Evaluation of the BCS Approximation for the Attractive Hubbard Model in One Dimension

The ground state energy and energy gap to the first excited state are calculated for the attractive Hubbard model in one dimension using both the Bethe Ansatz equations and the variational BCS wavefunction. Comparisons are provided as a function of coupling strength and electron density. While the ground state energies are always in very good agreement, the BCS energy gap is sometimes incorrect by an order of magnitude, particularly at half-filling. Finite size effects are also briefly discussed for cases where an exact solution in the thermodynamic limit is not possible. In general, the BCS result for the energy gap is poor compared to the exact result.Comment: 25 pages, 5 Postscript figure

Cooper pair dispersion relation for weak to strong coupling

Cooper pairing in two dimensions is analyzed with a set of renormalized equations to determine its binding energy for any fermion number density and all coupling assuming a generic pairwise residual interfermion interaction. \ Also considered are Cooper pairs (CPs) with nonzero center-of-mass momentum (CMM)--usually neglected in BCS theory--and their binding energy is expanded analytically in powers of the CMM up to quadratic terms. A Fermi-sea-dependent {\it linear} term in the CMM dominates the pair excitation energy in weak coupling (also called the BCS regime) while the more familiar quadratic term prevails in strong coupling (the Bose regime). The crossover, though strictly unrelated to BCS theory {\it per se,} is studied numerically as it is expected to play a central role in a model of superconductivity as a Bose-Einstein condensation of CPs where the transition temperature vanishes for all dimensionality $d\leq 2$ for quadratic dispersion, but is {\it nonzero} for all $d\geq 1$ for linear dispersion.Comment: 11 pages plus 3 figures, revised version accepted in Physical Review

Schizophrenia and complications of pregnancy and labor: an individual patient data meta-analysis.

Several epidemiological studies have reported an association between complications of pregnancy and delivery and schizophrenia, but none have had sufficient power to examine specific complications that, individually, are of low prevalence. We, therefore, performed an individual patient meta-analysis using the raw data from case control studies that used the Lewis-Murray scale. Data were obtained from 12 studies on 700 schizophrenia subjects and 835 controls. There were significant associations between schizophrenia and premature rupture of membranes, gestational age shorter than 37 weeks, and use of resuscitation or incubator. There were associations of borderline significance between schizophrenia and birthweight lower than 2,500 g and forceps delivery. There was no significant interaction between these complications and sex. We conclude that some abnormalities of pregnancy and delivery may be associated with development of schizophrenia. The pathophysiology may involve hypoxia and so future studies should focus on the accurate measurement of this exposure

Obstetric complications and age at onset in schizophrenia: an international collaborative meta-analysis of individual patient data.

OBJECTIVE: An excess of obstetric complications in the histories of schizophrenic patients is a well-replicated finding, but less consistent results have been found concerning the relationships between obstetric complications and family history of schizophrenia, age at onset of schizophrenia, and gender. Small sample size limited the power of previous studies that attempted to assess such relationships. The aim of this study was to use data on individual patients from all available studies to examine the links between a history of obstetric complications and family history of schizophrenia, age at onset, and gender. METHOD: Raw data from 854 schizophrenic patients concerning history of obstetric complications rated according to the Lewis and Murray scale were obtained from 11 different research groups. Weighted average estimates were calculated with the use of regression techniques. RESULTS: A significant association was found between age at onset of schizophrenia and obstetric complications: the earlier the age at onset, the more likely the history of obstetric complications. Subjects with onset of schizophrenia before age 22 were 2.7 times more likely than those with onset at a later age to have had a history of abnormal presentation at birth and 10 times more likely to have had a history of complicated Cesarean birth. No association was found between obstetric complications and family history of schizophrenia or gender. CONCLUSIONS: The association between obstetric complications and early age at onset of schizophrenia indicates that the pathophysiology of early-onset schizophrenia involves neurodevelopmental impairment