2,765 research outputs found
The dressed nonrelativistic electron in a magnetic field
We consider a nonrelativistic electron interacting with a classical magnetic
field pointing along the -axis and with a quantized electromagnetic
field. When the interaction between the electron and photons is turned off, the
electronic system is assumed to have a ground state of finite multiplicity.
Because of the translation invariance along the -axis, we consider the
reduced Hamiltonian associated with the total momentum along the -axis
and, after introducing an ultraviolet cutoff and an infrared regularization, we
prove that the reduced Hamiltonian has a ground state if the coupling constant
and the total momentum along the -axis are sufficiently small. Finally
we determine the absolutely continuous spectrum of the reduced Hamiltonian.Comment: typos correction
Inverse scattering at fixed energy for layered media
AbstractIn this article we show that exponentially decreasing perturbations of the sound speed in a layered medium can be recovered from the scattering amplitude at fixed energy. We consider the unperturbed equation utt = c02(xn)ÎŽu in âĂâ, where n â„ 3. The unperturbed sound speed, c0(xn), is assumed to be bounded, strictly positive, and constant outside a bounded interval on the real axis. The perturbed sound speed, c(x), satisfies Šc.(x) - co(xn)Š < C exp(âΎŠxŠ) for some ÎŽ > 0. Our work is related to the recent results of H. Isozaki (J. Diff. Eq. 138) on the case where c0 takes the constant values c+ and câ on the positive and negative half-lines, and R. Weder on the case c0 = c+ for xn > h, c0 = ch, for 0 < xn, < h, and c0 = câ for xn < 0 (IIMAS-UNAM Preprint 70, November, 1997)
Spectral theory for a mathematical model of the weak interaction: The decay of the intermediate vector bosons W+/-. I
We consider a Hamiltonian with cutoffs describing the weak decay of spin one
massive bosons into the full family of leptons. The Hamiltonian is a
self-adjoint operator in an appropriate Fock space with a unique ground state.
We prove a Mourre estimate and a limiting absorption principle above the ground
state energy and below the first threshold for a sufficiently small coupling
constant. As a corollary, we prove absence of eigenvalues and absolute
continuity of the energy spectrum in the same spectral interval.Comment: Correction of minor misprint
Effect of turbulence on collisions of dust particles with planetesimals in protoplanetary disks
Planetesimals in gaseous protoplanetary disks may grow by collecting dust
particles. Hydrodynamical studies show that small particles generally avoid
collisions with the planetesimals because they are entrained by the flow around
them. This occurs when , the Stokes number, defined as the ratio of the
dust stopping time to the planetesimal crossing time, becomes much smaller than
unity. However, these studies have been limited to the laminar case, whereas
these disks are believed to be turbulent. We want to estimate the influence of
gas turbulence on the dust-planetesimal collision rate and on the impact
speeds. We used three-dimensional direct numerical simulations of a fixed
sphere (planetesimal) facing a laminar and turbulent flow seeded with small
inertial particles (dust) subject to a Stokes drag. A no-slip boundary
condition on the planetesimal surface is modeled via a penalty method. We find
that turbulence can significantly increase the collision rate of dust particles
with planetesimals. For a high turbulence case (when the amplitude of turbulent
fluctuations is similar to the headwind velocity), we find that the collision
probability remains equal to the geometrical rate or even higher for , i.e., for dust sizes an order of magnitude smaller than in the laminar
case. We derive expressions to calculate impact probabilities as a function of
dust and planetesimal size and turbulent intensity
Coalescence in the 1D Cahn-Hilliard model
We present an approximate analytical solution of the Cahn-Hilliard equation
describing the coalescence during a first order phase transition. We have
identified all the intermediate profiles, stationary solutions of the noiseless
Cahn-Hilliard equation. Using properties of the soliton lattices, periodic
solutions of the Ginzburg-Landau equation, we have construct a family of ansatz
describing continuously the processus of destabilization and period doubling
predicted in Langer's self similar scenario
Twisting algebras using non-commutative torsors
Non-commutative torsors (equivalently, two-cocycles) for a Hopf algebra can
be used to twist comodule algebras. After surveying and extending the
literature on the subject, we prove a theorem that affords a presentation by
generators and relations for the algebras obtained by such twisting. We give a
number of examples, including new constructions of the quantum affine spaces
and the quantum tori.Comment: 27 pages. Masuoka is a new coauthor. Introduction was revised.
Sections 1 and 2 were thoroughly restructured. The presentation theorem in
Section 3 is now put in a more general framework and has a more general
formulation. Section 4 was shortened. All examples (quantum affine spaces and
tori, twisting of SL(2), twisting of the enveloping algebra of sl(2)) are
left unchange
Quelques commentaires sur la linéarisation de l'erreur de l'observation multi-sorties
International audienceCe papier donne quelques idées et commentaires sur les conditions géométriques qui permettent de dire si un systÚme non linéaire multi sorties possÚde, à un changement de coordonnées prÚs, une erreur d'observation linéaire. Plus précisément, nous allons concentrer notre point de vu sur les travaux de Krener et Respondek d'une part et ceux de Xia et Gao d'autre part. Nous allons aussi commenter le "soit disant" contre exemple de Xia et Gao. Puis, nous allons présenter l'algorithme de la linéarisation de l'erreur de l'observation par extension dynamique
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