Open problem: Violation of locality for Schr\"odinger operators with complex potentials

TL;DR

This paper discusses how Schrödinger operators with complex potentials challenge traditional notions of locality and Weyl's asymptotics, highlighting an open problem in mathematical physics.

Contribution

It identifies and articulates the violation of locality in Schrödinger operators with complex potentials and presents three open research questions.

Findings

Complex potentials lead to non-local behavior in Schrödinger operators

Violation of Weyl's asymptotics observed in these operators

Open problems proposed for further investigation

Abstract

We explain in which sense Schr\"odinger operators with complex potentials appear to violate locality (or Weyl's asymptotics), and we pose three open problems related to this phenomenon.