Monotonicity results and bounds for the inverse hyperbolic sine

In this note, we present monotonicity results of a function involving to the inverse hyperbolic sine. From these, we derive some inequalities for bounding the inverse hyperbolic sine.Comment: 3 page

Flavor-twisted boundary condition for simulations of quantum many-body systems

We present an approximative simulation method for quantum many-body systems based on coarse graining the space of the momentum transferred between interacting particles, which leads to effective Hamiltonians of reduced size with the flavor-twisted boundary condition. A rapid, accurate, and fast convergent computation of the ground-state energy is demonstrated on the spin-1/2 quantum antiferromagnet of any dimension by employing only two sites. The method is expected to be useful for future simulations and quick estimates on other strongly correlated systems.Comment: 6 pages, 2 figure

Decay and Continuity of Boltzmann Equation in Bounded Domains

Boundaries occur naturally in kinetic equations and boundary effects are crucial for dynamics of dilute gases governed by the Boltzmann equation. We develop a mathematical theory to study the time decay and continuity of Boltzmann solutions for four basic types of boundary conditions: inflow, bounce-back reflection, specular reflection, and diffuse reflection. We establish exponential decay in $L^{\infty}$ norm for hard potentials for general classes of smooth domains near an absolute Maxwellian. Moreover, in convex domains, we also establish continuity for these Boltzmann solutions away from the grazing set of the velocity at the boundary. Our contribution is based on a new $L^{2}$ decay theory and its interplay with delicate $$ decay analysis for the linearized Boltzmann equation, in the presence of many repeated interactions with the boundary.Comment: 89 pages

Magnetic and thermodynamic properties of cobalt doped iron pyrite: Griffiths Phase in a magnetic semiconductor

Doping of the band insulator FeS$_2$ with Co on the Fe site introduces a small density of itinerant carriers and magnetic moments. The lattice constant, AC and DC magnetic susceptibility, magnetization, and specific heat have been measured over the $0\le x\le 0.085$ range of Co concentration. The variation of the AC susceptibility with hydrostatic pressure has also been measured in a small number of our samples. All of these quantities show systematic variation with $x$ including a paramagnetic to disordered ferromagnetic transition at $x=0.007\pm 0.002$. A detailed analysis of the changes with temperature and magnetic field reveal small power law dependencies at low temperatures for samples near the critical concentration for magnetism, and just above the Curie temperature at higher $x$. In addition, the magnetic susceptibility and specific heat are non-analytic around H=0 displaying an extraordinarily sharp field dependence in this same temperature range. We interpret this behavior as due to the formation of Griffiths phases that result from the quenched disorder inherent in a doped semiconductor.Comment: 22 pages including 27 figure

Evidence for a full energy gap for nickel-pnictide LaNiAsO_{1-x}F_x superconductors by ^{75}As nuclear quadrupole resonance

We report systematic ^{75}As-NQR and ^{139}La-NMR studies on nickel-pnictide superconductors LaNiAsO_{1-x}F_x (x=0, 0.06, 0.10 and 0.12). The spin lattice relaxation rate 1/T_1 decreases below T_c with a well-defined coherence peak and follows an exponential decay at low temperatures. This result indicates that the superconducting gap is fully opened, and is strikingly different from that observed in iron-pnictide analogs. In the normal state, 1/T_1T is constant in the temperature range T_c \sim 4 K < T <10 K for all compounds and up to T=250 K for x=0 and 0.06, which indicates weak electron correlations and is also different from the iron analog. We argue that the differences between the iron and nickel pnictides arise from the different electronic band structure. Our results highlight the importance of the peculiar Fermi-surface topology in iron-pnictides.Comment: 4 pages, 5 figure

Antiferromagnetic Spin Fluctuation above the Superconducting Dome and the Full-Gaps Superconducting State in LaFeAsO1-xFx Revealed by 75As-Nuclear Quadrupole Resonance

We report a systematic study by 75As nuclear-quadrupole resonance in LaFeAsO1-xFx. The antiferromagnetic spin fluctuation (AFSF) found above the magnetic ordering temperature TN = 58 K for x = 0.03 persists in the regime 0.04 < x < 0.08 where superconductivity sets in. A dome-shaped x-dependence of the superconducting transition temperature Tc is found, with the highest Tc = 27 K at x = 0.06 which is realized under significant AFSF. With increasing x further, the AFSF decreases, and so does Tc. These features resemble closely the cuprates La2-xSrxCuO4. In x = 0.06, the spin-lattice relaxation rate (1/T1) below Tc decreases exponentially down to 0.13 Tc, which unambiguously indicates that the energy gaps are fully-opened. The temperature variation of 1/T1 below Tc is rendered nonexponential for other x by impurity scattering.Comment: 5 pages, 5 figures, more references adde