[seminar] Seminar FO , Veselić

[hbuljan at phy.hr]

Poštovani kolege,

pozivam Vas na seminar kolege Ivana Veselića koji će se održati
u srijedu 14.03. u 14.15 sati na Fizičkom odsjeku (soba F201);
seminar će biti u stilu predavanja kreda + ploča.

Seminar je naslovljen:

"Spectral averaging in the mathematical theory of Anderson localization"

a sažetak je u nastavku poruke.

Srdačan pozdrav
Hrvoje Buljan


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SEMINAR FIZIČKOG ODSJEKA
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Vrijeme:   srijeda, 14. 3. 2012., 14:15 sati (točno)
Mjesto:     Fizički odsjek, Bijenička c. 32, predavaonica F201

Spectral averaging in the mathematical theory of Anderson localization

        Ivan Veselić
Technical University of Chemnitz, Faculty of Mathematics

Anderson localization is a widely studied topic in theoretical and
computational physics. It is also an active field of research in
mathematics, even though only a part of the results suggested by physical
arguing can be proven (or in rare occasions disproven) on the mathematical
level of rigour.

Spectral averaging is the pheonomenon that certain types of disorder
regularize and smooth out spectral data, like the density of states.  It
implies that resonances on large scales can  occur only with small
probability, thus being crucial for the understanding of the localization
of eigenfunctions. It also allows to prove that eigenvalues are
non-stationary w.r.t. fluctuations of the disorder

We discuss several features of the underlying random Hamiltonian which
play a key  role in the rigourous mathematical analysis of Anderson
localization and have an appealing physical meaning, e.g.
- continuously distributed random variables, versus  Bernoulli
distributetd ones: For the latter,  spectral averaging is harder to prove,
 in fact the density of states need not be smooth
- positive definite versus semindefinite random perturbations:
For the latter it is not clear whether certain spectral subspaces remain
unaffected by the disorder.
- monotone versus non-monotone random perturbations:
For the latter it is not clear how to quantitatively estimate the movement
or flow of eigenvalues.


					Hrvoje Buljan, hbuljan at phy.hr