论文标题
量子动态和快速争夺的确切通用界限
Exact universal bounds on quantum dynamics and fast scrambling
论文作者
论文摘要
量子速度限制（例如Mandelstam-Tamm或Margolus-Levitin界限）提供了限制短时动力学的能源不确定性原理的定量公式。我们表明，光谱形式是量子混乱中的中心数量，它设置了一个通用状态独立于任意长时间内一组初始状态的量子动力学的束缚，这比已知速度限制设置的相应状态独立界限更紧密。这进一步概括了不存在能量谱的时间依赖性或耗散系统的实时动力学。我们使用此结果来限制交互的多体系统中信息的争夺。对于哈密顿系统，我们表明，最快的争夺时间的基本问题（没有对相互作用结构的任何限制）映射到涉及辅助傅立叶变换非负性的状态密度的纯粹数学特性。我们在Sachdev-Ye-Kitaev模型中说明了这些界限，我们表明，尽管具有“最大混乱”的性质，但通过纠缠产生的足够大的费米昂子系统的持续争夺仍需要在子系统大小中呈指数级的时间。
Quantum speed limits such as the Mandelstam-Tamm or Margolus-Levitin bounds offer a quantitative formulation of the energy-time uncertainty principle that constrains dynamics over short times. We show that the spectral form factor, a central quantity in quantum chaos, sets a universal state-independent bound on the quantum dynamics of a complete set of initial states over arbitrarily long times, which is tighter than the corresponding state-independent bounds set by known speed limits. This bound further generalizes naturally to the real-time dynamics of time-dependent or dissipative systems where no energy spectrum exists. We use this result to constrain the scrambling of information in interacting many-body systems. For Hamiltonian systems, we show that the fundamental question of the fastest possible scrambling time -- without any restrictions on the structure of interactions -- maps to a purely mathematical property of the density of states involving the non-negativity of Fourier transforms. We illustrate these bounds in the Sachdev-Ye-Kitaev model, where we show that despite its "maximally chaotic" nature, the sustained scrambling of sufficiently large fermion subsystems via entanglement generation requires an exponentially long time in the subsystem size.
