We have carried out experimental and theoretical studies of the electric field-dependent ion transport in disordered materials and in disordered potential landscapes, respectively. In our experiments, we work in an electric field range up to 100 kV cm(-1), which is characterised by a weak nonlinear response of the mobile ions. We detect remarkable differences between different ion-conducting glasses regarding the temperature dependence of the nonlinear response. Theoretically, we study one-dimensional hopping models and continuous disordered potential models, respectively. When comparing theoretical and experimental data, we find both analogies and discrepancies.

We analyze in detail recent experiments on ultracold dilute 87 Rb-40 K mixtures in Hamburg and in Florence within a mean-field theory. To this end we determine how the stationary bosonic and fermionic density profiles in this mixture depend in the Thomas-Fermi limit on the respective particle numbers. Furthermore, we investigate how the observed stability of the Bose-Fermi mixture with respect to collapse is crucially related to the value of the interspecies s-wave scattering length.PACS numbers: 03.75.Hh I. INTRODUCTIONSix years after the first experimental achievement of Bose-Einstein condensation (BEC) of trapped atomic gases in 1995 fermionic atomic gases were brought together with bosonic atoms to quantum degeneracy in a 7 Li-6 Li mixture [1,2], 23 Na-6 Li mixture [3], and 87 Rb-40 K mixture [4]. In contrast to a pure Bose system, quantum degeneracy in a Fermi system with only one spin component means for T ≪ T F = E F /k B that all energy states below the Fermi energy E F are occupied with one fermion each, whereas all states above E F remain empty. The main problem to achieve quantum degeneracy in a Fermi gas is the inability of fermions to be directly evaporatively cooled. Due to the Pauli exclusion principle, fermions in the same spin polarized hyperfine state are not allowed to be close together, so that they can not collide via short-range contact interaction to rethermalize the gas during the evaporative cooling.This handicap was circumvented in the experiment of Ref. [5], where a mixture with two different spin states of 40 K was simultaneously evaporated by mutual cooling. In combination with a Bose gas the fermions are sympathetically cooled by elastic interactions with the bosons in the overlapping region [4,6].Beside the exploration of quantum degeneracy, one is also interested in studying how the two-particle interaction influences the system properties. Mixtures with a strong interspecies interaction, with the prominent example of 4 He-3 He liquid [7,8], lead to new phenomena like phase separation or BEC-induced interactions between fermions. * Electronic address: steffen.roethel@uni-muenster.de † Electronic address: axel.pelster@uni-duisburg-essen.de

The modelling of the ion conduction in disordered systems is analysed from two different perspectives. First, molecular dynamics simulations are employed to extract some basic properties of the hopping dynamics. It turns out that the dynamical processes can be described to a very good approximation as vacancy hopping processes. Second, the information content of nonlinear conductivity experiments, using high electric fields, is elucidated. For this purpose the single-particle dynamics on 1D and 2D model energy landscapes is elucidated numerically and partly analytically. The approaches encompass discrete as well as continuous energy landscapes, yielding complementary results about the dynamics. The impact for the interpretation of experimental data is discussed.

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