408 research outputs found
Instability of a Pseudo-Relativistic Model of Matter with Self-Generated Magnetic Field
For a pseudo-relativistic model of matter, based on the no-pair Hamiltonian,
we prove that the inclusion of the interaction with the self-generated magnetic
field leads to instability for all positive values of the fine structure
constant. This is true no matter whether this interaction is accounted for by
the Breit potential, by an external magnetic field which is chosen to minimize
the energy, or by the quantized radiation field.Comment: 13 pages, AMS-LaTe
Asymptotic Completeness for Compton Scattering
Scattering in a model of a massive quantum-mechanical particle, an
``electron'', interacting with massless, relativistic bosons, ``photons'', is
studied. The interaction term in the Hamiltonian of our model describes
emission and absorption of ``photons'' by the ``electron''; but
``electron-positron'' pair production is suppressed. An ultraviolet cutoff and
an (arbitrarily small, but fixed) infrared cutoff are imposed on the
interaction term. In a range of energies where the propagation speed of the
dressed ``electron'' is strictly smaller than the speed of light, unitarity of
the scattering matrix is proven, provided the coupling constant is small
enough; (asymptotic completeness of Compton scattering). The proof combines a
construction of dressed one--electron states with propagation estimates for the
``electron'' and the ``photons''.Comment: gap of previous version closed, large parts rewritten, more general
results and more comprehensive exposition. 64 pages, 3 figure
Uniqueness of the ground state in the Feshbach renormalization analysis
In the operator theoretic renormalization analysis introduced by Bach,
Froehlich, and Sigal we prove uniqueness of the ground state.Comment: 10 page
Daughter Zion and the Mississippi Delta
In the Book of Lamentations, Jerusalem 587 BCE is personified as the suffering and persecuted Daughter Zion.1 The biblical Daughter Zion and the present-day Mississippi Delta are separated in time by 2,604 years and separated in distance by 7,000 miles. Despite the vast expanse of space and time between the two, interesting and noteworthy comparisons can be drawn. In this paper, I will show how contemporary afflictions and persecutions facing the Mississippi Delta can be poetically retrieved through a consideration of the afflictions and persecutions related to the fall of Jerusalem. The cry of both dramas tragically emerges from the pages of Lamentations and find further expression in the classic musical laments of the Delta, known as the Delta Blues. I will note the correlations between the Book of Lamentations and Blues music in general and then parallel the narrative of the Book of Lamentations with the contemporary history of the Mississippi Delta. I will then present relevant lyrics from the Delta Blues to reveal the common laments of both sisters in persecution: Daughter Zion and the Mississippi Delta.
1 Kathleen M. O’Connor, Lamentations and the Tears of the World (Maryknoll, NY: Orbis, 2002), 14
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
Asymptotic Completeness for Compton Scattering
Scattering in a model of a massive quantum-mechanical particle, an ‘‘electron'', interacting with massless, relativistic bosons, ‘‘photons'', is studied. The interaction term in the Hamiltonian of our model describes emission and absorption of ‘‘photons'' by the ‘‘electron''; but ‘‘electron-positron'' pair production is suppressed. An ultraviolet cutoff and an (arbitrarily small, but fixed) infrared cutoff are imposed on the interaction term. In a range of energies where the propagation speed of the dressed ‘‘electron'' is strictly smaller than the speed of light, unitarity of the scattering matrix is proven, provided the coupling constant is small enough; (asymptotic completeness of Compton scattering). The proof combines a construction of dressed one-electron states with propagation estimates for the ‘‘electron'' and the ‘‘photons'
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