，从而为粒子输运的动力学提供了额外的见解。我们的结果对于长程跳跃和长程相互作用下的任意初始状态都成立，从而解决了通用玻色子系统中粒子输运的开放问题。