Competing Orders in a Dipolar Bose-Fermi Mixture on a Square Optical Lattice: Mean-Field Perspective

We consider a mixture of a two-component Fermi gas and a single-component dipolar Bose gas in a square optical lattice and reduce it into an effective Fermi system where the Fermi-Fermi interaction includes the attractive interaction induced by the phonons of a uniform dipolar Bose-Einstein condensate. Focusing on this effective Fermi system in the parameter regime that preserves the symmetry of $D_4$, the point group of a square, we explore, within the Hartree-Fock-Bogoliubov mean-field theory, the phase competition among density wave orderings and superfluid pairings. We construct the matrix representation of the linearized gap equation in the irreducible representations of $D_4$. We show that in the weak coupling regime, each matrix element, which is a four-dimensional (4D) integral in momentum space, can be put in a separable form involving a 1D integral, which is only a function of temperature and the chemical potential, and a pairing-specific "effective" interaction, which is an analytical function of the parameters that characterize the Fermi-Fermi interactions in our system. We analyze the critical temperatures of various competing orders as functions of different system parameters in both the absence and presence of the dipolar interaction. We find that close to half filling, the d_{x^{2}-y^{2}}-wave pairing with a critical temperature in the order of a fraction of Fermi energy (at half filling) may dominate all other phases, and at a higher filling factor, the p-wave pairing with a critical temperature in the order of a hundredth of Fermi energy may emerge as a winner. We find that tuning a dipolar interaction can dramatically enhance the pairings with $d_{xy}$- and g-wave symmetries but not enough for them to dominate other competing phases.Comment: 18 pages, 9 figure

Reduced serum angiotensin converting enzyme activity in children with congenital hypothyroidism

In this study levels of serum angiotensin converting enzyme (SACE) were evaluated using colorimetric method in 24 children with congenital hypothyroidism, 28 children from an iodine deficient zone (14 euthyroid, 14 subclinically hypothyroid) and 21 normal children. In the children with congenital hypothyroidism SACE levels (28.15 +/- 6.67 nmol/ml/min) were significantly lower (p < 0.05) than SACE levels in normal children (33.87 +/- 7.00 nmol/ml/min) and in children from an iodine deficient zone (subclinical hypothyroid: 36.05 +/- 7.88 nmol/ml/min or euthyroid: 39.61 +/- 6.83 nmol/ml/min). No statistical difference in SACE levels was revealed in either normal subjects or children from an iodine deficient zone. SACE levels among all the groups were not shown to be different in relation to sex. Average TSH levels, as expected, were significantly higher (p < 0.05) in children with congenital hypothyroidism. The correlation between SACE and TSH levels did not demonstrate a statistical significance in any of the groups studied. In conclusion, our data demonstrated that levels of SACE were significantly reduced in children with congenital hypothyroidism