85 research outputs found
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 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 , with the
Neumann boundary condition at a segment of length of one of the
boundaries, and Dirichlet otherwise. For small enough this operator has
a single eigenvalue ; we show that there are positive
such that . An analogous conclusion holds for a pair of Dirichlet strips, of
generally different widths, with a window of length 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 .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
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