286 research outputs found
Rotational and vibrational spectra of quantum rings
One can confine the two-dimensional electron gas in semiconductor
heterostructures electrostatically or by etching techniques such that a small
electron island is formed. These man-made ``artificial atoms'' provide the
experimental realization of a text-book example of many-particle physics: a
finite number of quantum particles in a trap. Much effort was spent on making
such "quantum dots" smaller and going from the mesoscopic to the quantum
regime. Far-reaching analogies to the physics of atoms, nuclei or metal
clusters were obvious from the very beginning: The concepts of shell structure
and Hund's rules were found to apply -- just as in real atoms! In this Letter,
we report the discovery that electrons confined in ring-shaped quantum dots
form rather rigid molecules with antiferromagnetic order in the ground state.
This can be seen best from an analysis of the rotational and vibrational
excitations
Phase Diagram of the Heisenberg Spin Ladder with Ring Exchange
We investigate the phase diagram of a generalized spin-1/2 quantum
antiferromagnet on a ladder with rung, leg, diagonal, and ring-exchange
interactions. We consider the exactly soluble models associated with the
problem, obtain the exact ground states which exist for certain parameter
regimes, and apply a variety of perturbative techniques in the regime of strong
ring-exchange coupling. By combining these approaches with considerations
related to the discrete Z_4 symmetry of the model, we present the complete
phase diagram.Comment: 17 pages, 10 figure
Skymrion lattice melting in the quantum Hall system
The melting and magnetic disordering of the skyrmion lattice in the quantum
Hall system at filling factor are studied. A
Berezinskii-Kosterlitz-Thouless renormalization group theory is employed to
describe the coupled magnetic and translational degrees of freedom. The
non-trivial magnetic properties of the skyrmion system stem from the in-plane
components of the non-collinear magnetization in the vicinity of skyrmions,
which are described by an antiferromagnetic XY model. In a Coulomb gas
formulation the `particles' are the topological defects of the XY model
(vortices) and of the lattice (dislocations and disclinations). The latter
frustrate the antiferromagnetic order and acquire fractional vorticity in order
to minimize their energy. We find a number of melting/disordering scenarios for
various lattice types. While these results do not depend on a particular model,
we also consider a simple classical model for the skyrmion system. It results
in a rich T=0 phase diagram. We propose that the triangular and square skyrmion
lattices are generically separated by a centered rectangular phase in the
quantum Hall system.Comment: 15 pages with 5 figures. Minor revisions. Important reference to M.
Rao, S. Sengupta, and R. Shankar, Phys. Rev. Lett. 79, 3998 (1997) adde
The nature and distribution of flowing features in a weakly karstified porous limestone aquifer
The nature and distribution of flowing features in boreholes in an area of approximately 400 km2 in a weakly karstic porous limestone aquifer (the Chalk) was investigated using single borehole dilution tests (SBDTs) and borehole imaging. One-hundred and twenty flowing features identified from SBDTs in 24 boreholes have densities which decrease from ∼0.3 m−1 near the water table to ∼0.07 m−1 at depths of more than 40 m below the water table; the average density is 0.20 m−1. There is some evidence of regional lithological control and borehole imaging of three boreholes indicated that most flowing features are associated with marls, hardgrounds and flints that may be developed at a more local scale.
Borehole imaging also demonstrated that many flowing features are solutionally enlarged fractures, suggesting that even in carbonate aquifers where surface karst is developed on only a small scale, groundwater flow is still strongly influenced by dissolution. Fully connected solutional pathways can occur over 100s, sometimes 1000s of metres. However, conduits, tubules and fissures may not always be individually persistent along a flowpath, instead being connected together and also connected to unmodified fractures to create a relatively dense network of voids with variable apertures (15 cm). Groundwater therefore moves along flowpaths made up of voids with varying shape and character. Local solutional development of fractures at significant depths below the surface suggests that mixing corrosion and in situ sources of acidity may contribute to solutional enhancement of fractures.
The study demonstrates that single borehole dilution testing is a useful method of obtaining a large dataset of flowing features at catchment-regional scales. The Chalk is a carbonate aquifer with small-scale surface karst development and this study raises the question of whether other carbonate aquifers with small-scale surface karst have similar characteristics, and what hydrological role small-scale dissolutional features play in highly karstic aquifers
The Klein-Gordon equation with the Kratzer potential in d dimensions
We apply the Asymptotic Iteration Method to obtain the bound-state energy
spectrum for the d-dimensional Klein-Gordon equation with scalar S(r) and
vector potentials V(r). When S(r) and V(r) are both Coulombic, we obtain all
the exact solutions; when the potentials are both of Kratzer type, we obtain
all the exact solutions for S(r)=V(r); if S(r) > V(r) we obtain exact solutions
under certain constraints on the potential parameters: in this case, a possible
general solution is found in terms of a monic polynomial, whose coefficients
form a set of elementary symmetric polynomials.Comment: 13 page
SYMBA: An end-to-end VLBI synthetic data generation pipeline: Simulating Event Horizon Telescope observations of M 87
Context. Realistic synthetic observations of theoretical source models are essential for our understanding of real observational data. In using synthetic data, one can verify the extent to which source parameters can be recovered and evaluate how various data corruption effects can be calibrated. These studies are the most important when proposing observations of new sources, in the characterization of the capabilities of new or upgraded instruments, and when verifying model-based theoretical predictions in a direct comparison with observational data. Aims. We present the SYnthetic Measurement creator for long Baseline Arrays (SYMBA), a novel synthetic data generation pipeline for Very Long Baseline Interferometry (VLBI) observations. SYMBA takes into account several realistic atmospheric, instrumental, and calibration effects. Methods. We used SYMBA to create synthetic observations for the Event Horizon Telescope (EHT), a millimetre VLBI array, which has recently captured the first image of a black hole shadow. After testing SYMBA with simple source and corruption models, we study the importance of including all corruption and calibration effects, compared to the addition of thermal noise only. Using synthetic data based on two example general relativistic magnetohydrodynamics (GRMHD) model images of M 87, we performed case studies to assess the image quality that can be obtained with the current and future EHT array for different weather conditions. Results. Our synthetic observations show that the effects of atmospheric and instrumental corruptions on the measured visibilities are significant. Despite these effects, we demonstrate how the overall structure of our GRMHD source models can be recovered robustly with the EHT2017 array after performing calibration steps, which include fringe fitting, a priori amplitude and network calibration, and self-calibration. With the planned addition of new stations to the EHT array in the coming years, images could be reconstructed with higher angular resolution and dynamic range. In our case study, these improvements allowed for a distinction between a thermal and a non-thermal GRMHD model based on salient features in reconstructed images
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