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DTSTART;TZID=Europe/Berlin:20241022T160000
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DTSTAMP:20260504T105157
CREATED:20250704T074401Z
LAST-MODIFIED:20250704T074401Z
UID:10000058-1729612800-1729612800@www.trr352.de
SUMMARY:DOS of Random Schrödinger Operators with negatively correlated Cauchy Distribution
DESCRIPTION:We study the generalised Lloyd model\, that is\, a random Schrödinger operator on the lattice Zd of the form H = −∆ + λV\, λ > 0\, with Vi = ∑j Tij Wj where Wj ∼ Cauchy(0\, 1) are iid random variables. If all coeffi- cients Tij are non-negative one can find an exact formula for the density of states (DOS) with the help of supersymmetry (SUSY). However\, the case of negative coefficients remains largely unexplored. To illustrate the complexities involved\, we study a simple model where only two lattice sites are negatively correlated. This model was already considered in a recent work of Disertori and Lager (MPAG2020)\, but here we develop a novel approach based on the regularisation of the distribu- tion of V . We derive the leading order expression for the DOS and recover the asymptote for the correction as the correlation strength is sent to zero. Finally\, I present my progress in extending these results to a model of infinitely many pairs of negative correlation which are well separated and placed periodically in Zd.
URL:https://www.trr352.de/event/dos-of-random-schrodinger-operators-with-negatively-correlated-cauchy-distribution/
LOCATION:Room 5608.03.011 (Seminarraum (M1/M7))\, Boltzmannstr. 3\, Garching b. München\, 85748\, Germany
CATEGORIES:Talks
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