Quantum entanglement and fixed-point bifurcations

How does the classical phase-space structure for a composite system relate to the entanglement characteristics of the corresponding quantum system? We demonstrate how the entanglement in nonlinear bipartite systems can be associated with a fixed-point bifurcation in the classical dynamics. Using the example of coupled giant spins we show that when a fixed point undergoes a supercritical pitchfork bifurcation, the corresponding quantum state-the ground state-achieves its maximum amount of entanglement near the critical point. We conjecture that this will be a generic feature of systems whose classical limit exhibits such a bifurcation.

Positive solutions for nonlinear m-point Eigenvalue problems

In this paper, we are concerned with determining values of lambda, for which there exist positive solutions of the nonlinear eigenvalue problem [GRAPHICS] where a, b, c, d is an element of [0, infinity), xi(i) is an element of (0, 1), alpha(i), beta(i) is an element of [0 infinity) (for i is an element of {1, ..., m - 2}) are given constants, p, q is an element of C ([0, 1], (0, infinity)), h is an element of C ([0, 1], [0, infinity)), and f is an element of C ([0, infinity), [0, infinity)) satisfying some suitable conditions. Our proofs are based on Guo-Krasnoselskii fixed point theorem. (C) 2004 Elsevier Inc. All rights reserved.

Entanglement and bifurcations in Jahn-Teller models

We compare and contrast the entanglement in the ground state of two Jahn-Teller models. The Exbeta system models the coupling of a two-level electronic system, or qubit, to a single-oscillator mode, while the Exepsilon models the qubit coupled to two independent, degenerate oscillator modes. In the absence of a transverse magnetic field applied to the qubit, both systems exhibit a degenerate ground state. Whereas there always exists a completely separable ground state in the Exbeta system, the ground states of the Exepsilon model always exhibit entanglement. For the Exbeta case we aim to clarify results from previous work, alluding to a link between the ground-state entanglement characteristics and a bifurcation of a fixed point in the classical analog. In the Exepsilon case we make use of an ansatz for the ground state. We compare this ansatz to exact numerical calculations and use it to investigate how the entanglement is shared between the three system degrees of freedom.

Existence of solutions to some equilibrium problems

The concept of a monotone family of functions, which need not be countable, and the solution of an equilibrium problem associated with the family are introduced. A fixed-point theorem is applied to prove the existence of solutions to the problem.

Quantum entanglement in the two-impurity Kondo model

In order to quantify quantum entanglement in two-impurity Kondo systems, we calculate the concurrence, negativity, and von Neumann entropy. The entanglement of the two Kondo impurities is shown to be determined by two competing many-body effects, namely the Kondo effect and the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction, I. Due to the spin-rotational invariance of the ground state, the concurrence and negativity are uniquely determined by the spin-spin correlation between the impurities. It is found that there exists a critical minimum value of the antiferromagnetic correlation between the impurity spins which is necessary for entanglement of the two impurity spins. The critical value is discussed in relation with the unstable fixed point in the two-impurity Kondo problem. Specifically, at the fixed point there is no entanglement between the impurity spins. Entanglement will only be created [and quantum information processing (QIP) will only be possible] if the RKKY interaction exchange energy, I, is at least several times larger than the Kondo temperature, T-K. Quantitative criteria for QIP are given in terms of the impurity spin-spin correlation.

The emergence of order in random walk resource discovery protocols

While others have attempted to determine, by way of mathematical formulae, optimal resource duplication strategies for random walk protocols, this paper is concerned with studying the emergent effects of dynamic resource propagation and replication. In particular, we show, via modelling and experimentation, that under any given decay (purge) rate the number of nodes that have knowledge of particular resource converges to a fixed point or a limit cycle. We also show that even for high rates of decay - that is, when few nodes have knowledge of a particular resource - the number of hops required to find that resource is small.

A reduced load approximation accounting for link interactions in a loss network

This paper is concerned with evaluating the performance of loss networks. Accurate determination of loss network performance can assist in the design and dimensioning of telecommunications networks. However, exact determination can be difficult and generally cannot be done in reasonable time. For these reasons there is much interest in developing fast and accurate approximations. We develop a reduced load approximation which improves on the famous Erlang fixed point approximation (EFPA) in a variety of circumstances. We illustrate our results with reference to a range of networks for which the EFPA may be expected to perform badly.

