Anomalous Flux Quantization in the Spin-Imbalanced Attractive Hubbard Ring

We investigate the one-dimensional Hubbard ring with attractive interaction in the presence of imbalanced spin populations by using the exact diagonalization method. The singlet pairing correlation function is found to show spatial oscillations with power-law decay as expected in the Fulde-Ferrell-Larkin-Ovchinnikov state of a Tomonaga-Luttinger liquid. In the strong coupling regime, the system shows an anomalous flux quantization of period h=4e, half of the superconducting flux quantum of h=2e, as recently predicted by mean-field analysis, together with various flux quanta smaller than h=4e. Notably, the observed flux quanta are determined by the difference between the system size NL and electron number N_e as h=(N_L-N_e)e.Comment: 6 pages, 8 figure

Bound state of a hole and a triplet spin in the t1t_1-t2t_2-J1J_1-J2J_2 model

We show that a hole and a triplet spin form a bound state in a nearly half-filled band of the one- and two-dimensional $t_1$-$t_2$-$J_1$-$J_2$ models. Numerical calculation indicates that the bound state is a spatially small object and moves as a composite particle with spin 1 and charge $+e$ in the spin-gapped background. Two bound states repulsively interact with each other in a short distance and move independently as long as they keep their distance. If a finite density of bound states behave as bosons, the system undergoes the Bose-Einstein condensation which means a superconductivity with charge $+e$.Comment: 10 pages, 13 figure

Scanning Electron Microscopy and Energy-Dispersive X-Ray Microanalysis Studies of Several Human Calculi Containing Calcium Phosphate Crystals

Human calcium phosphate calculi: two sialoliths, a urolith, a rhinolith, and a tonsillolith were investigated by scanning electron microscopy (SEM) and energy-dispersive X-ray analysis (EDX). The sialoliths and urolith had appositional shells with thick cortices, respectively, around several nuclei composed of calcospherulites and a rubber-film fragment. The rhinolith had a thin cortex with appositional laminations around a glomerulus-like mass of calcified cotton-like strings. The tonsillolith had a rough cortex with appositional laminations. Its porous interior was composed of numerous calcified conglomerates with microorganisms and calcified masses with fine appositional laminations around the conglomerates. The major crystals were identified as biological apatites (AP) with a sand-grain rather than a needle-like shape, and plate-shaped octacalcium phosphate (OCP). The AP deposits of the rhinolith probably were associated with magnesium (Mg) phosphates or contained Mg. No OCP was found in the rhinolith. The AP deposits were mainly formed by extracellular calcification. Hexahedral crystals, identified as Mg-containing whitlockite (WH), were precipitated in the internal spaces of the AP and OCP deposits. The rhinolith nucleus consisted of WH crystal deposits only