99 research outputs found
Nucleation of bulk superconductivity close to critical magnetic field
We consider the two-dimensional Ginzburg-Landau functional with constant
applied magnetic field. For applied magnetic fields close to the second
critical field and large Ginzburg-Landau parameter, we provide
leading order estimates on the energy of minimizing configurations. We obtain a
fine threshold value of the applied magnetic field for which bulk
superconductivity contributes to the leading order of the energy. Furthermore,
the energy of the bulk is related to that of the Abrikosov problem in a
periodic lattice. A key ingredient of the proof is a novel -bound
which is of independent interest
On the energy of bound states for magnetic Schr\"odinger operators
We provide a leading order semiclassical asymptotics of the energy of bound
states for magnetic Neumann Schr\"odinger operators in two dimensional
(exterior) domains with smooth boundaries. The asymptotics is valid all the way
up to the bottom of the essential spectrum. When the spectral parameter is
varied near the value where bound states become allowed in the interior of the
domain, we show that the energy has a boundary and a bulk component. The
estimates rely on coherent states, in particular on the construction of
`boundary coherent states', and magnetic Lieb-Thirring estimates.Comment: 26 page
A new proof of the analyticity of the electronic density of molecules
We give a new, short proof of the regularity away from the nuclei of the
electronic density of a molecule obtained in [1,2]. The new argument is based
on the regularity properties of the Coulomb interactions underlined in [3,4]
and on well-known elliptic technics. [1] S. Fournais, M. Hoffmann-Ostenhof, T.
Hoffmann-Ostenhof, T. Oe stergaard Soerensen: The electron density is smooth
away from the nuclei. Comm. Math. Phys. 228, no. 3 (2002), 401-415. [2] S.
Fournais, M. Hoffmann-Ostenhof, T. Hoffmann-Ostenhof, T. Oestergaard Soerensen:
Analyticity of the density of electronic wave functions. Ark. Mat. 42, no. 1
(2004), 87-106. [3] W. Hunziker: Distortion analyticity and molecular
resonances curves. Ann. Inst. H. Poincar\'e, s. A, t. 45, no 4, 339-358 (1986).
[4] M. Klein, A. Martinez, R. Seiler, X.P. Wang: On the Born-Oppenheimer
expansion for polyatomic molecules. Comm. Math. Phys. 143, no. 3, 607-639
(1992). The paper is published in Letters in Mathematical Physics 93, number 1,
pp. 73-83, 2010. The original publication is available at "
www.springerlink.com "
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