Measurement of free drug and clinical end-point by high-performance liquid chromatography-mass spectrometry: Applications and implications for pharmacokinetic and pharmacodynamic studies

Free drug measurement and pharmacodymanic markers provide the opportunity for a better understanding of drug efficacy and toxicity. High-performance liquid chromatography (HPLC)-mass spectrometry (MS) is a powerful analytical technique that could facilitate the measurement of free drug and these markers. Currently, there are very few published methods for the determination of free drug concentrations by HPLC-MS. The development of atmospheric pressure ionisation sources, together with on-line microdialysis or on-line equilibrium dialysis and column switching techniques have reduced sample run times and increased assay efficiency. The availability of such methods will aid in drug development and the clinical use of certain drugs, including anti-convulsants, anti-arrhythmics, immunosuppressants, local anaesthetics, anti-fungals and protease inhibitors. The history of free drug measurement and an overview of the current HPLC-MS applications for these drugs are discussed. Immunosuppressant drugs are used as an example for the application of HPLC-MS in the measurement of drug pharmacodynamics. Potential biomarkers of immunosuppression that could be measured by HPLC-MS include purine nucleoside/nucleotides, drug-protein complexes and phosphorylated peptides. At the proteomic level, two-dimensional gel electrophoresis combined with matrix-assisted laser desorption/ionisation time-of-flight (TOF) MS is a powerful tool for identifying proteins involved in the response to inflammatory mediators. (C) 2003 Elsevier Science B.V. All rights reserved.

Time-evolution of highly localized positive-energy states of the free Dirac electron

Highly localized positive-energy states of the free Dirac electron are constructed and shown to evolve in a simple way under the action of Dirac's equation. When the initial uncertainty in position is small on the scale of the Compton wavelength, there is an associated uncertainty in the mean energy that is large compared with the rest mass of the electron. However, this does not lead to any breakdown of the one-particle description, associated with the possibility of pair-production, but rather leads to a rapid expansion of the probability density outwards from the point of localization, at speeds close to the speed of light.

Effect of temperature and free ammonia on nitrification and nitrite accumulation in landfill leachate and analysis of its nitrifying bacterial community by FISH

The cause of seasonal failure of a nitrifying municipal landfill leachate treatment plant utilizing a fixed biofilm was investigated by wastewater analyses and batch respirometric tests at every treatment stage. Nitrification of the leachate treatment plant was severely affected by the seasonal temperature variation. High free ammonia (NH3-N) inhibited not only nitrite oxidizing bacteria (NOB) but also ammonia oxidizing bacteria (AOB). In addition, high pH also increased free ammonia concentration to inhibit nitrifying activity especially when the NH4-N level was high. The effects of temperature and free ammonia of landfill leachate on nitrification and nitrite accumulation were investigated with a semi-pilot scale biofilm airlift reactor. Nitrification rate of landfill leachate increased with temperature when free ammonia in the reactor was below the inhibition level for nitrifiers. Leachate was completely nitrified up to a load of 1.5 kg NH4-N m(-3) d(-1) at 28 degrees C. The activity of NOB was inhibited by NH3-N resulting in accumulation of nitrite. NOB activity decreased more than 50% at 0.7 mg NH3-N L-1. Fluorescence in situ hybridization (FISH) was carried out to analyze the population of AOB and NOB in the nitrite accumulating nitrifying biofilm. NOB were located close to AOB by forming small clusters. A significant fraction of AOB identified by probe Nso1225 specifically also hybridized with the Nitrosonlonas specific probe Nsm156. The main NOB were Nitrobacter and Nitrospira which were present in almost equal amounts in the biofilm as identified by simultaneous hybridization with Nitrobacter specific probe Nit3 and Nitrospira specific probe Ntspa662. (c) 2005 Elsevier Ltd. All rights reserved.

Crystallography of carbide-free bainite in a hard bainitic steel

The convergent beam Kikuchi line diffraction technique has been used to accurately determine the orientation relationships between bainitic ferrite and retained austenite in a hard bainitic steel. A reproducible orientation relationship has been uniquely observed for both the upper and lower bainite. It is [GRAPHICS] However, the habit plane of upper bainite is different from that of lower bainite. The former has habit plane that is either within 5 degrees of (221)(A) or of (259)(A). The latter only corresponds with a habit plane that is within 5 degrees of (259)(A). The determined orientation relationship is completely consistent with reported results determined using the same technique with an accuracy of +/- 0.5 degrees in lath martensite in an Fe-20 wt.% Ni-6 wt.% Mn alloy and in a low carbon low alloy steel. It also agrees well with the orientation relationship between granular bainite and austenite in an Fe-19 wt.% Ni-3.5 wt.% Mn-0.15 wt.% C steel. Hence it is believed that, at least from a crystallographic point view, the bainite transformation has the characteristics of martensitic transformation. (c) 2006 Elsevier B.V. All rights reserved.