A Nonstandard Supersymmetric KP Hierarchy

We show that the supersymmetric nonlinear Schr\"odinger equation can be written as a constrained super KP flow in a nonstandard representation of the Lax equation. We construct the conserved charges and show that this system reduces to the super mKdV equation with appropriate identifications. We construct various flows generated by the general nonstandard super Lax equation and show that they contain both the KP and mKP flows in the bosonic limits. This nonstandard supersymmetric KP hierarchy allows us to construct a new super KP equation which is nonlocal.Comment: 18 pages, plain TeX, UR-1367, ER-40685-81

Qubit thermometry for micromechanical resonators

We address estimation of temperature for a micromechanical oscillator lying arbitrarily close to its quantum ground state. Motivated by recent experiments, we assume that the oscillator is coupled to a probe qubit via Jaynes-Cummings interaction and that the estimation of its effective temperature is achieved via quantum limited measurements on the qubit. We first consider the ideal unitary evolution in a noiseless environment and then take into account the noise due to non dissipative decoherence. We exploit local quantum estimation theory to assess and optimize the precision of estimation procedures based on the measurement of qubit population, and to compare their performances with the ultimate limit posed by quantum mechanics. In particular, we evaluate the Fisher information (FI) for population measurement, maximize its value over the possible qubit preparations and interaction times, and compare its behavior with that of the quantum Fisher information (QFI). We found that the FI for population measurement is equal to the QFI, i.e., population measurement is optimal, for a suitable initial preparation of the qubit and a predictable interaction time. The same configuration also corresponds to the maximum of the QFI itself. Our results indicate that the achievement of the ultimate bound to precision allowed by quantum mechanics is in the capabilities of the current technology.Comment: 9 pages, 5 figures, revised version, to appear on PR

A Lax Equation for the Non-Linear Sigma Model

We propose a Lax equation for the non-linear sigma model which leads directly to the conserved local charges of the system. We show that the system has two infinite sets of such conserved charges following from the Lax equation, much like dispersionless systems. We show that the system has two Hamiltonian structures which are compatible so that it is truly a bi-Hamiltonian system. However, the two Hamiltonian structures act on the two distinct sets of charges to give the dynamical equations, which is quite distinct from the behavior in conventional integrable systems. We construct two recursion operators which connect the conserved charges within a given set as well as between the two sets. We show explicitly that the conserved charges are in involution with respect to either of the Hamiltonian structures thereby proving complete integrability of the system. Various other interesting features are also discussed.Comment: Latex, 13 page

Supersymmetric Non-local Gas Equation

In this paper we study systematically the question of supersymmetrization of the non-local gas equation. We obtain both the N=1 and the N=2 supersymmetric generalizations of the system which are integrable. We show that both the systems are bi-Hamiltonian. While the N=1 supersymmetrization allows the hierarchy of equations to be extended to negative orders (local equations), we argue that this is not the case for the N=2 supersymmetrization. In the bosonic limit, however, the N=2 system of equations lead to a new coupled integrable system of equations.Comment: RevTex, 7page

The Algebra of Non-Local Charges in Non-Linear Sigma Models

We obtain the exact Dirac algebra obeyed by the conserved non-local charges in bosonic non-linear sigma models. Part of the computation is specialized for a symmetry group $O(N)$. As it turns out the algebra corresponds to a cubic deformation of the Kac-Moody algebra. The non-linear terms are computed in closed form. In each Dirac bracket we only find highest order terms (as explained in the paper), defining a saturated algebra. We generalize the results for the presence of a Wess-Zumino term. The algebra is very similar to the previous one, containing now a calculable correction of order one unit lower.Comment: 27 pages + figures available via ftp, Plain TeX, IFUSP/P-106

A Nonliearly Dispersive Fifth Order Integrable Equation and its Hierarchy

In this paper, we study the properties of a nonlinearly dispersive integrable system of fifth order and its associated hierarchy. We describe a Lax representation for such a system which leads to two infinite series of conserved charges and two hierarchies of equations that share the same conserved charges. We construct two compatible Hamiltonian structures as well as their Casimir functionals. One of the structures has a single Casimir functional while the other has two. This allows us to extend the flows into negative order and clarifies the meaning of two different hierarchies of positive flows. We study the behavior of these systems under a hodograph transformation and show that they are related to the Kaup-Kupershmidt and the Sawada-Kotera equations under appropriate Miura transformations. We also discuss briefly some properties associated with the generalization of second, third and fourth order Lax operators.Comment: 11 pages, LaTex, version to be published in Journal of Nonlinear Mathematical Physics, has expanded discussio

Composite nanostructured solid-acid fuel-cell electrodes via electrospray deposition

Stable, porous, nanostructured composite electrodes were successfully fabricated via the inexpensive and scalable method of electrospray deposition, in which a dissolved solute is deposited onto a substrate using an electric field to drive droplet migration. The desirable characteristics of high porosity and high surface area were obtained under conditions that favored complete solvent evaporation from the electrospray droplets prior to contact with the substrate. Solid acid (CsH_2PO_4) feature sizes of 100 nm were obtained from electrosprayed water–methanol solutions with 10 g L^(−1) CsH_2PO_4 and 5 g L^(−1) Pt catalyst particles suspended using polyvinylpyrrolidone (PVP). Alternative additives such as Pt on carbon and carbon-nanotubes (CNTs) were also successfully incorporated by this route, and in all cases the PVP could be removed from the electrode by oxygen plasma treatment without damage to the structure. In the absence of additives (Pt, Pt/C and CNTs), the feature sizes were larger, 300 nm, and the structure morphologically unstable, with significant coarsening evident after exposure to ambient conditions for just two days. Electrochemical impedance spectroscopy under humidified hydrogen at 240 °C indicated an interfacial impedance of ~1.5 Ω cm^2 for the Pt/CsH_2PO_4 composite electrodes with a total Pt loading of 0.3 ± 0.2 mg cm^(−2). This result corresponds to a 30-fold decrease in Pt loading relative to mechanically milled electrodes with comparable activity, but further increases in activity and Pt utilization are required if solid acid fuel cells are to attain widespread commercial adoption

Does the revised cardiac risk index predict cardiac complications following elective lung resection?

Background: Revised Cardiac Risk Index (RCRI) score and Thoracic Revised Cardiac Risk Index (ThRCRI) score were developed to predict the risks of postoperative major cardiac complications in generic surgical population and thoracic surgery respectively. This study aims to determine the accuracy of these scores in predicting the risk of developing cardiac complications including atrial arrhythmias after lung resection surgery in adults. Methods: We studied 703 patients undergoing lung resection surgery in a tertiary thoracic surgery centre. Observed outcome measures of postoperative cardiac morbidity and mortality were compared against those predicted by risk. Results: Postoperative major cardiac complications and supraventricular arrhythmias occurred in 4.8% of patients. Both index scores had poor discriminative ability for predicting postoperative cardiac complications with an area under receiver operating characteristic (ROC) curve of 0.59 (95% CI 0.51-0.67) for the RCRI score and 0.57 (95% CI 0.49-0.66) for the ThRCRI score. Conclusions: In our cohort, RCRI and ThRCRI scores failed to accurately predict the risk of cardiac complications in patients undergoing elective resection of lung cancer. The British Thoracic Society (BTS) recommendation to seek a cardiology referral for all asymptomatic pre-operative lung resection patients with > 3 RCRI risk factors is thus unlikely to be of clinical benefit