Algebraic Bethe ansatz method for the exact calculation of energy spectra and form factors: applications to models of Bose-Einstein condensates and metallic nanograins

In this review we demonstrate how the algebraic Bethe ansatz is used for the calculation of the-energy spectra and form factors (operator matrix elements in the basis of Hamiltonian eigenstates) in exactly solvable quantum systems. As examples we apply the theory to several models of current interest in the study of Bose-Einstein condensates, which have been successfully created using ultracold dilute atomic gases. The first model we introduce describes Josephson tunnelling between two coupled Bose-Einstein condensates. It can be used not only for the study of tunnelling between condensates of atomic gases, but for solid state Josephson junctions and coupled Cooper pair boxes. The theory is also applicable to models of atomic-molecular Bose-Einstein condensates, with two examples given and analysed. Additionally, these same two models are relevant to studies in quantum optics; Finally, we discuss the model of Bardeen, Cooper and Schrieffer in this framework, which is appropriate for systems of ultracold fermionic atomic gases, as well as being applicable for the description of superconducting correlations in metallic grains with nanoscale dimensions.; In applying all the above models to. physical situations, the need for an exact analysis of small-scale systems is established due to large quantum fluctuations which render mean-field approaches inaccurate.

Exact form factors for the Josephson tunneling current and relative particle number fluctuations in a model of two coupled Bose-Einstein condensates

Form factors are derived for a model describing the coherent Josephson tunneling between two coupled Bose-Einstein condensates. This is achieved by studying the exact solution of the model within the framework of the algebraic Bethe ansatz. In this approach the form factors are expressed through determinant representations which are functions of the roots of the Bethe ansatz equations.

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 Bardeen, Cooper, and Schrieffer 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 and correlation functions that describe superconducting pairing.

Integrability and exact spectrum of a pairing model for nucleons

A pairing model for nucleons, introduced by Richardson in 1966, which describes proton-neutron pairing as well as proton-proton and neutron-neutron pairing, is re-examined in the context of the quantum inverse scattering method. Specifically, this shows that the model is integrable by enabling the explicit construction of the conserved operators. We determine the eigenvalues of these operators in terms of the Bethe ansatz, which in turn leads to an expression for the energy eigenvalues of the Hamiltonian.

Exact solution at integrable coupling of a model for the Josephson effect between small metallic grains

A model is introduced for two reduced BCS systems which are coupled through the transfer of Cooper pairs between the systems. The model may thus be used in the analysis of the Josephson effect arising from pair tunneling between two strongly coupled small metallic grains. At a particular coupling strength the model is integrable and explicit results are derived for the energy spectrum, conserved operators, integrals of motion, and wave function scalar products. It is also shown that form factors can be obtained for the calculation of correlation functions. Furthermore, a connection with perturbed conformal field theory is made.

Solvable models of Bose-Einstein condensates: A new algebraic Bethe ansatz scheme

A new algebraic Bethe ansatz scheme is proposed to diagonalize classes of integrable models relevant to the description of Bose-Einstein condensation in dilute alkali gases. This is achieved by introducing the notion of Z-graded representations of the Yang-Baxter algebra. (C) 2003 American Institute of Physics.

Exact solution, scaling behaviour and quantum dynamics of a model of an atom-molecule Bose-Einstein condensate

0We study the exact solution for a two-mode model describing coherent coupling between atomic and molecular Bose-Einstein condensates (BEC), in the context of the Bethe ansatz. By combining an asymptotic and numerical analysis, we identify the scaling behaviour of the model and determine the zero temperature expectation value for the coherence and average atomic occupation. The threshold coupling for production of the molecular BEC is identified as the point at which the energy gap is minimum. Our numerical results indicate a parity effect for the energy gap between ground and first excited state depending on whether the total atomic number is odd or even. The numerical calculations for the quantum dynamics reveals a smooth transition from the atomic to the molecular BEC.

Leaking urine: Prevalence and associated factors in Australian women

The Women's Health Australia project provided the opportunity to examine the prevalence of leaking urine and associated variables in three large cohorts of Australian women 18-23 years of age (young N = 14,761), 45-50 (mid-age N = 14,070), and 70-75 (older N = 12,893). The proportion of women reporting leaking urine was 12.8% (95% CI: 12.2-13.3), 36.1% (35.2-37.0), and 35% (34.1-35.9) in each of the three cohorts, respectively. Logistic regression analysis showed significant associations between leaking urine and parity in the young and mid-age women, and between leaking urine and constipation, other bowel symptoms, body mass index, and urine that burns or stings in all three groups. in the mid-age and older cohorts, women who reported having both hysterectomy and prolapse repair, or prolapse repair alone, were also more likely to report leaking urine. Lower scores on the physical and mental component summary scores of the medical outcomes survey short form (36 items) questionnaire suggest lower quality of life among women who report leaking urine, compared with those who do not. (C) 1999 Wiley-Liss,Inc.

