arXiv subjects

A. Suvorov

Publications and source records attributed to A. Suvorov.

2 recordsLinked to original sources

arXiv2015

Ultra high energy resolution focusing monochromator for inelastic X-ray scattering spectrometer

A further development of a focusing monochromator concept for X-ray energy resolution of 0.1 meV and below is presented. Theoretical analysis of several optical layouts based on this concept was supported by numerical simulations performed in the "Synchrotron Radiation Workshop" software package using the physical-optics approach and careful modeling of partially-coherent synchrotron (undulator) radiation. Along with the energy resolution, the spectral shape of the energy resolution function was investigated. It was shown that under certain conditions the decay of the resolution function tails can be faster than that of the Gaussian function.

physics.optics↗

arXiv1999

Spectral estimations for Laplace operator for the discrete Heisenberg group

Let H be the discrete 3-dimensional Heisenberg group with the standard generators x, y, z. The element Delta of the group algebra for H of the form Delta= (x+x^{-1}+y+y^{-1})/4 is called the Laplace operator. This operator can also be defined as transition operator for random walk on the group. The spectrum of Delta in the regular representation of H is the interval [-1,1]. Let E(A), where A is a subset of [-1,1], be a family of spectral projectors for Delta and m(A)=(E(A)e, e) be the corresponding spectral measure. Here e is the characteristic function of the unit element of the group H. We estimate the value m([-1,-1+t] \cup [1-t,1]) when t tends to 0. More precisely we prove the inequality m([-1,-1+t] \cup [1-t,1]) > const t^{2+alpha} for any positive alpha.

math.SP↗