Determinant formula for the six-vertex model with reflecting end

Using the Quantum Inverse Scattering Method for the XXZ model with open boundary conditions, we obtained the determinant formula for the six vertex model with reflecting end.Comment: 10 page

Melting and metallization of silica in the cores of gas giants, ice giants and super Earths

The physical state and properties of silicates at conditions encountered in the cores of gas giants, ice giants and of Earth like exoplanets now discovered with masses up to several times the mass of the Earth remains mostly unknown. Here, we report on theoretical predictions of the properties of silica, SiO$_2$, up to 4 TPa and about 20,000K using first principle molecular dynamics simulations based on density functional theory. For conditions found in the Super-Earths and in ice giants, we show that silica remains a poor electrical conductor up to 10 Mbar due to an increase in the Si-O coordination with pressure. For Jupiter and Saturn cores, we find that MgSiO$_3$ silicate has not only dissociated into MgO and SiO$_2$, as shown in previous studies, but that these two phases have likely differentiated to lead to a core made of liquid SiO$_2$ and solid (Mg,Fe)O.Comment: 5 pages, 4 figure

Landau damping of Bogoliubov excitations in optical lattices at finite temperature

We study the damping of Bogoliubov excitations in an optical lattice at finite temperatures. For simplicity, we consider a Bose-Hubbard tight-binding model and limit our analysis to the lowest excitation band. We use the Popov approximation to calculate the temperature dependence of the number of condensate atoms $n^{\rm c 0}(T)$ in each lattice well. We calculate the Landau damping of a Bogoliubov excitation in an optical lattice due to coupling to a thermal cloud of excitations. While most of the paper concentrates on 1D optical lattices, we also briefly present results for 2D and 3D lattices. For energy conservation to be satisfied, we find that the excitations in the collision process must exhibit anomalous dispersion ({\it i.e.} the excitation energy must bend upward at low momentum), as also exhibited by phonons in superfluid $^4\rm{He}$. This leads to the sudden disappearance of all damping processes in $D$-dimensional simple cubic optical lattice when $U n^{\rm c 0}\ge 6DJ$, where $U$ is the on-site interaction, and $J$ is the hopping matrix element. Beliaev damping in a 1D optical lattice is briefly discussed.Comment: 28 pages, 9 figure

Damping of Bogoliubov Excitations in Optical Lattices

Extending recent work to finite temperatures, we calculate the Landau damping of a Bogoliubov excitation in an optical lattice, due to coupling to a thermal cloud of such excitations. For simplicity, we consider a 1D Bose-Hubbard model and restrict ourselves to the first energy band. For energy conservation to be satisfied, the excitations in the collision processes must exhibit ``anomalous dispersion'', analogous to phonons in superfluid $^4\rm{He}$. This leads to the disappearance of all damping processes when $U n^{\rm c 0}\ge 6t$, where $U$ is the on-site interaction, $t$ is the hopping matrix element and $n^{\rm c 0}(T)$ is the number of condensate atoms at a lattice site. This phenomenon also occurs in 2D and 3D optical lattices. The disappearance of Beliaev damping above a threshold wavevector is noted.Comment: 4pages, 5figures, submitted to Phys. Rev. Let