278 research outputs found
Quasi-classical versus non-classical spectral asymptotics for magnetic Schroedinger operators with decreasing electric potentials
We consider the Schroedinger operator H on L^2(R^2) or L^2(R^3) with constant
magnetic field and electric potential V which typically decays at infinity
exponentially fast or has a compact support. We investigate the asymptotic
behaviour of the discrete spectrum of H near the boundary points of its
essential spectrum. If the decay of V is Gaussian or faster, this behaviour is
non-classical in the sense that it is not described by the quasi-classical
formulas known for the case where V admits a power-like decay.Comment: Corrected versio
On the semi-classical analysis of the groundstate energy of the Dirichlet Pauli operator in non-simply connected domains
We consider the Dirichlet Pauli operator in bounded connected domains in the
plane, with a semi-classical parameter. We show, in particular, that the ground
state energy of this Pauli operator will be exponentially small as the
semi-classical parameter tends to zero and estimate this decay rate. This
extends our results, discussing the results of a recent paper by
Ekholm--Kova\v{r}\'ik--Portmann, to include also non-simply connected domains.Comment: 15 pages, 4 figure
A trace formula and high energy spectral asymptotics for the perturbed Landau Hamiltonian
A two-dimensional Schr\"odinger operator with a constant magnetic field
perturbed by a smooth compactly supported potential is considered. The spectrum
of this operator consists of eigenvalues which accumulate to the Landau levels.
We call the set of eigenvalues near the 'th Landau level an 'th
eigenvalue cluster, and study the distribution of eigenvalues in the 'th
cluster as . A complete asymptotic expansion for the eigenvalue
moments in the 'th cluster is obtained and some coefficients of this
expansion are computed. A trace formula involving the first eigenvalue moments
is obtained.Comment: 23 page
The Choice of a Design of the Device for Production of Compound Feed
In the work the analysis of the equipment and technology of its production for production of the granulated forages is carried out, it is shown that the most responsible element is the matrix. Ways of increase in its resource are planned
Distant foreground and the Planck-derived Hubble constant
It is possible to reduce the discrepancy between the local measurement of the
cosmological parameter and the value derived from the
measurements of the Cosmic Microwave Background (CMB) by considering
contamination of the CMB by emission from some medium around distant
extragalactic sources, such as extremely cold coarse-grain dust. Though being
distant, such a medium would still be in the foreground with respect to the
CMB, and, as any other foreground, it would alter the CMB power spectrum. This
could contribute to the dispersion of CMB temperature fluctuations. By
generating a few random samples of CMB with different dispersions, we have
checked that the increased dispersion leads to a smaller estimated value of
, the rest of the cosmological model parameters remaining fixed. This
might explain the reduced value of the -derived parameter with
respect to the local measurements. The signature of the distant foreground in
the CMB traced by SNe was previously reported by the authors of this paper --
we found a correlation between the SN redshifts, , and CMB
temperature fluctuations at the SNe locations, . Here we have used
the slopes of the regression lines corresponding to
different {\it Planck} wave bands in order to estimate the possible temperature
of the distant extragalactic medium, which turns out to be very low, about
5\,K. The most likely ingredient of this medium is coarse-grain () dust,
which is known to be almost undetectable, except for the effect of dimming
remote extragalactic sources.Comment: 5 pages, 4 figures, 1 tabl
Asymptotic Density of Eigenvalue Clusters for the Perturbed Landau Hamiltonian
We consider the Landau Hamiltonian (i.e. the 2D Schroedinger operator with
constant magnetic field) perturbed by an electric potential V which decays
sufficiently fast at infinity. The spectrum of the perturbed Hamiltonian
consists of clusters of eigenvalues which accumulate to the Landau levels.
Applying a suitable version of the anti-Wick quantization, we investigate the
asymptotic distribution of the eigenvalues within a given cluster as the number
of the cluster tends to infinity. We obtain an explicit description of the
asymptotic density of the eigenvalues in terms of the Radon transform of the
perturbation potential V.Comment: 30 pages. The explicit dependence on B and V in Theorem 1.6 (i) -
(ii) indicated. Typos corrected. To appear in Communications in Mathematical
Physic
- …