Spectral edge regularity of magnetic Hamiltonians

We analyse the spectral edge regularity of a large class of magnetic Hamiltonians when the perturbation is generated by a globally bounded magnetic field. We can prove Lipschitz regularity of spectral edges if the magnetic field perturbation is either constant or slowly variable. We also recover an older result by G. Nenciu who proved Lipschitz regularity up to a logarithmic factor for general globally bounded magnetic field perturbations.Comment: 18 pages, submitte

d=4+1 gravitating nonabelian solutions with bi-azimuthal symmetry

We construct static, asymptotically flat solutions of SU(2) Einstein-Yang-Mills theory in 4+1 dimensions, subject to bi-azimuthal symmetry. Both particle-like and black hole solutions are considered for two different sets of boundary conditions in the Yang--Mills sector, corresponding to multisolitons and soliton-antisoliton pairs. For gravitating multi-soliton solutions, we find that their mass per unit charge is lower than the mass of the corresponding unit charge, spherically symmetric soliton.Comment: 13 pages, 5 figures; v2: typos corrected, published versio

Solitons and soliton-antisoliton pairs of a Goldstone model in 3+1 dimensions

We study finite energy static solutions to a global symmetry breaking model in 3+1 dimensions described by an isovector scalar field. The basic features of two different types of configurations are discussed, one of them corresponding to axially symmetric multisolitons with topological charge $n$, and the other one to unstable soliton-antisoliton pairs with zero topological charge.Comment: 13 pages, 5 figure

Peierls' substitution for low lying spectral energy windows

We consider a $2d$ magnetic Schr\"odinger operator perturbed by a weak magnetic field which slowly varies around a positive mean. In a previous paper we proved the appearance of a `Landau type' structure of spectral islands at the bottom of the spectrum, under the hypothesis that the lowest Bloch eigenvalue of the unperturbed operator remained simple on the whole Brillouin zone, even though its range may overlap with the range of the second eigenvalue. We also assumed that the first Bloch spectral projection was smooth and had a zero Chern number. In this paper we extend our previous results to the only two remaining possibilities: either the first Bloch eigenvalue remains isolated while its corresponding spectral projection has a non-zero Chern number, or the first two Bloch eigenvalues cross each other.Comment: 27 page