Boltzmann-type approach to transport in weakly interacting one-dimensional fermionic systems

We investigate transport properties of one-dimensional fermionic tight binding models featuring nearest and next-nearest neighbor hopping, where the fermions are additionally subject to a weak short range mutual interaction. To this end we employ a pertinent approach which allows for a mapping of the underlying Schr\"odinger dynamics onto an adequate linear quantum Boltzmann equation. This approach is based on a suitable projection operator method. From this Boltzmann equation we are able to numerically obtain diffusion coefficients in the case of non-vanishing next-nearest neighbor hopping, i.e., the non-integrable case, whereas the diffusion coefficient diverges without next-nearest neighbor hopping. For the latter case we analytically investigate the decay behavior of the current with the result that arbitrarily small parts of the current relax arbitrarily slowly which suggests anomalous diffusive transport behavior within the scope of our approach.Comment: 6 pages, 4 figures, accepted for publication in Phys. Rev.

Transition from diffusive to ballistic dynamics for a class of finite quantum models

The transport of excitation probabilities amongst weakly coupled subunits is investigated for a class of finite quantum systems. It is demonstrated that the dynamical behavior of the transported quantity depends on the considered length scale, e. g., the introduced distinction between diffusive and ballistic transport appears to be a scale-dependent concept, especially since a transition from diffusive to ballistic behavior is found in the limit of small as well as in the limit of large length scales. All these results are derived by an application of the time-convolutionless projection operator technique and are verified by the numerical solution of the full time-dependent Schroedinger equation which is obtained by exact diagonalization for a range of model parameters.Comment: 4 pages, 5 figures, approved for publication in Physical Review Letter

Dynamical typicality of quantum expectation values

We show that the vast majority of all pure states featuring a common expectation value of some generic observable at a given time will yield very similar expectation values of the same observable at any later time. This is meant to apply to Schroedinger type dynamics in high dimensional Hilbert spaces. As a consequence individual dynamics of expectation values are then typically well described by the ensemble average. Our approach is based on the Hilbert space average method. We support the analytical investigations with numerics obtained by exact diagonalization of the full time-dependent Schroedinger equation for some pertinent, abstract Hamiltonian model. Furthermore, we discuss the implications on the applicability of projection operator methods with respect to initial states, as well as on irreversibility in general.Comment: 4 pages, 1 figure, accepted for publication in Phys. Rev. Let

Projection operator approach to transport in complex single-particle quantum systems

We discuss the time-convolutionless (TCL) projection operator approach to transport in closed quantum systems. The projection onto local densities of quantities such as energy, magnetization, particle number, etc. yields the reduced dynamics of the respective quantities in terms of a systematic perturbation expansion. In particular, the lowest order contribution of this expansion is used as a strategy for the analysis of transport in "modular" quantum systems corresponding to quasi one-dimensional structures which consist of identical or similar many-level subunits. Such modular quantum systems are demonstrated to represent many physical situations and several examples of complex single-particle models are analyzed in detail. For these quantum systems lowest order TCL is shown to represent an efficient tool which also allows to investigate the dependence of transport on the considered length scale. To estimate the range of validity of the obtained equations of motion we extend the standard projection to include additional degrees of freedom which model non-Markovian effects of higher orders.Comment: 13 pages, 11 figures, accepted for publication in Eur. Phys. J.

Multi-heme Cytochromes in Shewanella oneidensis MR-1:Structures, functions and opportunities

Multi-heme cytochromes are employed by a range of microorganisms to transport electrons over distances of up to tens of nanometers. Perhaps the most spectacular utilization of these proteins is in the reduction of extracellular solid substrates, including electrodes and insoluble mineral oxides of Fe(III) and Mn(III/IV), by species of Shewanella and Geobacter. However, multi-heme cytochromes are found in numerous and phylogenetically diverse prokaryotes where they participate in electron transfer and redox catalysis that contributes to biogeochemical cycling of N, S and Fe on the global scale. These properties of multi-heme cytochromes have attracted much interest and contributed to advances in bioenergy applications and bioremediation of contaminated soils. Looking forward there are opportunities to engage multi-heme cytochromes for biological photovoltaic cells, microbial electrosynthesis and developing bespoke molecular devices. As a consequence it is timely to review our present understanding of these proteins and we do this here with a focus on the multitude of functionally diverse multi-heme cytochromes in Shewanella oneidensis MR-1. We draw on findings from experimental and computational approaches which ideally complement each other in the study of these systems: computational methods can interpret experimentally determined properties in terms of molecular structure to cast light on the relation between structure and function. We show how this synergy has contributed to our understanding of multi-heme cytochromes and can be expected to continue to do so for greater insight into natural processes and their informed exploitation in biotechnologies

Geochemie und mikroskalige Elementverteilung in lateritischen Verwitterungsresiduen - Bohnerze

Bohnerze der oberjurassischen Kalkgebiete Süddeutschlands gelten aufgrund neuerer Studien als umgelagerte Residuen eines lateritischen Verwitterungsregimes während der Kreide und des Eozäns. Durch mineralogisch-chemische Analysen sowie der Erstellung von Elementbildern gelang eine näherungsweise Zuordnung von morphologisch unterscheidbaren Bohnerzformen zu den einzelnen Bereichen eines Lateritprofils. Dabei entsprechen pisoidische Bohnerze lateritischen Konkretionen aus dem Degradationsbereich am Übergang einer Eisenkruste (eigentlicher Laterit/Ferricrete) zum Bereich der Oberflächenverwitterung. Bei den nodulären Bohnerze handelt es sich zum Einen um Goethit-imprägnierte Bohnerztonaggregate und zum Anderen um Bruchstücke einer massiven Eisenkruste

Global and local relaxation of a spin-chain under exact Schroedinger and master-equation dynamics

We solve the Schroedinger equation for an interacting spin-chain locally coupled to a quantum environment with a specific degeneracy structure. The reduced dynamics of the whole spin-chain as well as of single spins is analyzed. We show, that the total spin-chain relaxes to a thermal equilibrium state independently of the internal interaction strength. In contrast, the asymptotic states of each individual spin are thermal for weak but non-thermal for stronger spin-spin coupling. The transition between both scenarios is found for couplings of the order of $0.1 \times \Delta E$, with $\Delta E$ denoting the Zeeman-splitting. We compare these results with a master equation treatment; when time averaged, both approaches lead to the same asymptotic state and finally with analytical results.Comment: RevTeX, 8 pages, 14 figures, added DOI and forgotten reference

Length scale dependent diffusion in the Anderson model at high temperatures

We investigate a single particle on a 3-dimensional, cubic lattice with a random on-site potential (3D Anderson model). We concretely address the question whether or not the dynamics of the particle is in full accord with the diffusion equation. Our approach is based on the time-convolutionless (TCL) projection operator technique and allows for a detailed investigation of this question at high temperatures. It turns out that diffusive dynamics is to be expected for a rather short range of wavelengths, even if the amount of disorder is tuned to maximize this range. Our results are partially counterchecked by the numerical solution of the full time-dependent Schroedinger equation.Comment: 6 pages, 4 figures, accepted for publication in Physica