The expression of fibroblast growth factors and their receptors in the embryonic and neonatal mouse inner ear

Four different fibroblast growth factor receptors (FGFR) are known, three of which have splice variants (known as the b and c variants) in the FGF-binding domain, to give different patterns of sensitivity to the different FGFs. The expression of the b and c variants of the FGF receptors. together with the expression of the ligands FGF1. FGF2, FGF3, FGF7, FGF8b and FGF8c, was determined by quantitative reverse transcription-polymerase chain reaction in developing whole mouse inner ears, and in dissected components of the postnatal mouse inner ear. At embryonic age (E)10.5 days, when the otocyst is a simple closed sac, the receptor most heavily expressed was FGFR2b, relative to the postnatal day 0 level. Over the period E10.5-E12.5. during which the structures of the inner ear start to form, the expression of the different FGF receptors increased 10(2)-10(4) fold per unit of tissue, and there was a gradual switch towards expression of the 'c' splice variants of FGFR2 and FGFR3 rather than the 'b' variants. At E10.5, the ligands most heavily expressed, relative to the postnatal day 0 level, were FGF3, FGF8b and FGF8c. In the postnatal inner eat. the patterns of expression of receptors and ligands tended to be correlated, such that receptor variants were expressed in the same regions as the ligands that are known to activate them effectively. The neural/sensory region expressed high levels of FGFR3c, and high levels of the ligand FGF8b. The same area also expressed high levels of FGFR1b and FGFR2b, and high levels of FGF3. The lateral wall of the cochlea (including the stria vascularis and the spiral ligament) expressed high levels of FGFR1c and FGF1. 11 is suggested that the different FGF receptors and ligands are expressed in a spatially coordinated pattern to selectively program cochlear development. (C) 2001 Elsevier Science B.V. All rights reserved.

Aggregated personality, climate and demographic factors as predictors of departmental shrinkage

The present study investigated how demographic, personality, and climate variables act to predict departmental theft. Participants in the current field survey were 153 employees from 17 departments across two stores. The results of confirmatory factor analyses supported the construct validity of the Big Five Inventory (John, Donahue, & Kentle, 1991) and the Occupational Climate Questionnaire (Furnham & Gunter, 1997) in UK work settings. The results of regression analysis indicate that the variability in departmental theft is accountable in terms of a linear combination of demographic, personality, and climate factors. We concluded that an expanded theoretical perspective (utilizing demographic, personality, and climate variables) explained more variance than might otherwise be expected from any single perspective. Indeed, climate, personality, and demographic variables operated legitimately at the departmental level. Finally, we explained aggregated personality as a form of social interaction which is the by-product of individual differences.

Product form approximations for highly linear loss networks with trunk reservation

Admission controls, such as trunk reservation, are often used in loss networks to optimise their performance. Since the numerical evaluation of performance measures is complex, much attention has been given to finding approximation methods. The Erlang Fixed-Point (EFP) approximation, which is based on an independent blocking assumption, has been used for networks both with and without controls. Several more elaborate approximation methods which account for dependencies in blocking behaviour have been developed for the uncontrolled setting. This paper is an exploratory investigation of extensions and synthesis of these methods to systems with controls, in particular, trunk reservation. In order to isolate the dependency factor, we restrict our attention to a highly linear network. We will compare the performance of the resulting approximations against the benchmark of the EFP approximation extended to the trunk reservation setting. By doing this, we seek to gain insight into the critical factors in constructing an effective approximation. (C) 2003 Elsevier Ltd. All rights reserved.

Factors affecting the formation of a skin reservoir for topically applied solutes

The reservoir function of the skin is an important determinant of the duration of action of a topical solute. The reservoir can exist in the stratum corneum, in the viable avascular tissue (viable epidermis and supracapillary dermis) and in the dermis. A steroid reservoir in the stratum corneum has been demonstrated by the reactivation of a vasoconstrictor effect by occlusion or application of a placebo cream to the skin some time after the original topical application of steroid. Other solutes have also been reported to show a reservoir effect in the skin after topical application. A simple compartmental model is used to understand why reactivation of vasoconstriction some time after a topical steroid application shows dependency on time, topical solute concentration and the product used to cause reactivation. The model is also used to show which solutes are likely to show a reservoir effect and could be potentially affected by desquamation, especially when the turnover of the skin is abnormally rapid. A similar form of the model can be used to understand the promotion of reservoir function in the viable tissue and in the dermis in terms of effective removal by blood perfusing the tissues. Copyright (C) 2004 S. Karger AG, Basel.

Factors affecting the design and construction of Lamella suspen-dome systems

The suspen-dome system is a new structural form that has become popular in the construction of long-span roof structures. These domes are very slender and lightweight, their configuration is complicated, and hence sequential consideration in the structural design is needed. This paper focuses on these considerations, which include the method for designing cable prestress force, a simplified analysis method, and the estimation of buckling capacity. Buckling is one of the most important problems for dome structures. This paper presents the findings of an intensive buckling study of the Lamella suspen-dome system that takes geometric imperfection, asymmetric loading, rise-to-span ratio, and connection rigidity into consideration. Finally, suggested design and construction guidelines are given in the conclusion of this paper. (c) 2005 Elsevier Ltd. All rights reserved.

Factor structure and internal consistency of the Young Schema Questionnaire (Short Form) in Korean and Australian samples

We investigated cross-cultural differences in the factor structure and psychometric properties of the 75-item Young Schema Questionnaire-Short Form (YSQ-SF). Participants were 833 South Korean and 271 Australian undergraduate students. The South Korean sample was randomly divided into two sub-samples. Sample A was used for Exploratory Factor Analysis (EFA) and sample B was used for Confirmatory Factor Analysis (CFA). EFA for the South Korean sample revealed a 13-factor solution to be the best fit for the data, and CFA on the data from sample B confirmed this result. CFA on the data from the Australian sample also revealed a 13-factor solution. The overall scale of the YSQ-SF demonstrated a high level of internal consistency in the South Korean and Australian groups. Furthermore, adequate internal consistencies for all subscales in the South Korean and Australian samples were demonstrated. In conclusion, the results showed that YSQ-SF with 13 factors has good psychometric properties and reliability for South Korean and Australian University students. Korean samples had significantly higher YSD scores on most of the 13 subscales than the Australian sample. However, limitations of the current study preclude the generalisability of the findings to beyond undergraduate student populations. (c) 2006 Elsevier B.V. All rights reserved.