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1. Entanglement entropy for Schrödinger operators

The aim is to extend asymptotic trace expansions known in the free case to Schrödinger operators $-\Delta +V$.


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      Problem 1.1.

      Universal upper bounds on local entanglement entropy for Schrödinger operators: under which condition is it true that for local Schrödinger operators such as $-\Delta +V$ with bounded (not necessarily ergodic) potential $V$ the EE is asymptotically bounded by $L^{d-1}\log L$?


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          Problem 1.2.

          Which effect do cusps/corners have on the leading/lower order of trace asymptotics for ergodic Scrödinger operators?


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              Problem 1.3.

              Entanglement impurity asymptotics in $d=1$: at which order of the asymptotic expansion of the entanglement entropy can the impact of a local perturbation (e.g. $V$ short-range potential) be observed?


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                  Problem 1.4.

                  Closure of the asymptotics: up to which order can known (full) asymptotics for both symbol and test function smooth be closed for non-smooth test functions such as $h(x) = -x\log(x) -(1-x)\log(1-x)$?

                      Cite this as: AimPL: Fisher-Hartwig asymptotics and Szego expansions, available at http://aimpl.org/fhszego.