Algebraic Bethe Ansatz for a discrete-state BCS pairing model

We show in detail how Richardson's exact solution of a discrete-state BCS (DBCS) model can be recovered as a special case of an algebraic Bethe Ansatz solution of the inhomogeneous XXX vertex model with twisted boundary conditions: by implementing the twist using Sklyanin's K-matrix construction and taking the quasiclassical limit, one obtains a complete set of conserved quantities, H_i, from which the DBCS Hamiltonian can be constructed as a second order polynomial. The eigenvalues and eigenstates of the H_i (which reduce to the Gaudin Hamiltonians in the limit of infinitely strong coupling) are exactly known in terms of a set of parameters determined by a set of on-shell Bethe Ansatz equations, which reproduce Richardson's equations for these parameters. We thus clarify that the integrability of the DBCS model is a special case of the integrability of the twisted inhomogeneous XXX vertex model. Furthermore, by considering the twisted inhomogeneous XXZ model and/or choosing a generic polynomial of the H_i as Hamiltonian, more general exactly solvable models can be constructed. -- To make the paper accessible to readers that are not Bethe Ansatz experts, the introductory sections include a self-contained review of those of its feature which are needed here.Comment: 17 pages, 5 figures, submitted to Phys. Rev.

Bose-Einstein condensation and entanglement in magnetic systems

We present a study of magnetic field induced quantum phase transitions in insulating systems. A generalized scaling theory is used to obtain the temperature dependence of several physical quantities along the quantum critical trajectory ($H=H_{C}$, $T\to0$) where $H$ is a longitudinal external magnetic field and $H_{C}$ the critical value at which the transition occurs. We consider transitions from a spin liquid at a critical field $H_{C1}$ and from a fully polarized paramagnet, at $H_{C2}$, into phases with long range order in the transverse components. The transitions at $H_{C1}$ and $H_{C2}$ can be viewed as Bose-Einstein condensations of magnons which however belong to different universality classes since they have different values of the dynamic critical exponent $z$. Finally, we use that the magnetic susceptibility is an entanglement witness to discuss how this type of correlation sets in as the system approaches the quantum critical point along the critical trajectory, $H=H_{C2}$, $T\to0$.Comment: 7 pages, 1 Table; accepted version; changes in text and new reference

Effects of the foal at the milking and dietary supplementation with extra virgin olive oil on jennet milk production

The effects of the foal at the milking and the extra virgin olive oil supplementation in the diet, on the milk obtained by 12 Ragusana jennets were studied. The jennets were each fed 3.5+1.5 kg/d of concentrate+bran, and hay ad libitum. They were divided into 2 equal groups with one group receiving an additional dietary supplement of 100 ml/d of olive oil. Milk was collected at day 20 post foal- ing and every 15-18 d for 5 times. At each collection period jennets were milked 4-times per day. At 07:30 h foals were separated from the jennets and after a 4 hour interval were milked manually (1MNF;1st milking, foal absent). At the end of the 1MNF, each jennet was milked again, with the foals kept near the udder, but prevented from suckling (2MYF; 2nd milking, foal present). After 2MYF, foals were removed a second time and the sequence repeated after another 4 hour interval for the 3rd (3MNF) and 4th (4MYF) milkings. Milk yield was recorded at each milking and samples analyzed for qualitative variables. The milk yield was 26% higher than that reported by Giosue et al. (2008) in similar conditions. The milk fat content were positively influenced by the presence of the foal at the milking but was not effect by the dietary supplement of olive oil

A PRELIMINARY INVESTIGATION INTO THERMAL SPRAY AND OTHER METAL/POLYMER DEPOSITION PROCESSES AND THEIR POTENTIAL USE IN THE OIL INDUSTRY

Polymeric coatings are being used in a raising number of applications, contributing to protection against weather conditions and localized corrosion, also reducing erosion wear. The coatings may be deposited by various processes and thermal spray is being recently investigated as a new alternative. This paper reports an exploratory study into various polymer deposition processes and evaluates their influence on the quality of the produced coating, concerning dispersion, cohesiveness and adhesion onto steel substrates. Different content aluminum/MDPE (medium density polyethylene) mixtures and processing parameters were studied as an attempt to identify the most promising parameters regarding their future application to produce coatings for the oil industry. The material characterization was carried out via mechanical testing (ASTM D638). The coating adhesion was evaluated by bend and ASTM C633-79 tensile tests. A microscopy evaluation of the coatings was also carried out. The produced films showed low friction surfaces and adequate adhesion to steel substrates. The presence of MAN (maleic anhydride) in the composite was responsible for the MDPE to recover its ductility, with a small increase of strength and rigidity, as well as a significant enhancement of coating adhesion to substrate

The elementary excitations of the exactly solvable Russian doll BCS model of superconductivity

The recently proposed Russian doll BCS model provides a simple example of a many body system whose renormalization group analysis reveals the existence of limit cycles in the running coupling constants of the model. The model was first studied using RG, mean field and numerical methods showing the Russian doll scaling of the spectrum, E(n) ~ E0 exp(-l n}, where l is the RG period. In this paper we use the recently discovered exact solution of this model to study the low energy spectrum. We find that, in addition to the standard quasiparticles, the electrons can bind into Cooper pairs that are different from those forming the condensate and with higher energy. These excited Cooper pairs can be described by a quantum number Q which appears in the Bethe ansatz equation and has a RG interpretation.Comment: 36 pages, 12 figure

Out of equilibrium correlation functions of quantum anisotropic XY models: one-particle excitations

We calculate exactly matrix elements between states that are not eigenstates of the quantum XY model for general anisotropy. Such quantities therefore describe non equilibrium properties of the system; the Hamiltonian does not contain any time dependence. These matrix elements are expressed as a sum of Pfaffians. For single particle excitations on the ground state the Pfaffians in the sum simplify to determinants.Comment: 11 pages, no figures; revtex. Minor changes in the text; list of refs. modifie

Superconducting correlations in metallic nanoparticles: exact solution of the BCS model by the algebraic Bethe ansatz

Superconducting pairing of electrons in nanoscale metallic particles with discrete energy levels and a fixed number of electrons is described by the reduced BCS model Hamiltonian. We show that this model is integrable by the algebraic Bethe ansatz. The eigenstates, spectrum, conserved operators, integrals of motion, and norms of wave functions are obtained. Furthermore, the quantum inverse problem is solved, meaning that form factors and correlation functions can be explicitly evaluated. Closed form expressions are given for the form factors that describe superconducting pairing.Comment: revised version, 5 pages, revtex, no figure