Search

Abstract  We prove quantum dynamical lower bounds for one-dimensional continuum Schrödinger operators that possess critical energies for which there is slow growth of transfer matrix norms and a large class of compactly supported initial states. This general result is applied to a number of models, including the Bernoulli–Anderson model with a constant single-site potential. [ABSTRACT FROM AUTHOR]

Abstract. We consider continuum random Schrödinger operators of the type H? = -? + V0 + V? with a deterministic background potential V0. We establish criteria for the absence of continuous and absolutely continuous spectrum, respectively, outside the spectrum of -? + V0. The models we treat include random surface potentials as well as sparse or slowly decaying random potentials. In particular, we establish absence of absolutely continuous surface spectrum for random potentials supported near a one-dimensional surface (“random tube”) in arbitrary dimension. [ABSTRACT FROM AUTHOR]

We prove exponential localization at all energies for two types of one-dimen\-sional random Schrödinger operators: the Poisson model and the random displacement model. As opposed to Anderson-type models, these operators are not monotonic in the random parameters. Therefore the classical one-parameter version of spectral averaging, as used in localization proofs for Anderson models, breaks down. We use the new method of two-parameter spectral averaging and apply it to the Poisson as well as the displacement case. In addition, we apply results from inverse spectral theory, which show that two-parameter spectral averaging works for sufficiently many energies (all but a discrete set) to conclude localization at all energies. [ABSTRACT FROM AUTHOR]

Concrete models of interacting quantum systems for which expected manifestations of the many-body localized phase can be rigorously verified are in short supply. Recent work by Seiringer and Warzel (2016 New J. Phys.18 035002) succeeds in deriving such properties for a disordered Tonks–Girardeau gas. This provides a first example of a Boson gas in the strong Bose glass phase, characterized by the absence of Bose–Einstein condensation as well as the absence of superfluidity at zero temperature. The derivation exploits new mathematical tools to overcome problems arising from the non-locality of Fermionic wave functions associated with the states of a Tonks–Girardeau gas. [ABSTRACT FROM AUTHOR]