This letter considers the problem of approximating a semialgebraic set with sublevel-set polynomial using sum-of-squares optimization. In this setting, it is standard to seek minimum volume outer approximation or maximum inner approximation. made difficult by lack known relationship between coefficients an arbitrary and its sublevel sets. Previous works have proposed heuristics based on determi...

Many dynamical systems described by nonlinear ODEs are unstable. Their associated solutions do not converge towards an equilibrium point, but rather some invariant subset of the state space called attractor set. For a given ODE, in general, existence, shape and structure sets ODE unknown. Fortunately, sublevel Lyapunov functions can provide bounds on ODEs. In this paper we propose new character...

We theoretically explore a Rashba spin-orbit coupling scheme which operates entirely in the absolute ground state manifold of an alkali atom, thereby minimizing all inelastic processes. An energy gap between ground eigenstates of the proposed coupling can be continuously opened or closed by modifying laser polarizations. Our technique uses far-detuned 'Raman' laser coupling to create the Rashba...

The first experimental magnetic substate scattering-angle-integrated cross sections following ionization–excitation of He(1s) S to Heþ(2p) P in the e þHe collision system have been determined using a combination of total cross sections and polarization fraction measurements in the extreme ultraviolet range. The derived magnetic sublevel cross sections, r0 and r1, for ML 1⁄4 0, 1 have been studi...

Quantum state-resolved reactivity measurements probe the role of vibrational symmetry on the vibrational activation of the dissociative chemisorption of CH4 on Pt(111). IR-IR double resonance excitation in a molecular beam is used to prepare CH4 in all three different vibrational symmetry components A1, E, and F2 of the 2ν3 antisymmetric stretch overtone vibration. Methyl dissociation products ...