Exponentially fast dynamics of chaotic many-body systems

We demonstrate analytically and numerically that in isolated quantum systems of many interacting particles,\r\nthe number of many-body states participating in the evolution after a quench increases exponentially in time,\r\nprovided the eigenstates are delocalized in the energy shell. The rate of the exponential growth is defined by\r\nthe width of the local density of states and is associated with the Kolmogorov-Sinai entropy for systems with\r\na well-defined classical limit. In a finite system, the exponential growth eventually saturates due to the finite\r\nvolume of the energy shell. We estimate the timescale for the saturation and show that it is much larger than\r\nh/¯ . Numerical data obtained for a two-body random interaction model of bosons and for a dynamical model of\r\ninteracting spin-1/2 particles show excellent agreement with the analytical predictions