1,961 research outputs found
The Gravitational Sector in the Connes-Lott Formulation of the Standard Model
We study the Riemannian aspect and the Hilbert-Einstein gravitational action
of the non-commutative geometry underlying the Connes-Lott construction of the
action functional of the standard model. This geometry involves a two-sheeted,
Euclidian space-time. We show that if we require the space of forms to be
locally isotropic and the Higgs scalar to be dynamical, then the Riemannian
metrics on the two sheets of Euclidian space-time must be identical. We also
show that the distance function between the two sheets is determined by a
single, real scalar field whose VEV sets the weak scale.Comment: Latex file, 29 page
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
On the Mean-Field Limit of Bosons with Coulomb Two-Body Interaction
In the mean-field limit the dynamics of a quantum Bose gas is described by a
Hartree equation. We present a simple method for proving the convergence of the
microscopic quantum dynamics to the Hartree dynamics when the number of
particles becomes large and the strength of the two-body potential tends to 0
like the inverse of the particle number. Our method is applicable for a class
of singular interaction potentials including the Coulomb potential. We prove
and state our main result for the Heisenberg-picture dynamics of "observables",
thus avoiding the use of coherent states. Our formulation shows that the
mean-field limit is a "semi-classical" limit.Comment: Corrected typos and included an elementary proof of the Kato
smoothing estimate (Lemma 6.1
A model with simultaneous first and second order phase transitions
We introduce a two dimensional nonlinear XY model with a second order phase
transition driven by spin waves, together with a first order phase transition
in the bond variables between two bond ordered phases, one with local
ferromagnetic order and another with local antiferromagnetic order. We also
prove that at the transition temperature the bond-ordered phases coexist with a
disordered phase as predicted by Domany, Schick and Swendsen. This last result
generalizes the result of Shlosman and van Enter (cond-mat/0205455). We argue
that these phenomena are quite general and should occur for a large class of
potentials.Comment: 7 pages, 7 figures using pstricks and pst-coi
Translation-invariance of two-dimensional Gibbsian point processes
The conservation of translation as a symmetry in two-dimensional systems with
interaction is a classical subject of statistical mechanics. Here we establish
such a result for Gibbsian particle systems with two-body interaction, where
the interesting cases of singular, hard-core and discontinuous interaction are
included. We start with the special case of pure hard core repulsion in order
to show how to treat hard cores in general.Comment: 44 pages, 6 figure
Influence of damping on the excitation of the double giant resonance
We study the effect of the spreading widths on the excitation probabilities
of the double giant dipole resonance. We solve the coupled-channels equations
for the excitation of the giant dipole resonance and the double giant dipole
resonance. Taking Pb+Pb collisions as example, we study the resulting effect on
the excitation amplitudes, and cross sections as a function of the width of the
states and of the bombarding energy.Comment: 8 pages, 3 figures, corrected typo
Phase Transition in Ferromagnetic Ising Models with Non-Uniform External Magnetic Fields
In this article we study the phase transition phenomenon for the Ising model
under the action of a non-uniform external magnetic field. We show that the
Ising model on the hypercubic lattice with a summable magnetic field has a
first-order phase transition and, for any positive (resp. negative) and bounded
magnetic field, the model does not present the phase transition phenomenon
whenever , where is the external
magnetic field.Comment: 11 pages. Published in Journal of Statistical Physics - 201
An alternative approach for the dynamics of polarons in one dimension
We developed a new method based on functional integration to treat the
dynamics of polarons in one-dimensional systems. We treat the acoustical and
the optical case in an unified manner, showing their differences and
similarities. The mobility and diffusion coefficients are calculated in the
Markovian approximation in the strong coupling limit.Comment: 57 page
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