Kosterlitz-Thouless transition of the quasi two-dimensional trapped Bose gas

We present Quantum Monte Carlo calculations with up to N=576000 interacting bosons in a quasi two-dimensional trap geometry closely related to recent experiments with atomic gases. The density profile of the gas and the non-classical moment of inertia yield intrinsic signatures for the Kosterlitz--Thouless transition temperature T_KT. From the reduced one-body density matrix, we compute the condensate fraction, which is quite large for small systems. It decreases slowly with increasing system sizes, vanishing in the thermodynamic limit. We interpret our data in the framework of the local-density approximation, and point out the relevance of our results for the analysis of experiments.Comment: 4 pages, 4 figure

The Finite Size Error in Many-body Simulations with long-Ranged Interactions

We discuss the origin of the finite size error of the energy in many-body simulation of systems of charged particles and we propose a correction based on the random phase approximation at long wave lengths. The correction comes from contributions mainly determined by the organized collective oscillations of the interacting system. Finite size corrections, both on kinetic and potential energy, can be calculated within a single simulation. Results are presented for the electron gas and silicon.Comment: 4 pages, 4 figures, submitted to PRL; corrected typo

A facile wet chemistry approach towards unilamellar tin sulfide nanosheets from Li4xSn1-xS2 solid solutions

We report on the facile production of single-layered tin sulfide nanosheets by a direct solid-state reaction, followed by quantitative liquid exfoliation in water. The new solid solution of SnS2 and Li2S with composition Li4xSn1-xS2 serves as a versatile solid-state precursor with tunable relative lithium and tin content. The end member Li2SnS3, corresponding to the solid solution composition Li-3xLixSn1-xS2], crystallizes in the well-known A(2)BO(3) structure type with mixed Li/Sn layers alternating with pure Li layers in the cationic substructure, which is interleaved with sulfur layers. The bonding in the Li layers can be regarded as ionic, while the Sn-S bonds have substantial covalent character. The resulting inherent anisotropy allows for the facile production of unilamellar chalcogenide nanosheets with thicknesses below 1 nm and lateral sizes of tens of microns, simply by shaking the crystalline precursor in water. The quantitative exfoliation into single-layered nanosheets was confirmed using optical microscopy, AFM, TEM, as well as X-ray diffraction of freestanding films produced from the colloidal suspension by centrifugation. Upon annealing, the as-obtained nanosheets are converted into SnS2 without sacrificing their favorable dispersion properties in water. The presented method allows for the cheap and scalable production of unilamellar chalogenide nanosheets for various potential applications, such as in electronic devices, solar cells, sensors, or battery technology. We expect this method to be generic and transferable to the synthesis of other metal chalcogenides. The use of solid solutions as solid-state precursors, featuring a large compositional range and potential for doping with other metals, may ultimately allow for the controlled introduction of defect levels and rational band-gap engineering in nanosheet materials

Transition temperature of a dilute homogeneous imperfect Bose gas

The leading-order effect of interactions on a homogeneous Bose gas is theoretically predicted to shift the critical temperature by an amount \Delta\Tc = # a_{scatt} n^{1/3} T_0 from the ideal gas result T_0, where a_{scatt} is the scattering length and n is the density. There have been several different theoretical estimates for the numerical coefficient #. We claim to settle the issue by measuring the numerical coefficient in a lattice simulation of O(2) phi^4 field theory in three dimensions---an effective theory which, as observed previously in the literature, can be systematically matched to the dilute Bose gas problem to reproduce non-universal quantities such as the critical temperature. We find # = 1.32 +- 0.02.Comment: 4 pages, submitted to Phys. Rev. Lett; minor changes due to improvement of analysis in the longer companion pape

ScAmPER: generating test suites to maximise code coverage in interactive fiction games

We present ScAmPER, a tool that generates test suites that maximise coverage for a class of interactive fiction computer games from the early 1980s. These games customise a base game engine with scripts written in a simple language. The tool uses a heuristic-guided search to evaluate whether these lines of code can in fact be executed during gameplay and, if so, outputs a sequence of game inputs that achieves this. Equivalently, the tool can be seen as attempting to generate a set of test cases that maximises coverage of the scripted code. The tool also generates a visualisation of the search process

Vortex Formation in Two-Dimensional Bose Gas

We discuss the stability of a homogeneous two-dimensional Bose gas at finite temperature against formation of isolated vortices. We consider a patch of several healing lengths in size and compute its free energy using the Euclidean formalism. Since we deal with an open system, which is able to exchange particles and angular momentum with the rest of the condensate, we use the symmetry-breaking (as opposed to the particle number conserving) formalism, and include configurations with all values of angular momenta in the partition function. At finite temperature, there appear sphaleron configurations associated to isolated vortices. The contribution from these configurations to the free energy is computed in the dilute gas approximation. We show that the Euclidean action of linearized perturbations of a vortex is not positive definite. As a consequence the free energy of the 2D Bose gas acquires an imaginary part. This signals the instability of the gas. This instability may be identified with the Berezinskii, Kosterlitz and Thouless (BKT) transition.Comment: RevTeX, 13 pages, 3 figure

Measuring Electron Correlation. The Impact of Symmetry and Orbital Transformations

In this perspective, the various measures of electron correlation used in wavefunction theory, density functional theory and quantum information theory are briefly reviewed. We then focus on a more traditional metric based on dominant weights in the full configuration solution and discuss its behaviour with respect to the choice of the $N$-electron and the one-electron basis. The impact of symmetry is discussed and we emphasize that the distinction between determinants, configuration state functions and configurations as reference functions is useful because the latter incorporate spin-coupling into the reference and should thus reduce the complexity of the wavefunction expansion. The corresponding notions of single determinant, single spin-coupling and single configuration wavefunctions are discussed and the effect of orbital rotations on the multireference character is reviewed by analysing a simple model system. In molecular systems, the extent of correlation effects should be limited by finite system size and in most cases the appropriate choices of one-electron and $N$-electron bases should be able to incorporate these into a low-complexity reference function, often a single configurational one