University thesis:
Habilitationsschrift, Albert-Ludwigs-Universität Freiburg, 2016
Footnote:
Description:
Abstract: In this thesis we give a rather descriptive presentation of the results obtained on the theoretical analysis of different probing techniques of localisation in quantum systems, and their implications. Detailed procedures and technical discussions can be found in the list of selected publications attached at the end of the manuscript. <br><br>Chapter 2 is devoted to disorder-induced localisation, in particular to numerical studies of the critical properties of the Anderson transition in d=3 dimensions. There, we explain the meaning of multifractality at the critical point, its characterisation and its potential to provide an alternative perspective on the metal-to-insulator transition. We formalise a generalised multifractal analysis which exploits the persistence of multifractal fluctuations in the wavefunction around the transition. This approach is used to obtain high-precision estimates of critical parameters and multifractal exponents simultaneously in a combined analysis. <br><br>In Chapter 3 we treat the problem of localisation in interacting systems. This includes interaction-induced localisation in disorder-free systems and driving-induced localisation in Coulomb systems. The first topic is studied in the context of the Bose-Hubbard model: Combining analytical and numerical calculations we perform a characterisation of the superfluid-to-Mott-insulator transition using scattering of matter waves. We explain why and how localisation is revealed by the behaviour of the inelastic scattering cross section. The second topic deals with two-electron Rydberg atoms in the presence of a periodic electromagnetic driving. We present a direct observation of localisation in energy space obtained numerically; the impact of the Coulomb repulsion between the electrons on localisation and on the photoionisation of the atom is analysed. <br><br>We close with a discussion about future research directions and relevant open questions in Chapter 4. We comment on the potential of localisation engineering, including a brief description of some of our additional results, and on certain aspects of many-body localisation