12 research outputs found
Mathematical analysis of the photoelectric effect
We study the photoelectric effect on the example of a simplified model of an
atom with a single bound state, coupled to the quantized electromagnetic field.
For this model, we show that Einstein's prediction for the photoelectric effect
is qualitatively and quantitatively correct to leading order in the coupling
parameter. More specifically, considering the ionization of the atom by an
incident photon cloud consisting of photons, we prove that the total
ionized charge is additive in the involved photons. Furthermore, if the
photon cloud is approaching the atom from a large distance, the kinetic energy
of the ejected electron is shown to be given by the difference of the photon
energy of each single photon in the photon cloud and the ionization energy.Comment: See also http://www.intlpress.com/ATM
The Integrated Density of States for an Interacting Multiparticle Homogeneous Model and Applications to the Anderson Model
For a system of n interacting particles moving in the background of a ``homogeneous'' potential, we show that if the single particle Hamiltonian admits a density of states, so does the interacting n-particle Hamiltonian. Moreover, this integrated density of states coincides with that of the free particle Hamiltonian. For the interacting n-particle Anderson model, we prove regularity properties of the integrated density of states by establishing a Wegner estimate. Copyright (C) 2009 F. Klopp and H. Zenk
Asymptotic Electromagnetic Fields in Non-relativistic QED: the Problem of Existence Revisited
This paper is devoted to the scattering of photons at electrons in models of
non-relativistic quantum mechanical particles coupled minimally to the soft
modes of the quantized electromagnetic field. We prove existence of scattering
states involving an arbitrary number of asymptotic photons of arbitrarily high
energy. Previously, upper bounds on the photon energies seemed necessary in the
case of asymptotic photons and non-confined, non-relativistic charged
particles.Comment: 12 page
Ionisation by quantised electromagnetic fields: The photoelectric effect
In this paper we explain the photoelectric effect in a variant of the
standard model of non relativistic quantum electrodynamics, which is in some
aspects more closely related to the physical picture, than the one studied in
[BKZ]: Now we can apply our results to an electron with more than one bound
state and to a larger class of electron-photon interactions. We will specify a
situation, where ionisation probability in second order is a weighted sum of
single photon terms. Furthermore we will see, that Einstein's equality
for the maximal kinetic energy of
the electron, energy of the photon and ionisation gap
is the crucial condition for these single photon terms to be nonzero.Comment: 59 pages, LATEX2
On the Atomic Photoeffect in Non-relativistic QED
In this paper we present a mathematical analysis of the photoelectric effect
for one-electron atoms in the framework of non-relativistic QED. We treat
photo-ionization as a scattering process where in the remote past an atom in
its ground state is targeted by one or several photons, while in the distant
future the atom is ionized and the electron escapes to spacial infinity. Our
main result shows that the ionization probability, to leading order in the
fine-structure constant, , is correctly given by formal time-dependent
perturbation theory, and, moreover, that the dipole approximation produces an
error of only sub-leading order in . In this sense, the dipole
approximation is rigorously justified.Comment: 25 page
The Integrated Density of States for an Interacting Multiparticle Homogeneous Model and Applications to the Anderson Model
For a system of n interacting particles moving in the background of a ``homogeneous'' potential, we show that if the single particle Hamiltonian admits a density of states, so does the interacting n-particle Hamiltonian. Moreover, this integrated density of states coincides with that of the free particle Hamiltonian. For the interacting n-particle Anderson model, we prove regularity properties of the integrated density of states by establishing a Wegner estimate. Copyright (C) 2009 F. Klopp and H. Zenk