5 research outputs found
Binding of Polarons and Atoms at Threshold
If the polaron coupling constant is large enough, bipolarons or
multi-polarons will form. When passing through the critical from
above, does the radius of the system simply get arbitrarily large or does it
reach a maximum and then explodes? We prove that it is always the latter. We
also prove the analogous statement for the Pekar-Tomasevich (PT) approximation
to the energy, in which case there is a solution to the PT equation at
. Similarly, we show that the same phenomenon occurs for atoms, e.g.,
helium, at the critical value of the nuclear charge. Our proofs rely only on
energy estimates, not on a detailed analysis of the Schr\"odinger equation, and
are very general. They use the fact that the Coulomb repulsion decays like
, while `uncertainty principle' localization energies decay more rapidly,
as .Comment: 19 page
A new approach to the modelling of local defects in crystals: the reduced Hartree-Fock case
This article is concerned with the derivation and the mathematical study of a
new mean-field model for the description of interacting electrons in crystals
with local defects. We work with a reduced Hartree-Fock model, obtained from
the usual Hartree-Fock model by neglecting the exchange term. First, we recall
the definition of the self-consistent Fermi sea of the perfect crystal, which
is obtained as a minimizer of some periodic problem, as was shown by Catto, Le
Bris and Lions. We also prove some of its properties which were not mentioned
before. Then, we define and study in details a nonlinear model for the
electrons of the crystal in the presence of a defect. We use formal analogies
between the Fermi sea of a perturbed crystal and the Dirac sea in Quantum
Electrodynamics in the presence of an external electrostatic field. The latter
was recently studied by Hainzl, Lewin, S\'er\'e and Solovej, based on ideas
from Chaix and Iracane. This enables us to define the ground state of the
self-consistent Fermi sea in the presence of a defect. We end the paper by
proving that our model is in fact the thermodynamic limit of the so-called
supercell model, widely used in numerical simulations.Comment: Final version, to appear in Comm. Math. Phy
On the structure of the discrete spectrum of multiparticle hamiltonians with increasing magnetic fields
SIGLEAvailable from TIB Hannover: RR 6329(2000,5) / FIZ - Fachinformationszzentrum Karlsruhe / TIB - Technische InformationsbibliothekStiftung Volkswagenwerk, Hannover (Germany)DEGerman