Dipartimento di Matematica e Fisica and Interdisciplinary Laboratories for Advanced Materials Physics, Università Cattolica, via Musei 41, 25121 Brescia, Italy.
Istituto Nazionale di Fisica Nucleare, Sezione di Pavia, via Bassi 6, I-27100, Pavia, Italy.
Phys Rev E. 2019 Jan;99(1-1):010101. doi: 10.1103/PhysRevE.99.010101.
We demonstrate analytically and numerically that in isolated quantum systems of many interacting particles, the number of many-body states participating in the evolution after a quench increases exponentially in time, provided the eigenstates are delocalized in the energy shell. The rate of the exponential growth is defined by the width Γ of the local density of states and is associated with the Kolmogorov-Sinai entropy for systems with a well-defined classical limit. In a finite system, the exponential growth eventually saturates due to the finite volume of the energy shell. We estimate the timescale for the saturation and show that it is much larger than ℏ/Γ. Numerical data obtained for a two-body random interaction model of bosons and for a dynamical model of interacting spin-1/2 particles show excellent agreement with the analytical predictions.
我们从理论和数值上证明，在经历过淬火过程后的孤立量子多体系统中，如果本征态在能量壳中是弥散的，那么参与演化的多体态的数量将随时间呈指数增长。这种指数增长的速率由局域态密度的宽度 Γ 所定义，并与具有明确经典极限的系统的Kolmogorov-Sinai 熵相关联。在有限的系统中，由于能量壳的有限体积，指数增长最终会饱和。我们估计了饱和的时间尺度，并表明它远大于 ħ/Γ。对于玻色子的双体随机相互作用模型和相互作用的自旋-1/2 粒子的动力学模型，我们得到的数值数据与解析预测结果非常吻合。
