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Уважаемые сотрудники ИТФ,<br>
<br>
В пятницу 5 апреля состоится коллоквиум, на котором будет заслушан
доклад:<br>
<br>
Владимир Кравцов<br>
<b>Correlation-induced localization</b><br>
<br>
Conventional Anderson localization is due to destructive
interference of matter waves described by local random Hamiltonians.
Correlations in random diagonal elements of such a Hamiltonian are
known to favor delocalization. Recently systems with non-local
Hamiltonians become experimentally accessible. We consider two
families of such random matrix Hamiltonians with correlations in the
long-range hopping terms and demonstrate that localization is
enhanced and the wave function ergodicity is progressively degrading
as the correlations become stronger. We review the
localization/delocalization criteria of Mott and Anderson and show
that the former is the sufficient criterion of weak ergodicity and
the latter is the sufficient criterion of localization. The fact
that these two criteria are not complimentary is the reason why the
non-ergodic extended (multifractal) states may exist when neither
the Mott, nor the Anderson criterion is fulfilled.<br>
We suggest a new class of random matrix models (Toeplitz RMT) with
translation-invariant hopping integrals and identify the character
of eigenfunction and eigenvalue statistics in them. We formulate the
principles of level statistics if the type of eigenfunction
statistics is known both in the coordinate and in the momentum basis
and demonstrate that for the Toeplitz RMT the ergodic delocalization
in the coordinate space may coexist with the Poisson level
statistics.<br>
Finally, we suggest a matrix-inversion trick that allows to identify
uniquely the type of eigenfunction statistics and prove the absence
of delocalized states in the bulk of spectrum of long-range
Hamiltonians with deterministic (fully correlated) hopping. <br>
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