In this note we search for the ground state, in infinite volume, of theD = 3WilsonFisher conformal O(4) model, at nonzero values of the two independent charge densities ρ1,2. Using an effective theory valid on scales longer than the scale defined by the charge density, we show that the ground-state configuration is inhomogeneous for generic ratios ρ1/ρ2. This result confirms, within the context...

We study global dynamics for the focusing nonlinear Klein-Gordon equation with the energy-critical nonlinearity in two or higher dimensions when the energy equals the threshold given by the ground state of a mass-shifted equation, and prove that the solutions are divided into scattering and blowup. In short, the Kenig-Merle scattering/blowup dichotomy [10, 11] extends to the threshold energy in...

We present a heuristic matching algorithm for the generation of ground states of the short-range * J spin glass in two dimensions. It is much faster than previous heuristic algorithms. I t achieves near optimal solutions in time O( N ) in contrast to the best known exact algorithm which needs a time of O ( N S ” ) . From simulations with lattice sizes of up to 210 x 210 we confirm a phase trans...

We consider radial solutions of a mass supercritical monic NLS and we prove the existence of a set, which looks like a hypersurface, in the space of finite energy functions, invariant for the flow and formed by solutions which converge to ground states. §

We consider the asymptotic solutions to the Bethe ansatz equations of the integrable model of interacting bosons in the weakly interacting limit. In this limit we establish that the ground state maps to the highest energy state of a strongly-coupled repulsive bosonic pairing model.

We express radial solutions of semilinear elliptic equations on Rn as convergent power series in r, and then use Pade approximants to compute both ground state solutions, and solutions to Dirichlet problem. Using a similar approach we have discovered existence of singular solutions for a class of subcritical problems. We prove convergence of the power series by modifying the classical method of...

We prove that the Cauchy problem of the mass-critical generalized KdV equation is globally well-posed in Sobolev spaces Hs(R) for s > 6/13; we require that the mass is strictly less than that of the ground state in the focusing case. The main approach is the “I-method” together with some multilinear correction analysis. The result improves the previous works of Fonseca, Linares, Ponce (2003) an...

In this paper I construct lattice models with an underlying U q osp(2, 2) su-peralgebra symmetry. I find new solutions to the graded Yang-Baxter equation. These trigonometric R-matrices depend on three continuous parameters, the spectral parameter, the deformation parameter q and the U (1) parameter, b, of the superalgebra. It must be emphasized that the parameter q is generic and the parameter...

We review our joint result with E. Lenzmann about the uniqueness of ground state solutions of non-linear equations involving the fractional Laplacian and provide an alternate uniqueness proof for an equation related to the intermediate long-wave equation.

In this paper we establish the existence of certain classes of solutions to the energy critical nonlinear wave equation in dimensions 3 and 5 assuming that the energy exceeds the ground state energy only by a small amount. No radial assumption is made. We find that there exist four sets in Ḣ × L with nonempty interiors which correspond to all possible combinations of finite-time blowup on the o...