Department of Physics • University of Cologne

For a particle in a one-dimensional random potential all eigenstates are localized (Anderson localization). Interplay between interactions and disorder can lead to a localization-delocalization transition: in disordered bosonic fluids, the ground state is either a superfluid or in a localized phase called Bose glass. The associated phase diagram is well understood, but there is little study of the precise properties of the Bose-glass phase. Using a functional implementation of the Renormalization Group, I will describe the Bose-glass phase and some of its glassy properties linked to the existence of metastable states. I will then discuss the chaotic behavior of the Bose glass, i.e. its extreme sensitivity to external parameters. Finally, I will consider the effect of long-range interactions, which can induce a new disordered phase called Mott glass.

A record is an entry in a time series that is greater or smaller than all previous entries. The public perception of climate change is particularly sensitive to record-breaking weather events, which often receive extensive media coverage. As a consequence, a number of recent studies have been aimed at detecting and quantifying the effects of a warming climate on the frequency of temperature records. The mathematical theory of records makes universal and sometimes counter-intuitive predictions about the temporal statistics of record events, but it is largely restricted to stationary time series. After an introduction to the classic theory, I will explain the extensions needed to deal with trends, and the effect of warming on temperature records will be described at different levels of resolution. In the last part of the talk I will discuss time series of precipitation records, where the presence of dry days of zero precipitation induces nontrivial correlations between record-breaking events.