185 research outputs found
Effect of magnetic field on electron spectrum in spherical nano-structures
The effect of a magnetic field on the energy spectrum and on the wave
functions of an electron in spherical nano-structures such as single quantum
dot and spherical layer is investigated. It is shown that the magnetic field
removes the spectrum degeneration with respect to the magnetic quantum number.
An increasing magnetic field induction entails a monotonous character of
electron energy for the states with and a non-monotonous one
for the states with . The electron wave functions of the ground state and
several excited states are studied considering the effect of the magnetic
field. It is shown that and states are degenerated in the spherical
layer driven by a strong magnetic field. In the limit case, a series of
size-quantized levels produce the Landau levels which are typical of bulk
crystals.Comment: 8 pages, 4 figure
Khintchine-type theorems on manifolds: the convergence case for standard and multiplicative versions
An analogue of the convergence part of the Khintchine-Groshev theorem, as
well as its multiplicative version, is proved for nondegenerate smooth
submanifolds in . The proof combines methods from metric number
theory with a new approach involving the geometry of lattices in Euclidean
spaces.Comment: 27 page
On the relation between values of integer polynomials, their derivatives and metric theory of diophantine approximations
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