Uniqueness of the electrostatic solution in Schwarzschild space

In this Brief Report we give the proof that the solution of any static test charge distribution in Schwarzschild space is unique. In order to give the proof we derive the first Green's identity written with p-forms on (pseudo) Riemannian manifolds. Moreover, the proof of uniqueness can be shown for either any purely electric or purely magnetic field configuration. The spacetime geometry is not crucial for the proof.Comment: 3 pages, no figures, uses revtex4 style file

Collective Atomic Motion in an Optical Lattice formed inside a High Finesse Cavity

We report on collective non-linear dynamics in an optical lattice formed inside a high finesse ring cavity in a so far unexplored regime, where the light shift per photon times the number of trapped atoms exceeds the cavity resonance linewidth. We observe bistability and self-induced squeezing oscillations resulting from the retro-action of the atoms upon the optical potential wells. We can well understand most of our observations within a simplified model assuming adiabaticity of the atomic motion. Non-adiabatic aspects of the atomic motion are reproduced by solving the complete system of coupled non-linear equations of motion for hundred atoms.Comment: 4 pages, 5 figure

Electronic correlations in vanadium chalcogenides: BaVSe3 versus BaVS3

Albeit structurally and electronically very similar, at low temperature the quasi-one-dimensional vanadium sulfide BaVS3 shows a metal-to-insulator transition via the appearance of a charge-density-wave state, while BaVSe3 apparently remains metallic down to zero temperature. This different behavior upon cooling is studied by means of density functional theory and its combination with the dynamical mean-field theory and the rotationally-invariant slave-boson method. We reveal several subtle differences between these chalcogenides that provide indications for the deviant behavior of BaVSe3 at low temperature. In this regard, a smaller Hubbard U in line with an increased relevance of the Hund's exchange J plays a vital role.Comment: 16 pages, 11 figures, published versio

The prismatic Sigma 3 (10-10) twin bounday in alpha-Al2O3 investigated by density functional theory and transmission electron microscopy

The microscopic structure of a prismatic $\Sigma 3$ $(10\bar{1}0)$ twin boundary in \aal2o3 is characterized theoretically by ab-initio local-density-functional theory, and experimentally by spatial-resolution electron energy-loss spectroscopy in a scanning transmission electron microscope (STEM), measuring energy-loss near-edge structures (ELNES) of the oxygen $K$-ionization edge. Theoretically, two distinct microscopic variants for this twin interface with low interface energies are derived and analysed. Experimentally, it is demonstrated that the spatial and energetical resolutions of present high-performance STEM instruments are insufficient to discriminate the subtle differences of the two proposed interface variants. It is predicted that for the currently developed next generation of analytical electron microscopes the prismatic twin interface will provide a promising benchmark case to demonstrate the achievement of ELNES with spatial resolution of individual atom columns

Distinct transcription kinetics of pluripotent cell states

Mouse embryonic stem cells (mESCs) can adopt naïve, ground, and paused pluripotent states that give rise to unique transcriptomes. Here, we use transient transcriptome sequencing (TT-seq) to define both coding and non-coding transcription units (TUs) in these three pluripotent states and combine TT-seq with RNA polymerase II occupancy profiling to unravel the kinetics of RNA metabolism genome-wide. Compared to the naïve state (serum), RNA synthesis and turnover rates are globally reduced in the ground state (2i) and the paused state (mTORi). The global reduction in RNA synthesis goes along with a genome-wide decrease of polymerase elongation velocity, which is related to epigenomic features and alterations in the Pol II termination window. Our data suggest that transcription activity is the main determinant of steady state mRNA levels in the naïve state and that genome-wide changes in transcription kinetics invoke ground and paused pluripotent states

Collective Sideband Cooling in an Optical Ring Cavity

We propose a cavity based laser cooling and trapping scheme, providing tight confinement and cooling to very low temperatures, without degradation at high particle densities. A bidirectionally pumped ring cavity builds up a resonantly enhanced optical standing wave which acts to confine polarizable particles in deep potential wells. The particle localization yields a coupling of the degenerate travelling wave modes via coherent photon redistribution. This induces a splitting of the cavity resonances with a high frequency component, that is tuned to the anti-Stokes Raman sideband of the particles oscillating in the potential wells, yielding cooling due to excess anti-Stokes scattering. Tight confinement in the optical lattice together with the prediction, that more than 50% of the trapped particles can be cooled into the motional ground state, promise high phase space densities.Comment: 4 pages, 1 figur

First-principles study of spontaneous polarization in multiferroic BiFeO3_3

The ground-state structural and electronic properties of ferroelectric BiFeO$_3$ are calculated using density functional theory within the local spin-density approximation and the LSDA+U method. The crystal structure is computed to be rhombohedral with space group $R3c$, and the electronic structure is found to be insulating and antiferromagnetic, both in excellent agreement with available experiments. A large ferroelectric polarization of 90-100 $\mu$C/cm$^2$ is predicted, consistent with the large atomic displacements in the ferroelectric phase and with recent experimental reports, but differing by an order of magnitude from early experiments. One possible explanation is that the latter may have suffered from large leakage currents. However both past and contemporary measurements are shown to be consistent with the modern theory of polarization, suggesting that the range of reported polarizations may instead correspond to distinct switching paths in structural space. Modern measurements on well-characterized bulk samples are required to confirm this interpretation.Comment: (9 pages, 5 figures, 5 tables

A general lower bound for collaborative tree exploration

We consider collaborative graph exploration with a set of $k$ agents. All agents start at a common vertex of an initially unknown graph and need to collectively visit all other vertices. We assume agents are deterministic, vertices are distinguishable, moves are simultaneous, and we allow agents to communicate globally. For this setting, we give the first non-trivial lower bounds that bridge the gap between small ($k \leq \sqrt n$) and large ($k \geq n$) teams of agents. Remarkably, our bounds tightly connect to existing results in both domains. First, we significantly extend a lower bound of $\Omega(\log k / \log\log k)$ by Dynia et al. on the competitive ratio of a collaborative tree exploration strategy to the range $k \leq n \log^c n$ for any $c \in \mathbb{N}$. Second, we provide a tight lower bound on the number of agents needed for any competitive exploration algorithm. In particular, we show that any collaborative tree exploration algorithm with $k = Dn^{1+o(1)}$ agents has a competitive ratio of $\omega(1)$, while Dereniowski et al. gave an algorithm with $k = Dn^{1+\varepsilon}$ agents and competitive ratio $O(1)$, for any $\varepsilon > 0$ and with $D$ denoting the diameter of the graph. Lastly, we show that, for any exploration algorithm using $k = n$ agents, there exist trees of arbitrarily large height $D$ that require $\Omega(D^2)$ rounds, and we provide a simple algorithm that matches this bound for all trees

Cavity Assisted Nondestructive Laser Cooling of Atomic Qubits

We analyze two configurations for laser cooling of neutral atoms whose internal states store qubits. The atoms are trapped in an optical lattice which is placed inside a cavity. We show that the coupling of the atoms to the damped cavity mode can provide a mechanism which leads to cooling of the motion without destroying the quantum information.Comment: 12 page