Vikram Amit, Galitski Victor
Joint Quantum Institute and Department of Physics, University of Maryland, College Park, Maryland 20742, USA.
Phys Rev Lett. 2024 Jan 26;132(4):040402. doi: 10.1103/PhysRevLett.132.040402.
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.
诸如曼德尔斯塔姆 - 塔姆或马戈卢斯 - 莱维廷界限之类的量子速度极限提供了能量 - 时间不确定性原理的定量表述，该原理在短时间内限制动力学。我们表明，谱形式因子作为量子混沌中的核心量，为任意长的时间内一组完整初始态的量子动力学设定了一个通用的与态无关的界限，这比已知速度极限所设定的相应与态无关的界限更严格。这个界限自然地进一步推广到不存在能谱的含时或耗散系统的实时动力学。我们利用这一结果来限制相互作用多体系统中信息的混洗。对于哈密顿系统，我们表明，在不对相互作用结构施加任何限制的情况下，关于最快可能混洗时间的基本问题映射到态密度的一个纯粹数学性质，该性质涉及傅里叶变换的非负性。我们在萨赫德夫 - 叶 - 基塔耶夫模型中说明了这些界限，在该模型中我们表明，尽管其具有“最大混沌”性质，但通过纠缠产生实现足够大的费米子子系统的持续混洗在子系统大小方面需要指数级长的时间。
