Coexistence of dynamical delocalization and spectral localization through stochastic dissipation

Anderson’s groundbreaking discovery that the presence of stochastic imperfections in a crystal may result in a sudden breakdown of conductivity1 revolutionized our understanding of disordered media. After stimulating decades of studies2, Anderson localization has found applications in various areas of physics3,4,5,6,7,8,9,10,11,12. A fundamental assumption in Anderson’s treatment is that no energy is exchanged with the environment. Recently, a number of studies shed new light on disordered media with dissipation14,15,16,17,18,19,20,21,22. In particular it has been predicted that random fluctuations solely in the dissipation, introduced by the underlying potential, could exponentially localize all eigenstates (spectral localization)14, similar to the original case without dissipation that Anderson considered. We show in theory and experiment that uncorrelated disordered dissipation can simultaneously cause spectral localization and wave spreading (dynamical delocalization). This discovery implies the breakdown of the commonly known correspondence between spectral and dynamical localization known from the Hermitian Anderson model with uncorrelated disorder.S.W., M.K. and A.S. thank the Deutsche Forschungsgemeinschaft (grant SZ 276/20-1) and the Krupp von-Bohlen-and-Halbach foundation for funding their research. S.L. acknowledges the Spanish State Research Agency through the Severo Ochoa and Maria de Maeztu Program for Centers and Units of Excellence in R&D (MDM-2017-0711)