Temperature-dependent classical phonons from efficient non-dynamical simulations

We present a rigorous and efficient approach to the calculation of classical lattice-dynamical quantities from simulations that do not require an explicit solution of the time evolution. We focus on the temperature-dependent vibrational spectrum. We start from the moment expansion of the relevant time-correlation function for a many-body system, and show that it can be conveniently rewritten by using a basis in which the low-order moments are diagonal. This allows us to compute the main spectral features (e.g., position and width of the phonon peaks) from thermal averages available from any statistical simulation. We successfully apply our method to a model system that presents a structural transition and strongly temperature-dependent phonons. Our theory clarifies the status of previous heuristic schemes to estimate phonon frequencies

Dimensional crossover and cold-atom realization of topological Mott insulators

We propose a cold-atom setup which allows for a dimensional crossover from a two-dimensional quantum spin Hall insulating phase to a three-dimensional strong topological insulator by tuning the hopping between the layers. We further show that additional Hubbard onsite interactions can give rise to spin liquid-like phases: weak and strong topological Mott insulators. They represent the celebrated paradigm of a quantum state of matter which merely exists because of the interplay of the non-trivial topology of the band structure and strong interactions. While the theoretical understanding of this phase has remained elusive, our proposal shall help to shed some light on this exotic state of matter by paving the way for a controlled experimental investigation in optical lattices.Comment: 4+ pages, 3 figures; includes Supplemental Material (3 pages, 1 figure

Social Deprivation and Exclusion of Immigrants in Germany

This paper aims at providing empirical evidence on social exclusion of immigrants in Germany. We demonstrate that when using a conventional definition of the social inclusion index typically applied in the literature, immigrants appear to experience a significant degree of social deprivation and exclusion, confirming much of the economic literature examining the economic assimilation of immigrants in Germany. We propose a weighting scheme that weights components of social inclusion by their subjective contribution to an overall measure of life satisfaction.Using this weighting scheme to calculate an index of social inclusion, we find that immigrants are in fact as "included" as Germans. This result is driven strongly by the disproportionately positive socio-demographic characteristics that immigrants possess as measured by the contribution to their life satisfaction.Social Exclusion, International Migration, Integration

Diversity in Shareholder Protection in Common Law Countries

Aktionär, Anlegerschutz, Common Law, Shareholders, Investor protection

UV spectra of iron-doped carbon clusters FeC_n n = 3-6

Electronic transitions of jet-cooled FeC$_n$ clusters ($n = 3 - 6$) were measured between 230 and 300 nm by a mass-resolved 1+1 resonant two-photon ionization technique. Rotational profiles were simulated based on previous calculations of ground state geometries and compared to experimental observations. Reasonable agreement is found for the planar fan-like structure of FeC$_3$. The FeC$_4$ data indicate a shorter distance between the Fe atom and the bent C$_4$ unit of the fan. The transitions are suggested to be $^{3}$A$_{2} \leftarrow ^{3}$B$_{1}$ for FeC$_3$ and $^{5}$A$_{1} \leftarrow ^{5}$A$_{1}$ for FeC$_4$. In contrast to the predicted C$_{\infty \text{v}}$ geometry, non-linear FeC$_5$ is apparently observed. Line width broadening prevents analysis of the FeC$_6$ spectrum.Comment: 6 pages, 5 figure

A universal scaling law for the evolution of granular gases

Dry, freely evolving granular materials in a dilute gaseous state coalesce into dense clusters only due to dissipative interactions. This clustering transition is important for a number of problems ranging from geophysics to cosmology. Here we show that the evolution of a dilute, freely cooling granular gas is determined in a universal way by the ratio of inertial flow and thermal velocities, that is, the Mach number. Theoretical calculations and direct numerical simulations of the granular Navier--Stokes equations show that irrespective of the coefficient of restitution, density or initial velocity distribution, the density fluctuations follow a universal quadratic dependence on the system's Mach number. We find that the clustering exhibits a scale-free dynamics but the clustered state becomes observable when the Mach number is approximately of $\mathcal{O}(1)$. Our results provide a method to determine the age of a granular gas and predict the macroscopic appearance of clusters

In vivo imaging of the tonoplast intrinsic protein family in Arabidopsis roots

Background: Tonoplast intrinsic proteins (TIPs) are widely used as markers for vacuolar compartments in higher plants. Ten TIP isoforms are encoded by the Arabidopsis genome. For several isoforms, the tissue and cell specific pattern of expression are not known. Results: We generated fluorescent protein fusions to the genomic sequences of all members of the Arabidopsis TIP family whose expression is predicted to occur in root tissues (TIP1;1 and 1;2; TIP2;1, 2;2 and 2;3; TIP4;1) and expressed these fusions, both individually and in selected pairwise combinations, in transgenic Arabidopsis. Analysis by confocal microscopy revealed that TIP distribution varied between different cell layers within the root axis, with extensive co-expression of some TIPs and more restricted expression patterns for other isoforms. TIP isoforms whose expression overlapped appeared to localise to the tonoplast of the central vacuole, vacuolar bulbs and smaller, uncharacterised structures. Conclusion: We have produced a comprehensive atlas of TIP expression in Arabidopsis roots, which reveals novel expression patterns for not previously studied TIPs

Highly Accurate Determination of Heterogeneously Stacked Van-der-Waals Materials by Optical Microspectroscopy

The composition of Van-der-Waals heterostructures is conclusively determined using a hybrid evaluation scheme of data acquired by optical microspectroscopy. This scheme deploys a parameter set comprising both change in reflectance and wavelength shift of distinct extreme values in reflectance spectra. Furthermore, the method is supported by an accurate analytical model describing reflectance of multilayer systems acquired by optical microspectroscopy. This approach allows uniquely for discrimination of 2D materials like graphene and hBN and, thus, quantitative analysis of Van-der-Waals heterostructures containing structurally very similar materials. The physical model features a transfer matrix method which allows for flexible, modular description of complex optical systems and may easily be extended to individual setups. It accounts for numerical apertures of applied objective lenses and a glass fiber which guides the light into the spectrometer by two individual weighting functions. The scheme is proven by highly accurate quantification of the number of layers of graphene and hBN in Van-der-Waals heterostructures. In this exemplary case, the fingerprint of graphene involves distinct deviations of reflectance accompanied by additional wavelength shifts of extreme values. In contrast to graphene the fingerprint of hBN reveals a negligible deviation in absolute reflectance causing this material being only detectable by spectral shifts of extreme values.Comment: 12 pages, 4 figure