arXiv subjects

Oliver Matte

Publications and source records attributed to Oliver Matte.

22 records · Page 2Linked to original sources

arXiv2009

Exponential localization of hydrogen-like atoms in relativistic quantum electrodynamics

We consider two different models of a hydrogenic atom in a quantized electromagnetic field that treat the electron relativistically. The first one is a no-pair model in the free picture, the second one is given by the semi-relativistic Pauli-Fierz Hamiltonian. We prove that the no-pair operator is semi-bounded below and that its spectral subspaces corresponding to energies below the ionization threshold are exponentially localized. Both results hold true, for arbitrary values of the fine-structure constant, $e^2$, and the ultra-violet cut-off, $Λ$, and for all nuclear charges less than the critical charge without radiation field, $Z_c=e^{-2}2/(2/π+π/2)$. We obtain similar results for the semi-relativistic Pauli-Fierz operator, again for all values of $e^2$ and $Λ$ and for nuclear charges less than $e^{-2}2/π$.

math-ph↗

arXiv2008

On the eigenfunctions of no-pair operators in classical magnetic fields

We consider a relativistic no-pair model of a hydrogenic atom in a classical, exterior magnetic field. First, we prove that the corresponding Hamiltonian is semi-bounded below, for all coupling constants less than or equal to the critical one known for the Brown-Ravenhall model, i.e., for vanishing magnetic fields. We give conditions ensuring that its essential spectrum equals [1,\infty) and that there exist infinitely many eigenvalues below 1. (The rest energy of the electron is 1 in our units.) Assuming that the magnetic vector potential is smooth and that all its partial derivatives increase subexponentially, we finally show that an eigenfunction corresponding to an eigenvalue λ<1 is smooth away from the nucleus and that its partial derivatives of any order decay pointwise exponentially with any rate a<(1-λ^2)^{1/2}, for λ\in[0,1), and a<1, for λ<0.

math-ph↗

arXiv2008

Spectral theory of no-pair Hamiltonians

We prove a HVZ theorem for a general class of no-pair Hamiltonians describing an atom or positively charged ion with several electrons in the presence of a classical external magnetic field. Moreover, we show that there exist infinitely many eigenvalues below the essential spectrum and that the corresponding eigenfunctions are exponentially localized. The novelty is that the electrostatic and magnetic vector potentials as well as a non-local exchange potential are included in the projection determining the model. As a main technical tool we derive various commutator estimates involving spectral projections of Dirac operators with external fields. Our results apply to all nuclear charges less than or equal to 137.

math-ph↗

arXiv2008

Correlation asymptotics for non-translation invariant lattice spin systems

We obtain asymptotic expressions for the Green kernels of certain non-translation invariant transition matrices using methods of semiclassical and microlocal analysis. Combined with a result by Bach and Møller this yields asymptotic formulas for the truncated two-point correlation functions of certain non-translation invariant lattice models of real-valued spins.

math-ph↗