Third Bose Fugacity Coefficient in One Dimension, as a Function of Asymptotic Quantities

In one of the very few exact quantum mechanical calculations of fugacity coefficients, Dodd and Gibbs (\textit{J. Math.Phys}.,\textbf{15}, 41 (1974)) obtained $b_{2}$ and $b_{3}$ for a one dimensional Bose gas, subject to repulsive delta-function interactions, by direct integration of the wave functions. For $b_{2}$, we have shown (\textit{Mol. Phys}.,\textbf{103}, 1301 (2005)) that Dodd and Gibbs' result can be obtained from a phase shift formalism, if one also includes the contribution of oscillating terms, usually contributing only in 1 dimension. Now, we develop an exact expression for $b_{3}-b_{3}^{0}$ (where $b_{3}^{0}$ is the free particle fugacity coefficient) in terms of sums and differences of 3-body eigenphase shifts. Further, we show that if we obtain these eigenphase shifts in a distorted-Born approximation, then, to first order, we reproduce the leading low temperature behaviour, obtained from an expansion of the two-fold integral of Dodd and Gibbs. The contributions of the oscillating terms cancel. The formalism that we propose is not limited to one dimension, but seeks to provide a general method to obtain virial coefficients, fugacity coefficients, in terms of asymptotic quantities. The exact one dimensional results allow us to confirm the validity of our approach in this domain.Comment: 29 page

Second virial coefficient in one dimension, as a function of asymptotic quantities

A result from Dodd and Gibbs[1] for the second virial coefficient of particles in 1 dimension, subject to delta-function interactions, has been obtained by direct integration of the wave functions. It is shown that this result can be obtained from a phase shift formalism, if one includes the contribution of oscillating terms. The result is important in work to follow, for the third virial coefficient, for which a similar formalism is being developed. We examine a number of fine points in the quantum mechanical formalisms.Comment: 7 pages, no figures, submitted to Molecular Physic

S-matrix poles and the second virial coefficient

For cutoff potentials, a condition which is not a limitation for the calculation of physical systems, the S-matrix is meromorphic. We can express it in terms of its poles, and then calculate the quantum mechanical second virial coefficient of a neutral gas. Here, we take another look at this approach, and discuss the feasibility, attraction and problems of the method. Among concerns are the rate of convergence of the 'pole' expansion and the physical significance of the 'higher' poles.Comment: 20 pages, 8 tables, submitted to J. Mol. Phy

Integral representation of one dimensional three particle scattering for delta function interactions

The Schr\"{o}dinger equation, in hyperspherical coordinates, is solved in closed form for a system of three particles on a line, interacting via pair delta functions. This is for the case of equal masses and potential strengths. The interactions are replaced by appropriate boundary conditions. This leads then to requiring the solution of a free-particle Schr\"{o}dinger equation subject to these boundary conditions. A generalized Kontorovich - Lebedev transformation is used to write this solution as an integral involving a product of Bessel functions and pseudo-Sturmian functions. The coefficient of the product is obtained from a three-term recurrence relation, derived from the boundary condition. The contours of the Kontorovich-Lebedev representation are fixed by the asymptotic conditions. The scattering matrix is then derived from the exact solution of the recurrence relation. The wavefunctions that are obtained are shown to be equivalent to those derived by McGuire. The method can clearly be applied to a larger number of particles and hopefully might be useful for unequal masses and potentials.Comment: 18 pages, 2 figures, to be published in J. Math. Phy

Three Bosons in One Dimension with Short Range Interactions I: Zero Range Potentials

We consider the three-boson problem with $\delta$-function interactions in one spatial dimension. Three different approaches are used to calculate the phase shifts, which we interpret in the context of the effective range expansion, for the scattering of one free particle a off of a bound pair. We first follow a procedure outlined by McGuire in order to obtain an analytic expression for the desired S-matrix element. This result is then compared to a variational calculation in the adiabatic hyperspherical representation, and to a numerical solution to the momentum space Faddeev equations. We find excellent agreement with the exact phase shifts, and comment on some of the important features in the scattering and bound-state sectors. In particular, we find that the 1+2 scattering length is divergent, marking the presence of a zero-energy resonance which appears as a feature when the pair-wise interactions are short-range. Finally, we consider the introduction of a three-body interaction, and comment on the cutoff dependence of the coupling.Comment: 9 figures, 2 table

