Stripe Formation in Fermionic Atoms on 2-D Optical Lattice inside a Box Trap: DMRG Studies for Repulsive Hubbard Model with Open Boundary Condition

We suggest that box shape trap enables to observe intrinsic properties of the repulsive Hubbard model in a fixed doping in contrast to the harmonic trap bringing about spatial variations of atom density profiles. In order to predict atomic density profile under the box trap, we apply the directly-extended density-matrix renormalization group method to 4-leg repulsive Hubbard model with the open boundary condition. Consequently, we find that stripe formation is universal in a low hole doping range and the stripe sensitively changes its structure with variations of $U/t$ and the doping rate. A remarkable change is that a stripe formed by a hole pair turns to one by a bi-hole pair when entering a limited strong $U/t$ range. Furthermore, a systematic calculation reveals that the Hubbard model shows a change from the stripe to the Friedel like oscillation with increasing the doping rate

Neutron-scattering study of spin correlations in La1.94-xSrxCe0.06CuO4

We performed a neutron-scattering experiment to investigate the effect of distortion of CuO2 planes on the low-energy spin correlation of La1.94-xSrxCe0.06CuO4 (LSCCO). Due to the carrier-compensation effect by co-doping of Sr and Ce, LSCCO has a smaller orthorhombic lattice distortion compared to La2-xSrxCuO4 (LSCO) with comparable hole concentration p. A clear gap with the edge-energy of 6~7 meV was observed in the energy spectrum of local dynamical susceptibility c"(w) for both x=0.18 (p~0.14) and x=0.24 (p~0.20) samples as observed for optimally-doped LSCO (x=0.15~0.18). For the x=0.14 (p~0.10) sample, in addition to the gap-like structure in c"(w) we observed a low-energy component within the gap which develops below 2~3meV with decreasing the energy. The low-energy component possibly coincides with the static magnetic correlation observed in this sample. These results are discussed from a view point of relationship between the stability of low-energy spin fluctuations and the distortion of CuO2 planes.Comment: 4 pages, 3 figures, proceeding for SNS2007 conferenc

Equation of State of Supercooled Water from the Sedimentation Profile

To study the coexistence of two liquid states of water within one simulation box, we implement an equilibrium sedimentation method--which involves applying a gravitational field to the system and measuring/calculating the resulting density profile in equilibrium. We simulate a system of particles interacting via the ST2 potential, a model for water. We detect the coexistence of two liquid phases at low temperature.Comment: 4 pages, 4 EPS figure

Distinguished self-adjoint extensions of Dirac operators via Hardy-Dirac inequalities

We prove some Hardy-Dirac inequalities with two different weights including measure valued and Coulombic ones. Those inequalities are used to construct distinguished self-adjoint extensions of Dirac operators for a class of diagonal potentials related to the weights in the above mentioned inequalities.Comment: 16 page

R-Process Nucleosynthesis In Neutrino-Driven Winds From A Typical Neutron Star With M = 1.4 Msun

We study the effects of the outer boundary conditions in neutrino-driven winds on the r-process nucleosynthesis. We perform numerical simulations of hydrodynamics of neutrino-driven winds and nuclear reaction network calculations of the r-process. As an outer boundary condition of hydrodynamic calculations, we set a pressure upon the outermost layer of the wind, which is approaching toward the shock wall. Varying the boundary pressure, we obtain various asymptotic thermal temperature of expanding material in the neutrino-driven winds for resulting nucleosynthesis. We find that the asymptotic temperature slightly lower than those used in the previous studies of the neutrino-driven winds can lead to a successful r-process abundance pattern, which is in a reasonable agreement with the solar system r-process abundance pattern even for the typical proto-neutron star mass Mns ~ 1.4 Msun. A slightly lower asymptotic temperature reduces the charged particle reaction rates and the resulting amount of seed elements and lead to a high neutron-to-seed ratio for successful r-process. This is a new idea which is different from the previous models of neutrino-driven winds from very massive (Mns ~ 2.0 Msun) and compact (Rns ~ 10 km) neutron star to get a short expansion time and a high entropy for a successful r-process abundance pattern. Although such a large mass is sometimes criticized from observational facts on a neutron star mass, we dissolve this criticism by reconsidering the boundary condition of the wind. We also explore the relation between the boundary condition and neutron star mass, which is related to the progenitor mass, for successful r-process.Comment: 14 pages, 2 figure

Energy Functions in Box Ball Systems

The box ball system is studied in the crystal theory formulation. New conserved quantities and the phase shift of the soliton scattering are obtained by considering the energy function (or $H$-function) in the combinatorial $R$-matrix.Comment: 15 pages, LaTeX2e: one paragraph replaced and reference added in Introduction, a paragraph added in Section 2.5, remark 2) after Th 4.6 adde

Hydrogen-Bonded Liquids: Effects of Correlations of Orientational Degrees of Freedom

We improve a lattice model of water introduced by Sastry, Debenedetti, Sciortino, and Stanley to give insight on experimental thermodynamic anomalies in supercooled phase, taking into account the correlations between intra-molecular orientational degrees of freedom. The original Sastry et al. model including energetic, entropic and volumic effect of the orientation-dependent hydrogen bonds (HBs), captures qualitatively the experimental water behavior, but it ignores the geometrical correlation between HBs. Our mean-field calculation shows that adding these correlations gives a more water-like phase diagram than previously shown, with the appearance of a solid phase and first-order liquid-solid and gas-solid phase transitions. Further investigation is necessary to be able to use this model to characterize the thermodynamic properties of the supercooled region.Comment: 7 pages latex, 3 figures EP