Smaczyński Marek, Tkocz Tomasz, Kuś Marek, Życzkowski Karol
Smoluchowski Institute of Physics, Jagiellonian University, Reymonta 4, 30-059 Cracow, Poland.
Mathematics Institute, University of Warwick, Coventry CV4 7AL, United Kingdom.
Phys Rev E Stat Nonlin Soft Matter Phys. 2013 Nov;88(5):052902. doi: 10.1103/PhysRevE.88.052902. Epub 2013 Nov 5.
Extremal spacings between eigenphases of random unitary matrices of size N pertaining to circular ensembles are investigated. Explicit probability distributions for the minimal spacing for various ensembles are derived for N=4. We study ensembles of tensor product of k random unitary matrices of size n which describe independent evolution of a composite quantum system consisting of k subsystems. In the asymptotic case, as the total dimension N=n(k) becomes large, the nearest neighbor distribution P(s) becomes Poissonian, but statistics of extreme spacings P(s(min)) and P(s(max)) reveal certain deviations from the Poissonian behavior.
研究了与圆形系综相关的大小为(N)的随机酉矩阵本征相位之间的极值间距。对于(N = 4)，推导了各种系综最小间距的显式概率分布。我们研究了大小为(n)的(k)个随机酉矩阵的张量积系综，它描述了由(k)个子系统组成的复合量子系统的独立演化。在渐近情况下，当总维数(N = n^k)变得很大时，最近邻分布(P(s))变为泊松分布，但极值间距(P(s_{min}))和(P(s_{max}))的统计显示出与泊松行为的某些偏差。
