Department of Physics, Yeshiva University, 245 Lexington Avenue, New York, New York 10016, USA.
Phys Rev Lett. 2012 Mar 2;108(9):094102. doi: 10.1103/PhysRevLett.108.094102. Epub 2012 Mar 1.
We study the transition to chaos and the emergence of statistical relaxation in isolated dynamical quantum systems of interacting particles. Our approach is based on the concept of delocalization of the eigenstates in the energy shell, controlled by the Gaussian form of the strength function. We show that, although the fluctuations of the energy levels in integrable and nonintegrable systems are different, the global properties of the eigenstates are quite similar, provided the interaction between particles exceeds some critical value. In this case, the statistical relaxation of the systems is comparable, irrespective of whether or not they are integrable. The numerical data for the quench dynamics manifest excellent agreement with analytical predictions of the theory developed for systems of two-body interactions with a completely random character.
我们研究了相互作用粒子的孤立动力量子系统中混沌的转变和统计弛豫的出现。我们的方法基于通过强度函数的高斯形式控制本征态在能壳中的离域化的概念。我们表明，尽管在可积和不可积系统中能级的涨落不同，但只要粒子之间的相互作用超过某个临界值，本征态的整体性质就非常相似。在这种情况下，系统的统计弛豫是可比的，而不管它们是否可积。淬火动力学的数值数据与针对具有完全随机特征的双体相互作用系统开发的理论的分析预测非常吻合。
