Stability of atoms in the Brown-Ravenhall model

We consider the Brown--Ravenhall model of a relativistic atom with N electrons and a nucleus of charge Z and prove the existence of an infinite number of discrete eigenvalues for N <= Z. As an intermediate result we prove a HVZ-type theorem for these systems.Comment: 31 pages, accepted to "Annales Henry Poincare". The error in Lemma 3 of the previous version is corrected and the corresponding changes are done in the proof of Theorem

Non-analyticity of the groud state energy of the Hamiltonian for Hydrogen atom in non-relativistic QED

We derive the ground state energy up to the fourth order in the fine structure constant $\alpha$ for the translation invariant Pauli-Fierz Hamiltonian for a spinless electron coupled to the quantized radiation field. As a consequence, we obtain the non-analyticity of the ground state energy of the Pauli-Fierz operator for a single particle in the Coulomb field of a nucleus

Asymptotic estimates for bound states in quantum waveguides coupled laterally through a narrow window

Consider the Laplacian in a straight planar strip of width $\,d\,$, with the Neumann boundary condition at a segment of length $\,2a\,$ of one of the boundaries, and Dirichlet otherwise. For small enough $\,a\,$ this operator has a single eigenvalue $\,\epsilon(a)\,$; we show that there are positive $\,c_1,c_2\,$ such that $\,-c_1 a^4 \le \epsilon(a)- \left(\pi/ d\right)^2 \le -c_2 a^4\,$. An analogous conclusion holds for a pair of Dirichlet strips, of generally different widths, with a window of length $\,2a\,$ in the common boundary.Comment: LaTeX file, 12 pages, no figure

Estimates on trapped modes in deformed quantum layers

We use a logarithmic Lieb-Thirring inequality for two-dimensional Schroedinger operators and establish estimates on trapped modes in geometrically deformed quantum layers

The increase of Binding Energy and Enhanced Binding in Non-Relativistic QED

We consider a Pauli-Fierz Hamiltonian for a particle coupled to a photon field. We discuss the effects of the increase of the binding energy and enhanced binding through coupling to a photon field, and prove that both effects are the results of the existence of the ground state of the self-energy operator with total momentum $P = 0$.Comment: 14 pages, Latex. Final version, accepted for publication in J. Math. Phy

Quantitative estimates on the enhanced binding for the Pauli-Fierz operator

For a quantum particle interacting with a short-range potential, we estimate from below the shift of its binding threshold, which is due to the particle interaction with a quantized radiation field