Integrity bases for local invariants of composite quantum systems

Unitary group branchings appropriate to the calculation of local invariants of density matrices of composite quantum systems are formulated using the method of $S$-function plethysms. From this, the generating function for the number of invariants at each degree in the density matrix can be computed. For the case of two two-level systems the generating function is $F(q) = 1 + q + 4q^{2} + 6 q^{3} + 16 q^{4} + 23 q^{5} + 52 q^{6} + 77 q^{7} + 150 q^{8} + 224 q^{9} + 396 q^{10} + 583 q^{11}+ O(q^{12})$. Factorisation of such series leads in principle to the identification of an integrity basis of algebraically independent invariants. This note replaces Appendix B of our paper\cite{us} J Phys {\bf A33} (2000) 1895-1914 (\texttt{quant-ph/0001076}) which is incorrect.Comment: Latex, 4 pages, correcting Appendix B of quant-ph/0001076 Error in $F(q)$ corrected and conclusions modified accordingl

Influence of Resonances on the Noise Performance of SQUID Susceptometers

Scanning Superconducting Quantum Interference Device (SQUID) Susceptometry simultaneously images the local magnetic fields and susceptibilities above a sample with sub-micron spatial resolution. Further development of this technique requires a thorough understanding of the current, voltage, and flux ( IVΦ ) characteristics of scanning SQUID susceptometers. These sensors often have striking anomalies in their current–voltage characteristics, which we believe to be due to electromagnetic resonances. The effect of these resonances on the performance of these SQUIDs is unknown. To explore the origin and impact of the resonances, we develop a model that qualitatively reproduces the experimentally-determined IVΦ characteristics of our scanning SQUID susceptometers. We use this model to calculate the noise characteristics of SQUIDs of different designs. We find that the calculated ultimate flux noise is better in susceptometers with damping resistors that diminish the resonances than in susceptometers without damping resistors. Such calculations will enable the optimization of the signal-to-noise characteristics of scanning SQUID susceptometers

Electromagnetic field near cosmic string

The retarded Green function of the electromagnetic field in spacetime of a straight thin cosmic string is found. It splits into a geodesic part (corresponding to the propagation along null rays) and to the field scattered on the string. With help of the Green function the electric and magnetic fields of simple sources are constructed. It is shown that these sources are influenced by the cosmic string through a self-interaction with their field. The distant field of static sources is studied and it is found that it has a different multipole structure than in Minkowski spacetime. On the other hand, the string suppresses the electric and magnetic field of distant sources--the field is expelled from regions near the string.Comment: 12 pages, 8 figures (low-resolution figures; for the version with high-resolution figures see http://utf.mff.cuni.cz/~krtous/papers/), v2: two references added, typos correcte

Cryogenic mechanisms for scanning and interchange of the Fabry-Perot interferometers in the ISO long wavelength spectrometer

The Infrared Space Observatory (ISO) is an ESA cornerstone mission for infrared astronomy. Schedules for launch in 1993, its four scientific instruments will provide unprecedented sensitivity and spectral resolution at wavelengths which are inaccessible using ground-based techniques. One of these, the Long Wavelength Spectrometer (LWS), will operate in the 45 to 180 micron region (Emery et. al., 1985) and features two Fabry-Perot interferometers mounted on an interchange mechanism. The entire payload module of the spacecraft, comprising the 60 cm telescope and the four focal plane instruments, is maintained at 2 to 4 K by an onboard supply of liquid helium. The mechanical design and testing of the cryogenic interferometer and interchange mechanisms are described

Frustration, interaction strength and ground-state entanglement in complex quantum systems

Entanglement in the ground state of a many-body quantum system may arise when the local terms in the system Hamiltonian fail to commute with the interaction terms in the Hamiltonian. We quantify this phenomenon, demonstrating an analogy between ground-state entanglement and the phenomenon of frustration in spin systems. In particular, we prove that the amount of ground-state entanglement is bounded above by a measure of the extent to which interactions frustrate the local terms in the Hamiltonian. As a corollary, we show that the amount of ground-state entanglement is bounded above by a ratio between parameters characterizing the strength of interactions in the system, and the local energy scale. Finally, we prove a qualitatively similar result for other energy eigenstates of the system.Comment: 11 pages, 3 figure

Applications of p-deficiency and p-largeness

We use Schlage-Puchta's concept of p-deficiency and Lackenby's property of p-largeness to show that a group having a finite presentation with p-deficiency greater than 1 is large, which implies that Schlage-Puchta's infinite finitely generated p-groups are not finitely presented. We also show that for all primes p at least 7, any group having a presentation of p-deficiency greater than 1 is Golod-Shafarevich, and has a finite index subgroup which is Golod-Shafarevich for the remaining primes. We also generalise a result of Grigorchuk on Coxeter groups to odd primes.Comment: 23 page

Predictive analysis of a hydrodynamics application on large-scale CMP clusters

We present the development of a predictive performance model for the high-performance computing code Hydra, a hydrodynamics benchmark developed and maintained by the United Kingdom Atomic Weapons Establishment (AWE). The developed model elucidates the parallel computation of Hydra, with which it is possible to predict its runtime and scaling performance on varying large-scale chip multiprocessor (CMP) clusters. A key feature of the model is its granularity; with the model we are able to separate the contributing costs, including computation, point-to-point communications, collectives, message buffering and message synchronisation. The predictions are validated on two contrasting large-scale HPC systems, an AMD Opteron/ InfiniBand cluster and an IBM BlueGene/P, both of which are located at the Lawrence Livermore National Laboratory (LLNL) in the US. We validate the model on up to 2,048 cores, where it achieves a > 85% accuracy in weak-scaling studies. We also demonstrate use of the model in exposing the increasing costs of collectives for this application, and also the influence of node density on network accesses, therefore highlighting the impact of machine choice when running this hydrodynamics application at scale