Bound states and scattering lengths of three two-component particles with zero-range interactions under one-dimensional confinement

The universal three-body dynamics in ultra-cold binary gases confined to one-dimensional motion are studied. The three-body binding energies and the (2 + 1)-scattering lengths are calculated for two identical particles of mass $m$ and a different one of mass $m_1$, which interactions is described in the low-energy limit by zero-range potentials. The critical values of the mass ratio $m/m_1$, at which the three-body states arise and the (2 + 1)-scattering length equals zero, are determined both for zero and infinite interaction strength $\lambda_1$ of the identical particles. A number of exact results are enlisted and asymptotic dependences both for $m/m_1 \to \infty$ and $\lambda_1 \to -\infty$ are derived. Combining the numerical and analytical results, a schematic diagram showing the number of the three-body bound states and the sign of the (2 + 1)-scattering length in the plane of the mass ratio and interaction-strength ratio is deduced. The results provide a description of the homogeneous and mixed phases of atoms and molecules in dilute binary quantum gases

Exact ground states for the four-electron problem in a Hubbard ladder

The exact ground state of four electrons in an arbitrary large two leg Hubbard ladder is deduced from nine analytic and explicit linear equations. The used procedure is described, and the properties of the ground state are analyzed. The method is based on the construction in r-space of the different type of orthogonal basis wave vectors which span the subspace of the Hilbert space containing the ground state. In order to do this, we start from the possible microconfigurations of the four particles within the system. These microconfigurations are then rotated, translated and spin-reversed in order to build up the basis vectors of the problem. A closed system of nine analytic linear equations is obtained whose secular equation, by its minimum energy solution, provides the ground state energy and the ground state wave function of the model.Comment: 10 pages, 7 figure

A922 Sequential measurement of 1 hour creatinine clearance (1-CRCL) in critically ill patients at risk of acute kidney injury (AKI)

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Effectiveness of an intervention for improving drug prescription in primary care patients with multimorbidity and polypharmacy:Study protocol of a cluster randomized clinical trial (Multi-PAP project)

This study was funded by the Fondo de Investigaciones Sanitarias ISCIII (Grant Numbers PI15/00276, PI15/00572, PI15/00996), REDISSEC (Project Numbers RD12/0001/0012, RD16/0001/0005), and the European Regional Development Fund ("A way to build Europe").Background: Multimorbidity is associated with negative effects both on people's health and on healthcare systems. A key problem linked to multimorbidity is polypharmacy, which in turn is associated with increased risk of partly preventable adverse effects, including mortality. The Ariadne principles describe a model of care based on a thorough assessment of diseases, treatments (and potential interactions), clinical status, context and preferences of patients with multimorbidity, with the aim of prioritizing and sharing realistic treatment goals that guide an individualized management. The aim of this study is to evaluate the effectiveness of a complex intervention that implements the Ariadne principles in a population of young-old patients with multimorbidity and polypharmacy. The intervention seeks to improve the appropriateness of prescribing in primary care (PC), as measured by the medication appropriateness index (MAI) score at 6 and 12months, as compared with usual care. Methods/Design: Design:pragmatic cluster randomized clinical trial. Unit of randomization: family physician (FP). Unit of analysis: patient. Scope: PC health centres in three autonomous communities: Aragon, Madrid, and Andalusia (Spain). Population: patients aged 65-74years with multimorbidity (≥3 chronic diseases) and polypharmacy (≥5 drugs prescribed in ≥3months). Sample size: n=400 (200 per study arm). Intervention: complex intervention based on the implementation of the Ariadne principles with two components: (1) FP training and (2) FP-patient interview. Outcomes: MAI score, health services use, quality of life (Euroqol 5D-5L), pharmacotherapy and adherence to treatment (Morisky-Green, Haynes-Sackett), and clinical and socio-demographic variables. Statistical analysis: primary outcome is the difference in MAI score between T0 and T1 and corresponding 95% confidence interval. Adjustment for confounding factors will be performed by multilevel analysis. All analyses will be carried out in accordance with the intention-to-treat principle. Discussion: It is essential to provide evidence concerning interventions on PC patients with polypharmacy and multimorbidity, conducted in the context of routine clinical practice, and involving young-old patients with significant potential for preventing negative health outcomes. Trial registration: Clinicaltrials.gov, NCT02866799Publisher PDFPeer reviewe