200 research outputs found
Enhanced binding revisited for a spinless particle in non-relativistic QED
We consider a spinless particle coupled to a quantized Bose field and show
that such a system has a ground state for two classes of short-range potentials
which are alone too weak to have a zero-energy resonance
Binding threshold for the Pauli-Fierz operator
For the Pauli-Fierz operator with a short range potential we study the
binding threshold as a function of the fine structure constant and
show that it converges to the binding threshold for the Schr\"odinger operator
in the small limit
Renormalized Electron Mass in Nonrelativistic QED
Within the framework of nonrelativistic QED, we prove that, for small values
of the coupling constant, the energy function, E_|P|, of a dressed electron is
twice differentiable in the momentum P in a neighborhood of P = 0. Furthermore,
(E_|P|)" is bounded from below by a constant larger than zero. Our results are
proven with the help of iterative analytic perturbation theory
Quantum Oscillations Can Prevent the Big Bang Singularity in an Einstein-Dirac Cosmology
We consider a spatially homogeneous and isotropic system of Dirac particles
coupled to classical gravity. The dust and radiation dominated closed
Friedmann-Robertson-Walker space-times are recovered as limiting cases. We find
a mechanism where quantum oscillations of the Dirac wave functions can prevent
the formation of the big bang or big crunch singularity. Thus before the big
crunch, the collapse of the universe is stopped by quantum effects and reversed
to an expansion, so that the universe opens up entering a new era of classical
behavior.
Numerical examples of such space-times are given, and the dependence on
various parameters is discussed. Generically, one has a collapse after a finite
number of cycles. By fine-tuning the parameters we construct an example of a
space-time which is time-periodic, thus running through an infinite number of
contraction and expansion cycles.Comment: 8 pages, LaTeX, 4 figures, statement on energy conditions correcte
Self-consistent solution for the polarized vacuum in a no-photon QED model
We study the Bogoliubov-Dirac-Fock model introduced by Chaix and Iracane
({\it J. Phys. B.}, 22, 3791--3814, 1989) which is a mean-field theory deduced
from no-photon QED. The associated functional is bounded from below. In the
presence of an external field, a minimizer, if it exists, is interpreted as the
polarized vacuum and it solves a self-consistent equation.
In a recent paper math-ph/0403005, we proved the convergence of the iterative
fixed-point scheme naturally associated with this equation to a global
minimizer of the BDF functional, under some restrictive conditions on the
external potential, the ultraviolet cut-off and the bare fine
structure constant . In the present work, we improve this result by
showing the existence of the minimizer by a variational method, for any cut-off
and without any constraint on the external field.
We also study the behaviour of the minimizer as goes to infinity
and show that the theory is "nullified" in that limit, as predicted first by
Landau: the vacuum totally kills the external potential. Therefore the limit
case of an infinite cut-off makes no sense both from a physical and
mathematical point of view.
Finally, we perform a charge and density renormalization scheme applying
simultaneously to all orders of the fine structure constant , on a
simplified model where the exchange term is neglected.Comment: Final version, to appear in J. Phys. A: Math. Ge
Quantitative estimates on the Hydrogen ground state energy in non-relativistic QED
In this paper, we determine the exact expression for the hydrogen binding
energy in the Pauli-Fierz model up to the order ,
where denotes the finestructure constant, and prove rigorous bounds on
the remainder term of the order . As a consequence,
we prove that the binding energy is not a real analytic function of ,
and verify the existence of logarithmic corrections to the expansion of the
ground state energy in powers of , as conjectured in the recent
literature.Comment: AMS Latex, 51 page
Scaling in a Nonconservative Earthquake Model of Self-Organised Criticality
We numerically investigate the Olami-Feder-Christensen model for earthquakes
in order to characterise its scaling behaviour. We show that ordinary finite
size scaling in the model is violated due to global, system wide events.
Nevertheless we find that subsystems of linear dimension small compared to the
overall system size obey finite (subsystem) size scaling, with universal
critical coefficients, for the earthquake events localised within the
subsystem. We provide evidence, moreover, that large earthquakes responsible
for breaking finite size scaling are initiated predominantly near the boundary.Comment: 6 pages, 6 figures, to be published in Phys. Rev. E; references
sorted correctl
A Minimization Method for Relativistic Electrons in a Mean-Field Approximation of Quantum Electrodynamics
We study a mean-field relativistic model which is able to describe both the
behavior of finitely many spin-1/2 particles like electrons and of the Dirac
sea which is self-consistently polarized in the presence of the real particles.
The model is derived from the QED Hamiltonian in Coulomb gauge neglecting the
photon field. All our results are non-perturbative and mathematically rigorous.Comment: 18 pages, 3 figure
A simple method for finite range decomposition of quadratic forms and Gaussian fields
We present a simple method to decompose the Green forms corresponding to a
large class of interesting symmetric Dirichlet forms into integrals over
symmetric positive semi-definite and finite range (properly supported) forms
that are smoother than the original Green form. This result gives rise to
multiscale decompositions of the associated Gaussian free fields into sums of
independent smoother Gaussian fields with spatially localized correlations. Our
method makes use of the finite propagation speed of the wave equation and
Chebyshev polynomials. It improves several existing results and also gives
simpler proofs.Comment: minor correction for t<
Ground State and Resonances in the Standard Model of Non-relativistic QED
We prove existence of a ground state and resonances in the standard model of
the non-relativistic quantum electro-dynamics (QED). To this end we introduce a
new canonical transformation of QED Hamiltonians and use the spectral
renormalization group technique with a new choice of Banach spaces.Comment: 50 pages change
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