2007/05/23 by Nurulla Azamov, Azamov, Nurulla · 1 citation
Computer Science · Mathematics · #Matrix Theory and Algorithms #Numerical methods in inverse problems #Spectral Theory in Mathematical Physics #math.SP #msc:47A11 #msc:47A55
paper · pdf · doi:10.48550/arxiv.0705.3282
12 pages, LaTeX; minor changes
arxiv created 2007/10/23 · arxiv updated 2009/12/01
In this note the notion of infinitesimal scattering matrix is introduced. It is shown that under certain assumption, the scattering operator of a pair of trace compatible operators is equal to the chronological exponential of the infinitesimal scattering matrix and that the trace of the infinitesimal scattering matrix is equal to the absolutely continuous part of the infinitesimal spectral flow. As a corollary, a variant of the Birman-Krein formula is derived. An interpretation of Pushnitski's μ-invariant is given.