
## 1. Entanglement entropy for Schrödinger operators

The aim is to extend asymptotic trace expansions known in the free case to Schrödinger operators $-\Delta +V$.
1. #### 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 $L^{d-1}\log L$?
• #### Problem 1.2.

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