25 research outputs found
On the Maximal Excess Charge of the Chandrasekhar-Coulomb Hamiltonian in Two Dimensions
We show that for the straightforward quantized relativistic Coulomb
Hamiltonian of a two-dimensional atom -- or the corresponding magnetic quantum
dot -- the maximal number of electrons does not exceed twice the nuclear
charge. It result is then generalized to the presence of external magnetic
fields and atomic Hamiltonians. This is based on the positivity of |\bx|
T(\bp) + T(\bp) |\bx| which -- in two dimensions -- is false for the
non-relativistic case T(\bp) = \bp^2, but is proven in this paper for T(\bp)
= |\bp|, i.e., the ultra-relativistic kinetic energy
A simple proof of Hardy-Lieb-Thirring inequalities
We give a short and unified proof of Hardy-Lieb-Thirring inequalities for
moments of eigenvalues of fractional Schroedinger operators. The proof covers
the optimal parameter range. It is based on a recent inequality by Solovej,
Soerensen, and Spitzer. Moreover, we prove that any non-magnetic Lieb-Thirring
inequality implies a magnetic Lieb-Thirring inequality (with possibly a larger
constant).Comment: 12 page
Resummation of the Divergent Perturbation Series for a Hydrogen Atom in an Electric Field
We consider the resummation of the perturbation series describing the energy
displacement of a hydrogenic bound state in an electric field (known as the
Stark effect or the LoSurdo-Stark effect), which constitutes a divergent formal
power series in the electric field strength. The perturbation series exhibits a
rich singularity structure in the Borel plane. Resummation methods are
presented which appear to lead to consistent results even in problematic cases
where isolated singularities or branch cuts are present on the positive and
negative real axis in the Borel plane. Two resummation prescriptions are
compared: (i) a variant of the Borel-Pade resummation method, with an
additional improvement due to utilization of the leading renormalon poles (for
a comprehensive discussion of renormalons see [M. Beneke, Phys. Rep. vol. 317,
p. 1 (1999)]), and (ii) a contour-improved combination of the Borel method with
an analytic continuation by conformal mapping, and Pade approximations in the
conformal variable. The singularity structure in the case of the LoSurdo-Stark
effect in the complex Borel plane is shown to be similar to (divergent)
perturbative expansions in quantum chromodynamics.Comment: 14 pages, RevTeX, 3 tables, 1 figure; numerical accuracy of results
enhanced; one section and one appendix added and some minor changes and
additions; to appear in phys. rev.
Summing up the perturbation series in the Schwinger Model
Perturbation series for the electron propagator in the Schwinger Model is
summed up in a direct way by adding contributions coming from individual
Feynman diagrams. The calculation shows the complete agreement between
nonperturbative and perturbative approaches.Comment: 10 pages (in REVTEX