We establish global well-posedness and scattering for solutions to the mass-critical nonlinear Schrödinger equation iut+∆u = ±|u|4/du for large spherically symmetric Lx(R d) initial data in dimensions d ≥ 3. In the focusing case we require that the mass is strictly less than that of the ground state. As a consequence, we obtain that in the focusing case, any spherically symmetric blowup solutio...

The equilibrium texture of nematic shells is studied as a function of their thickness. For ultrathin shells the ground state has four short 1/2 disclination lines but, as the thickness of the film increases, a three-dimensional escaped configuration composed of two pairs of half-hedgehogs becomes energetically favorable. We derive an exact solution for the nematic ground state in the one Frank ...

We introduce a suitable concept of weak evolution in the context of the radial quintic focussing semilinear wave equation on R3`1, that is adapted to continuation past type II singularities. We show that the weak extension leads to type I singularity formation for initial data corresponding to: (i) the Kenig-Merle blow-up solutions with initial energy below the ground state and (ii) the Krieger...

We consider a nonlinear Schrödinger equation with a bounded local potential in R3. The linear Hamiltonian is assumed to have three or more bound states with the eigenvalues satisfying some resonance conditions. Suppose that the initial data is localized and small of order n in H1, and that its ground state component is larger than n3−ǫ with ǫ > 0 small. We prove that the solution will converge ...

We consider the ground state of simple quantum systems coupled to an environment. In general the system is entangled with its environment. As a consequence, even at zero temperature, the energy of the system is not sharp: a projective measurement can find the system in an excited state. We show that energy fluctuation measurements at zero temperature provide entanglement information. For two-st...

Electroluminescence, the emission of light in the presence of an electric current, provides information on the allowed electronic transitions of a given system. It is commonly used to investigate the physics of strongly coupled light-matter systems, whose eigenfrequencies are split by the strong coupling with the photonic field of a cavity. Here we show that, together with the usual electrolumi...

Hugo Reinhardt† Institut für Theoretische Physik, Eberhard-Karls Universität zu Tübingen, D-72076 Tübingen, Federal Republic of Germany Abstract Mean-field treatments of Yang-Mills theory face the problem of how to treat the Gauss law constraint. In this paper we try to face this problem by studying the excited states instead of the ground state. For this purpose we extend the operator approach...

In this paper we prove the existence of a ground state solution for the nonlinear Klein-Gordon-Maxwell equations in the electrostatic case.

In supersymmetric models with the runaway vacua or with the stable but non-supersymmetric ground state there exist stable field configurations (vacua) which restore one half of supersymmetry and are characterized by constant positive energy density. The formal foundation for such vacua is provided by the central extension of the N = 1 superalgebra with the infinite central charge.

The Isgur-Wise functions for the ground state to ground state semileptonic decays involving b → c transitions are calculated from the (modified) MIT bag model. It is checked that the results for the decays B → Dlν and B → D * lν agree well with experiment. Predictions for the decays Λ b → Λ c lν, B s → D s lν and B s → D * s lν are given and discussed.