102 research outputs found
Weyl asymptotics for magnetic Schr\"odinger operators and de Gennes' boundary condition
This paper is concerned with the discrete spectrum of the self-adjoint
realization of the semi-classical Schr\"odinger operator with constant magnetic
field and associated with the de Gennes (Fourier/Robin) boundary condition. We
derive an asymptotic expansion of the number of eigenvalues below the essential
spectrum (Weyl-type asymptotics). The methods of proof relies on results
concerning the asymptotic behavior of the first eigenvalue obtained in a
previous work [A. Kachmar, J. Math. Phys. Vol. 47 (7) 072106 (2006)].Comment: 28 pages (revised version). to appear in Rev Math Phy
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
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
Thermal effects on CHNHPbI perovskite from ab-initio molecular dynamics simulations
We present a molecular dynamics simulation study of CHNHPbI based
on forces calculated from density functional theory. The simulation were
performed on model systems having 8 and 27 unit cells, and for a total
simulation time of 40 ps in each case. Analysis of the finite size effects, in
particular the mobility of the organic component, suggests that the smaller
system is over correlated through the long range electrostatic interaction. In
the larger system this finite size artifact is relaxed producing a more
reliable description of the anisotropic rotational behavior of the methyl
ammonium molecules. The thermal effects on the optical properties of the system
were also analyzed. The HOMO-LUMO energy gap fluctuates around its central
value with a standard deviation of approximately 0.1 eV. The projected density
of states consistently place the Fermi level on the orbitals of the I
atoms, and the lowest virtual state on orbitals of the Pb atoms throughout
the whole simulation trajectory.Comment: 16 pages, 11 figure
Quantum tunneling in deep potential wells and strong magnetic field revisited
Inspired by a recent paper by C. Fefferman, J. Shapiro and M. Weinstein,
we investigate quantum tunneling for a Hamiltonian with a symmetric double well
and a uniform magnetic field. In the simultaneous limit of strong magnetic
field and deep potential wells with disjoint supports, tunneling occurs and we
derive accurate estimates of its magnitude.
[Lower bound on quantum tunneling for strong magnetic fields. SIAM J.
Math. Anal. 54(1), 1105-1130 (2022).]Comment: Added Proposition 6.5 which improves the estimate in Theorem 1.4;
Appendix B contains the reduction to an interaction matrix; typos correcte
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