Trotter-Kato product formulae in Dixmier ideal

It is shown that for a certain class of the Kato functions the Trotter-Kato product formulae converge in Dixmier ideal C 1,$\infty$ in topology, which is defined by the $\times$ 1,$\infty$-norm. Moreover, the rate of convergence in this topology inherits the error-bound estimate for the corresponding operator-norm convergence. 1 since [24], [14]. Note that a subtle point of this program is the question about the rate of convergence in the corresponding topology. Since the limit of the Trotter-Kato product formula is a strongly continuous semigroup, for the von Neumann-Schatten ideals this topology is the trace-norm $\times$ 1 on the trace-class ideal C 1 (H). In this case the limit is a Gibbs semigroup [25]. For self-adjoint Gibbs semigroups the rate of convergence was estimated for the first time in [7] and [9]. The authors considered the case of the Gibbs-Schr{\"o}dinger semigroups. They scrutinised in these papers a dependence of the rate of convergence for the (exponential) Trotter formula on the smoothness of the potential in the Schr{\"o}dinger generator. The first abstract result in this direction was due to [19]. In this paper a general scheme of lifting the operator-norm rate convergence for the Trotter-Kato product formulae was proposed and advocated for estimation the rate of the trace-nor

Scattering Theory for Open Quantum Systems

Quantum systems which interact with their environment are often modeled by maximal dissipative operators or so-called Pseudo-Hamiltonians. In this paper the scattering theory for such open systems is considered. First it is assumed that a single maximal dissipative operator $A_D$ in a Hilbert space \sH is used to describe an open quantum system. In this case the minimal self-adjoint dilation $\widetilde K$ of $A_D$ can be regarded as the Hamiltonian of a closed system which contains the open system \{A_D,\sH\}, but since $\widetilde K$ is necessarily not semibounded from below, this model is difficult to interpret from a physical point of view. In the second part of the paper an open quantum system is modeled with a family $\{A(\mu)\}$ of maximal dissipative operators depending on energy $\mu$, and it is shown that the open system can be embedded into a closed system where the Hamiltonian is semibounded. Surprisingly it turns out that the corresponding scattering matrix can be completely recovered from scattering matrices of single Pseudo-Hamiltonians as in the first part of the paper. The general results are applied to a class of Sturm-Liouville operators arising in dissipative and quantum transmitting Schr\"{o}dinger-Poisson systems

VLBI2010 - The TWIN radio telescope project at Wettzell, Germany

The Twin Telescope Wettzell (TTW) Project is funded to be exec uted during the period of 2008-2011. The design of the TTW was based on the VLBI2010 vision of the corresponding IVS Working Group. In the first two project years the design passed the simulations with respect to its specifications and was approved for production. At the Geodetic Observatory Wettzell a thorough soil analysis was made in order to define the sites for the towers of the new radio telescopes. Meanwhile the construction work has begun and acceptance tests of several telescope parts, e.g. azimuth bearings, took place. The full assembly of the radio telescopes is scheduled for the next two years. In parallel to the construction work at the Wettzell site, the design work for the different feed options progressed

Statistical Physics of Self-Replication

Self-replication is a capacity common to every species of living thing, and simple physical intuition dictates that such a process must invariably be fueled by the production of entropy. Here, we undertake to make this intuition rigorous and quantitative by deriving a lower bound for the amount of heat that is produced during a process of self-replication in a system coupled to a thermal bath. We find that the minimum value for the physically allowed rate of heat production is determined by the growth rate, internal entropy, and durability of the replicator, and we discuss the implications of this finding for bacterial cell division, as well as for the pre-biotic emergence of self-replicating nucleic acids.Comment: 4+ pages, 1 figur

Soil Contamination due to Arsenic-Enriched Irrigation Water - Impact of Irrigation Practices

Increasing irrigation with arsenic (As) contaminated groundwater represents a growing problem in the densely populated delta and floodplain regions of SE Asia. The overarching aim of this study was to evaluate retention and mobility of As in soils in dependence of the irrigation practice. Irrigation of calcareous agricultural soils was simulated in a green-house experiment, in which artificial anoxic groundwater enriched in dissolved AsIII (10 mg/L) was applied regularly. We compared the following three different irrigation scenarios: permanently flooded, promoting reducing conditions (R); alternating flood irrigation, characterized by frequent changes in water saturation (RO); and sprinkler irrigation, maintaining permanently oxic conditions (O). Several wet chemical extraction procedures were carried out to characterize soil As storage pools at the end of the experiment. Pore water analysis reflected strongly reducing redox conditions (up to 42.9 mg/L dissolved Fe) for the R treatment, while less reducing conditions developed in the RO scenario (Fe max. 0.14 mg/L). Furthermore, As concentrations in pore water increased steadily to 1.34 (R) and 0.39 mg/L (O), respectively, with 20% (R) and 80% (RO) being present in the oxidized form AsV. The addition of As by irrigation water resulted in surprisingly similar depth distributions being independent of the irrigation treatment. Highest As contents (R: 52.2, RO: 49.6 and O: 43.9 mg/kg) occurred within the top 0-2 cm and decreased rapidly to values close the initial content (11.5 mg/kg) below 4 cm depth. This reflects a generally high sorption capacity of the soil for As. Even reductive dissolution of Fe-phases and the accompanying loss of sorption sites (R treatment) did not affect the As sorption behavior in general. However, pore water As concentrations and sequential extraction results point at a higher As mobility in case of the R treatment. This can be explained by the higher proportion of AsIII in the pore water, which is more mobile than AsV at the prevailing conditions. In sum, the three irrigation practices did not result in differences regarding the vertical distribution of As, but permanent flooding clearly increased the mobility of As as compared to the other treatments. The comparison of different wet chemical extraction procedures further emphasizes that protocol and sample treatment should be selected with caution, especially when redox conditions in the soil vary

Mean field approaches to the totally asymmetric exclusion process with quenched disorder and large particles

The process of protein synthesis in biological systems resembles a one dimensional driven lattice gas in which the particles (ribosomes) have spatial extent, covering more than one lattice site. Realistic, nonuniform gene sequences lead to quenched disorder in the particle hopping rates. We study the totally asymmetric exclusion process with large particles and quenched disorder via several mean field approaches and compare the mean field results with Monte Carlo simulations. Mean field equations obtained from the literature are found to be reasonably effective in describing this system. A numerical technique is developed for computing the particle current rapidly. The mean field approach is extended to include two-point correlations between adjacent sites. The two-point results are found to match Monte Carlo simulations more closely