Phase Retrieval for Probability Distributions on Quantum Groups and Braided Groups

For nilpotent quantum groups [as introduced by Franz et al. ⁽⁷⁾], we show that (in sharp contrast to the classical case) the symmetrization of a probability distribution and the first moments of together determine uniquely the original distribution .     

Spectroscopic observation of bipolaronic point defects in Ba(1-x)KxBiO3

An infrared-absorption band centered at 0.85 eV, which is below the big optical absorption at the charge-density-wave (CDW) gap energy of 1.85 eV, has been observed for semiconducting single crystalline Ba(1-x)KxBiO3. With substituting K for Ba, the spectral weight of the new band increases with x, while that of the CDW-gap excitation decreases. Since the impurity state with the K substitution is known to be nonmagnetic at low temperatures, Bi3+ the state with 6s2 electrons surrounded by the six Bi5+ ions forms a small bipolaron by losing a pair of electrons in the Rice-Sneddon model. The new band is assigned to a transition from the lower-Peierls band to a state of the bipolaronic point defect.     

Dynamics of a quantum phase transition

We present two approaches to the dynamics of a quench-induced phase transition in the quantum Ising model. One follows the standard treatment of thermodynamic second order phase transitions but applies it to the quantum phase transitions. The other approach is quantum, and uses Landau-Zener formula for transition probabilities in avoided level crossings. We show that predictions of the two approaches of how the density of defects scales with the quench rate are compatible, and discuss the ensuing insights into the dynamics of quantum phase transitions.     

Dynamical model for chemically driven running droplets

We propose coupled evolution equations for the thickness of a liquid film and the density of an adsorbate layer on a partially wetting solid substrate. Therein, running droplets are studied assuming a chemical reaction underneath the droplets that induces a wettability gradient on the substrate and provides the driving force for droplet motion. Two different regimes for moving droplets--reaction-limited and saturated regime--are described. They correspond to increasing and decreasing velocities with increasing reaction rates and droplet sizes, respectively. The existence of the two regimes offers a natural explanation of prior experimental observations.     

Highly resolved fluid flows: "liquid plasmas" at the kinetic level

Fluid flow around an obstacle was observed at the kinetic (individual particle) level using "complex (dusty) plasmas" in their liquid state. These "liquid plasmas" have bulk properties similar to water (e.g., viscosity), and a comparison in terms of similarity parameters suggests that they can provide a unique tool to model classical fluids. This allows us to study "nanofluidics" at the most elementary-the particle-level, including the transition from fluid behavior to purely kinetic transport. In this (first) experimental investigation we describe the kinetic flow topology, discuss our observations in terms of fluid theories, and follow this up with numerical simulations.     

Nonexistence of a Kruskal-Katona Type Theorem for Subword Orders

We consider the poset SO(n) of all words over an n-element alphabet ordered by the subword relation. It is known that SO(2) falls into the class of Macaulay posets, i. e. there is a theorem of Kruskal–Katona type for SO(2). As the corresponding linear ordering of the elements of SO(2) the vip-order can be chosen.Daykin introduced the V-order which generalizes the vip-order to the n2 case. He conjectured that the V-order gives a Kruskal–Katona type theorem for SO(n).We show that this conjecture fails for all n3 by explicitly giving a counterexample. Based on this, we prove that for no n3 the subword order SO(n) is a Macaulay poset.     

Localization ability with bimodal hearing aids and bilateral cochlear implants

After successful cochlear implantation in one ear, some patients continue to use a hearing aid at the contralateral ear. They report an improved reception of speech, especially in noise, as well as a better perception of music when the hearing aid and cochlear implant are used in this bimodal combination. Some individuals in this bimodal patient group also report the impression of an improved localization ability. Similar experiences are reported by the group of bilateral cochlear implantees. In this study, a survey of 11 bimodally and 4 bilaterally equipped cochlear implant users was carried out to assess localization ability. Individuals in the bimodal implant group were all provided with the same type of hearing aid in the opposite ear, and subjects in the bilateral implant group used cochlear implants of the same manufacturer on each ear. Subjects adjusted the spot of a computer-controlled laser-pointer to the perceived direction of sound incidence in the frontal horizontal plane by rotating a trackball. Two subjects of the bimodal group who had substantial residual hearing showed localization ability in the bimodal configuration, whereas using each single device only the subject with better residual hearing was able to discriminate the side of sound origin. Five other subjects with more pronounced hearing loss displayed an ability for side discrimination through the use of bimodal aids, while four of them were already able to discriminate the side with a single device. Of the bilateral cochlear implant group one subject showed localization accuracy close to that of normal hearing subjects. This subject was also able to discriminate the side of sound origin using the first implanted device alone. The other three bilaterally equipped subjects showed limited localization ability using both devices. Among them one subject demonstrated a side-discrimination ability using only the first implanted device.     

Ab initio calculation of hyperfine and superhyperfine interactions for shallow donors in semiconductors

For the shallow group V donors in Si we show that the hyperfine interaction for the donor nucleus and the superhyperfine interactions for the first five shells of Si ligands can be quite accurately calculated using the local spin-density approximation of the density-functional theory. We treat the impurity problem in a Green's function approach. Since we have to truncate the long-ranged part of the defect potential, we do not obtain a localized gap state. Instead we identify the resonance above the conduction band with the paramagnetic defect state. We show that the hf and shf interactions thus obtained are at least as accurate as those obtained from one-electron theories with fitting parameters. Application of this first principles method to other shallow donors could be an essential help in defect identification.