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Conférence - DimaScat : Théorie du scattering et asymptotiques spectrales d'opérateurs différentiels - en l'honneur de Dimitri Yafaev

Jeudi, 21 Avril, 2016 - 09:00 - 10:00
Leonid Pastur
Institute for Low Temperature Physics and Engineering, Karkov
Asymptotic trace formulas for ergodic operators and related topics of quantum informatics
Résumé:

We present a setting generalizing that for Szegö's theorem on asymptotics of Toeplitz determinants. The setting is given in terms of two functions (a test function and a symbol) and an underlying ergodic operator in $l^2(\mathbb{Z}^d)$, in particular, the Schrödinger operator with ergodic potential. The setting leads to a variety of asymptotic trace formulas determined by the smoothness of the two functions and mixing properties of the coefficients of ergodic operator. We discuss some of the formulas including those for the large block asymptotics of entanglement entropy of certain bipartite disordered quantum systems.