118 research outputs found
Quantitative Estimates on the Binding Energy for Hydrogen in Non-Relativistic QED. II. The spin case
The hydrogen binding energy in the Pauli-Fierz model with the spin Zeeman
term is determined up to the order alpha cube, where alpha denotes the
fine-structure constant
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
Binding conditions for atomic N-electron systems in non-relativistic QED
We examine the binding conditions for atoms in non-relativistic QED, and
prove that removing one electron from an atom requires a positive energy. As an
application, we establish the existence of a ground state for the Helium atom.Comment: LaTeX, uses AMS packag
Spectral gaps in graphene antidot lattices
We consider the gap creation problem in an antidot graphene lattice, i.e. a
sheet of graphene with periodically distributed obstacles. We prove several
spectral results concerning the size of the gap and its dependence on different
natural parameters related to the antidot lattice.Comment: 15 page
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
Some connections between Dirac-Fock and Electron-Positron Hartree-Fock
We study the ground state solutions of the Dirac-Fock model in the case of
weak electronic repulsion, using bifurcation theory. They are solutions of a
min-max problem. Then we investigate a max-min problem coming from the
electron-positron field theory of Bach-Barbaroux-Helffer-Siedentop. We show
that given a radially symmetric nuclear charge, the ground state of Dirac-Fock
solves this max-min problem for certain numbers of electrons. But we also
exhibit a situation in which the max-min level does not correspond to a
solution of the Dirac-Fock equations together with its associated
self-consistent projector
Dynamical localization of Dirac particles in electromagnetic fields with dominating magnetic potentials
We consider two-dimensional massless Dirac operators in a radially symmetric
electromagnetic field. In this case the fields may be described by
one-dimensional electric and magnetic potentials and . We show dynamical
localization in the regime when ,
where dense point spectrum occurs
Gevrey smoothing for weak solutions of the fully nonlinear homogeneous Boltzmann and Kac equations without cutoff for Maxwellian molecules
It has long been suspected that the non-cutoff Boltzmann operator has similar
coercivity properties as a fractional Laplacian. This has led to the hope that
the homogenous Boltzmann equation enjoys similar regularity properties as the
heat equation with a fractional Laplacian. In particular, the weak solution of
the fully nonlinear non-cutoff homogenous Boltzmann equation with initial datum
in , i.e., finite mass, energy
and entropy, should immediately become Gevrey regular for strictly positive
times. We prove this conjecture for Maxwellian molecules.Comment: 43 pages, 1 figur
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