Department of Physics, FMF, University of Ljubljana, Jadranska 19, 1000 Ljubljana, Slovenia.
Phys Rev Lett. 2013 Sep 20;111(12):124101. doi: 10.1103/PhysRevLett.111.124101. Epub 2013 Sep 16.
We propose to quantify the complexity of nonequilibrium steady state density operators, as well as of long-lived Liouvillian decay modes, in terms of the level spacing distribution of their spectra. Based on extensive numerical studies in a variety of models, some solvable and some unsolved, we conjecture that the integrability of density operators (e.g., the existence of an algebraic procedure for their construction in finitely many steps) is signaled by a Poissonian level statistics, whereas in the generic nonintegrable cases one finds level statistics of a Gaussian unitary ensemble of random matrices. Eigenvalue statistics can therefore be used as an efficient tool to identify integrable quantum nonequilibrium systems.
我们提出用谱的能隙分布来量化非平衡定态密度算符以及长寿命刘维尔衰减模式的复杂性。通过在各种模型中的广泛数值研究，包括可解和不可解模型，我们推测密度算符的可积性（例如，是否存在用有限步的代数过程来构造它们）由泊松分布的能级统计来指示，而在一般的不可积情况下，会发现随机矩阵的高斯幺正系综的能级统计。因此，本征值统计可以作为一种有效的工具来识别可积的量子非平衡系统。
