发表机构
Gran Sasso Science Institute; Memorial University of Newfoundland（格兰萨索科学研究所; 纽芬兰纪念大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究分析多体量子系统与玻色子储库强耦合下的空间退相干，提出在特定时间尺度下精确分辨退相干过程，并构建带误差控制的有效演化映射，严格描述宏观量子物体的位置局域化。
AI 中文摘要
我们研究一个与玻色子储库强相互作用的多体量子系统的动力学。耦合由系统的势算符给出，并且对场是线性的。我们证明，在无限耦合强度极限下，系统经历瞬时空间退相干。为了在时间上分辨退相干过程，我们考虑大耦合强度λ和按t∝λ^{-α}（α≥0）缩放的短时间，在λ→∞的极限下。在短时间尺度α>1时，动力学是平凡的，而在较长时间尺度0≤α<1时，退相干是瞬时的。我们证明，退相干过程在α=1时被精确分辨，定义了细粒度时间尺度τ=λt。我们构造了多体系统的近似有效演化映射，并带有受控误差估计。一般而言，有效动力学是马尔可夫的，但不是由动力学半群给出。作为物理应用，我们对宏观量子物体在位置空间中的局域化现象给出了严格的描述。
英文摘要
We study the dynamics of a many-body quantum system strongly interacting with a bosonic reservoir. The coupling is given by a potential operator for the system and it is linear in the field. We show that in the limit of infinite coupling strength the system undergoes instantaneous spatial decoherence. To resolve the decoherence process in time we consider large coupling strengths $λ$ and short times scaling as $t\propto λ^{-α}$, with $α\ge0$, in the limit $λ\rightarrow\infty$. On short time scales $α>1$ the dynamics is trivial while on longer ones $0\leα<1$ the decoherence is instantaneous. We show that the decoherence process is resolved exactly for $α=1$, defining the fine-grained time scale $τ=λt$. We construct an approximate effective evolution map of the many-body system with controlled error estimates. Generically, the effective dynamics is markovian, but not given by a dynamical semigroup. As a physical application we give a rigorous description of the phenomenon of localization of macroscopic quantum objects in position space.
Comments39 pages
