1 4 Ja n 20 09 The Fate of the Landau Levels under Perturbations of Constant Sign July 19 , 2009

The Fate of the Landau Levels under Perturbations of Constant Sign July 1 , 2009

We show that the Landau levels cease to be eigenvalues if we perturb the 2D Schrödinger operator with constant magnetic field, by bounded electric potentials of fixed sign. We also show that, if the perturbation is not of fixed sign, then any Landau level may be an eigenvalue of the perturbed problem. AMS 2000 Mathematics Subject Classification: 35J10, 81Q10, 35P20

The Fate of the Landau Levels under Perturbations of Constant Sign

We show that the Landau levels cease to be eigenvalues if we perturb the 2D Schrödinger operator with constant magnetic field, by bounded electric potentials of fixed sign. We also show that, if the perturbation is not of fixed sign, then any Landau level may be an eigenvalue of the perturbed problem. AMS 2000 Mathematics Subject Classification: 35J10, 81Q10, 35P20

ar X iv : 0 90 1 . 26 19 v 1 [ gr - q c ] 1 7 Ja n 20 09 The trapped region

I will discuss some recent results on marginally outer trapped surfaces, apparent horizons and the trapped region. A couple of applications of the results developed for marginally outer trapped surfaces to coalescence of black holes and to the characterization of the trapped region are given.

ar X iv : 0 90 2 . 00 45 v 1 [ he p - la t ] 3 1 Ja n 20 09 An improved lattice measurement of the critical coupling in φ 42 theory

We use Monte Carlo simulations to obtain an improved lattice measurement of the critical coupling constant [ λ/μ ] crit for the continuum (1 + 1)-dimensional (λ/4)φ theory. We find that the critical coupling constant depends logarithmically on the lattice coupling, resulting in a continuum value of [ λ/μ ] crit = 10.8 −.05, in considerable disagreement with the previously reported [ λ/μ ] crit ...

1 1 Ja n 20 09 Trace coordinates on Fricke spaces of some simple hyperbolic surfaces