title: Quantum Levy Flights and Multifractality of Dipolar Excitations in a Random System.
abstract: We consider dipolar excitations propagating via dipole-induced exchange among immobile molecules randomly spaced in a lattice. The character of the propagation is determined by long-range hops (Levy flights). We analyze the eigenenergy spectra and the multifractal structure of the wave functions. In 1D and 2D, all states are localized, although in 2D the localization length can be extremely large leading to an effective localization-delocalization crossover in realistic systems. In 3D, all eigenstates are extended but not always ergodic, and we identify the energy intervals of ergodic and nonergodic states. The reduction of the lattice filling induces an ergodic to nonergodic transition, and the excitations are mostly nonergodic at low filling.
authors.affiliation: Institut für Theoretische Physik, Leibniz Universität Hannover, Appelstrasse 2, 30167 Hannover, Germany.
authors.forename: X
authors.initials: X
authors.lastname: Deng
authors.affiliation: Physics Department, Columbia University, 538 West 120th Street, New York, New York 10027, USA.|Kavli Institute for Theoretical Physics, University of California, Santa Barbara, California 93106, USA.
authors.forename: B L
authors.initials: BL
authors.lastname: Altshuler
authors.affiliation: Kavli Institute for Theoretical Physics, University of California, Santa Barbara, California 93106, USA.|LPTMS, CNRS, Université Paris-Sud, Université Paris-Saclay, Orsay 91405, France.|Van der Waals-Zeeman Institute, University of Amsterdam, Science Park 904, 1098 XH Amsterdam, Netherlands.|Russian Quantum Center, Skolkovo, Moscow Region 143025, Russia.|Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, Wuhan 430071, People's Republic of China.
authors.forename: G V
authors.initials: GV
authors.lastname: Shlyapnikov
authors.affiliation: Institut für Theoretische Physik, Leibniz Universität Hannover, Appelstrasse 2, 30167 Hannover, Germany.
authors.forename: L
authors.initials: L
authors.lastname: Santos