Université de Toulouse, UPS, Laboratoire de Physique Théorique (IRSAMC), F-31062 Toulouse, France and CNRS, LPT (IRSAMC), F-31062 Toulouse, France.
Instituto de Investigaciones Físicas de Mar del Plata (IFIMAR), CONICET-UNMdP, Funes 3350, B7602AYL Mar del Plata, Argentina and Consejo Nacional de Investigaciones Científicas y Tecnológicas (CONICET), Avenida Rivadavia 1917, Ciudad Autónoma de Buenos Aires C1033AAJ, Argentina.
Phys Rev Lett. 2014 Jun 13;112(23):234101. doi: 10.1103/PhysRevLett.112.234101. Epub 2014 Jun 10.
We expose two scenarios for the breakdown of quantum multifractality under the effect of perturbations. In the first scenario, multifractality survives below a certain scale of the quantum fluctuations. In the other one, the fluctuations of the wave functions are changed at every scale and each multifractal dimension smoothly goes to the ergodic value. We use as generic examples a one-dimensional dynamical system and the three-dimensional Anderson model at the metal-insulator transition. Based on our results, we conjecture that the sensitivity of quantum multifractality to perturbation is universal in the sense that it follows one of these two scenarios depending on the perturbation. We also discuss the experimental implications.
我们揭示了在微扰影响下量子多重分形破裂的两种情况。在第一种情况中，多重分形在量子涨落的一定尺度以下仍然存在。在另一种情况中，波函数的涨落在每个尺度上都发生变化，每个多重分形维度平滑地趋近遍历值。我们使用一维动力学系统和金属-绝缘体转变的三维安德森模型作为通用示例。基于我们的结果，我们推测量子多重分形对微扰的敏感性在普遍意义上是通用的，即它根据微扰遵循这两种情况之一。我们还讨论了实验意义。
