The free energy of the two-dimensional dilute Bose gas. I. Lower bound

We prove a lower bound for the free energy (per unit volume) of the two-dimensional Bose gas in the thermodynamic limit. We show that the free energy at density and inverse temperature differs from the one of the noninteracting system by the correction term . Here, is the scattering length of the interaction potential, and is the inverse Berezinskii–Kosterlitz–Thouless critical temperature for superfluidity. The result is valid in the dilute limit and if

Cohesion and Repulsion in Bayesian Distance Clustering

Clustering in high-dimensions poses many statistical challenges. While traditional distance-based clustering methods are computationally feasible, they lack probabilistic interpretation and rely on heuristics for estimation of the number of clusters. On the other hand, probabilistic model-based clustering techniques often fail to scale and devising algorithms that are able to effectively explore the posterior space is an open problem. Based on recent developments in Bayesian distance-based clustering, we propose a hybrid solution that entails defining a likelihood on pairwise distances between observations. The novelty of the approach consists in including both cohesion and repulsion terms in the likelihood, which allows for cluster identifiability. This implies that clusters are composed of objects which have small "dissimilarities" among themselves (cohesion) and similar dissimilarities to observations in other clusters (repulsion). We show how this modelling strategy has interesting connection with existing proposals in the literature as well as a decision-theoretic interpretation. The proposed method is computationally efficient and applicable to a wide variety of scenarios. We demonstrate the approach in a simulation study and an application in digital numismatics.Comment: 1 supplementary PDF attached. To view the supplementary PDF, please download the attachment under "Ancilliary Files

Optomechanical quantum teleportation

Quantum teleportation, the faithful transfer of an unknown input state onto a remote quantum system, is a key component in long distance quantum communication protocols and distributed quantum computing. At the same time, high frequency nano-optomechanical systems hold great promise as nodes in a future quantum network, operating on-chip at low-loss optical telecom wavelengths with long mechanical lifetimes. Recent demonstrations include entanglement between two resonators, a quantum memory and microwave to optics transduction. Despite these successes, quantum teleportation of an optical input state onto a long-lived optomechanical memory is an outstanding challenge. Here we demonstrate quantum teleportation of a polarization-encoded optical input state onto the joint state of a pair of nanomechanical resonators. Our protocol also allows for the first time to store and retrieve an arbitrary qubit state onto a dual-rail encoded optomechanical quantum memory. This work demonstrates the full functionality of a single quantum repeater node, and presents a key milestone towards applications of optomechanical systems as quantum network nodes

Silicon anisotropy in a bi-dimensional optomechanical cavity

In this work, we study the effects of mechanical anisotropy in a 2D optomechanical crystal geometry. We fabricate and measure devices with different orientations, showing the dependence of the mechanical spectrum and the optomechanical coupling with the relative angle of the device to the crystallography directions of silicon. Our results show that the device orientation strongly affects its mechanical band structure, which makes the devices more susceptible to fabrication imperfections. Finally, we show that our device is compatible with cryogenic measurements reaching ground state occupancy of 0.2 phonons at mK temperature.Comment: 5 pages 4 figure

Project Briefing #1: Structure of Project 1 within the Cluster Net-Zero-2050

Clarification of the work focus and the connection of the different elements of the Helmholtz Climate Initiative‘s Cluster I Net-Zero-205

Development and evaluation of a custom bait design based on 469 single-copy protein-coding genes for exon capture of isopods (Philosciidae: Haloniscus)

Transcriptome-based exon capture approaches, along with next-generation sequencing, are allowing for the rapid and cost-effective production of extensive and informative phylogenomic datasets from non-model organisms for phylogenetics and population genetics research. These approaches generally employ a reference genome to infer the intron-exon structure of targeted loci and preferentially select longer exons. However, in the absence of an existing and well-annotated genome, we applied this exon capture method directly, without initially identifying intron-exon boundaries for bait design, to a group of highly diverse Haloniscus (Philosciidae), paraplatyarthrid and armadillid isopods, and examined the performance of our methods and bait design for phylogenetic inference. Here, we identified an isopod-specific set of single-copy protein-coding loci, and a custom bait design to capture targeted regions from 469 genes, and analysed the resulting sequence data with a mapping approach and newly-created post-processing scripts. We effectively recovered a large and informative dataset comprising both short (300 bp) exons, with high uniformity in sequencing depth. We were also able to successfully capture exon data from up to 16-year-old museum specimens along with more distantly related outgroup taxa, and efficiently pool multiple samples prior to capture. Our well-resolved phylogenies highlight the overall utility of this methodological approach and custom bait design, which offer enormous potential for application to future isopod, as well as broader crustacean, molecular studies

The state of the Martian climate

60°N was +2.0°C, relative to the 1981–2010 average value (Fig. 5.1). This marks a new high for the record. The average annual surface air temperature (SAT) anomaly for 2016 for land stations north of starting in 1900, and is a significant increase over the previous highest value of +1.2°C, which was observed in 2007, 2011, and 2015. Average global annual temperatures also showed record values in 2015 and 2016. Currently, the Arctic is warming at more than twice the rate of lower latitudes

A Cytoplasmic Complex Mediates Specific mRNA Recognition and Localization in Yeast

The localization of ash mRNA in yeast requires the binding of She2p and the myosin adaptor protein She3p to its localization element, which is highly specific and leads to the assembly of stable transport complexes