Non-hermitian approach to decaying ultracold bosonic systems

A paradigm model of modern atom optics is studied, strongly interacting ultracold bosons in an optical lattice. This many-body system can be artificially opened in a controlled manner by modern experimental techniques. We present results based on a non-hermitian effective Hamiltonian whose quantum spectrum is analyzed. The direct access to the spectrum of the metastable many-body system allows us to easily identify relatively stable quantum states, corresponding to previously predicted solitonic many-body structures

Exact numerical methods for a many-body Wannier Stark system

We present exact methods for the numerical integration of the Wannier-Stark system in a many-body scenario including two Bloch bands. Our ab initio approaches allow for the treatment of a few-body problem with bosonic statistics and strong interparticle interaction. The numerical implementation is based on the Lanczos algorithm for the diagonalization of large, but sparse symmetric Floquet matrices. We analyze the scheme efficiency in terms of the computational time, which is shown to scale polynomially with the size of the system. The numerically computed eigensystem is applied to the analysis of the Floquet Hamiltonian describing our problem. We show that this allows, for instance, for the efficient detection and characterization of avoided crossings and their statistical analysis. We finally compare the efficiency of our Lanczos diagonalization for computing the temporal evolution of our many-body system with an explicit fourth order Runge-Kutta integration. Both implementations heavily exploit efficient matrix-vector multiplication schemes. Our results should permit an extrapolation of the applicability of exact methods to increasing sizes of generic many-body quantum problems with bosonic statistics

Assessing the potential for reopening a building stone quarry : Newbigging Sandstone Quarry, Fife

Newbigging Sandstone Quarry in Fife is one of a number of former quarries in the Burntisland- Aberdour district which exploited the pale-coloured Grange Sandstone from Lower Carboniferous rocks. The quarry supplied building stone from the late 19th century, working intermittently from 1914 until closure in 1937, and again when reopened in the 1970s to the 1990s. The stone was primarily used locally and to supply the nearby markets in the Scottish Central Belt. Historical evidence indicates that prior to sandstone extraction, the area was dominated by largescale quarrying and mining of limestone, and substantial sandstone quarrying is likely to have begun after the arrival of the main railway line in 1890. It is probable that removal of the sandstone was directly associated with limestone exploitation, and that the quarried sandstone was effectively a by-product of limestone production. Sandstone extraction was probably viable due to the existing limestone quarry infrastructure (workforce, equipment, transportation) and the high demand for building stone in Central Scotland in the late 19th century. The geology within Newbigging Sandstone Quarry is dominated by thick-bedded uniform sandstone with a wide joint spacing, well-suited for obtaining large blocks. However, a mudstone (shale) band is likely to be present within a few metres of the principal (north) face of the quarry, around which the sandstone bed thickness and quality is likely to decrease. The mudstone bed forms a plane sloping at a shallow angle to the north, so that expansion of the quarry in this direction is likely to encounter a considerable volume of poor quality stone. Additionally, an east-west trending fault is present approximately 100 metres north of the quarry face, which is also likely to be associated with poor quality (fractured) stone

Explicit calculation of multi-fold contour integrals of certain ratios of Euler gamma functions. Part 1

In this paper we proceed to study properties of Mellin-Barnes (MB) transforms of Usyukina-Davydychev (UD) functions. In our previous papers [Nuclear Physics B 870 (2013) 243], [Nuclear Physics B 876 (2013) 322] we showed that multi-fold Mellin-Barnes (MB) transforms of Usyukina-Davydychev (UD) functions may be reduced to two-fold MB transforms and that the higher-order UD functions were obtained in terms of a differential operator by applying it to a slightly modified first UD function. The result is valid in $d=4$ dimensions and its analog in $d=4-2\varepsilon$ dimensions exits too [Theoretical and Mathematical Physics 177 (2013) 1515]. In [Nuclear Physics B 870 (2013) 243] the chain of recurrent relations for analytically regularized UD functions was obtained implicitly by comparing the left hand side and the right hand side of the diagrammatic relations between the diagrams with different loop orders. In turn, these diagrammatic relations were obtained due to the method of loop reduction for the triangle ladder diagrams proposed in 1983 by Belokurov and Usyukina. Here we reproduce these recurrent relations by calculating explicitly via Barnes lemmas the contour integrals produced by the left hand sides of the diagrammatic relations. In such a way we explicitly calculate a family of multi-fold contour integrals of certain ratios of Euler gamma functions. We make a conjecture that similar results for the contour integrals are valid for a wider family of smooth functions which includes the MB transforms of UD functions.Comment: 7 pages, 1 figure, minor changes in the text; accepted for publication in Nuclear Physics