Weak Measurements in Non-Hermitian Systems

TL;DR

This paper explores how weak measurements operate in quantum systems with non-Hermitian Hamiltonians, proposing modifications to the weak value concept and demonstrating these with numerical examples in a bound state scattering framework.

Contribution

It introduces a modified definition of weak values for non-Hermitian systems and applies it within a well-defined scattering theory context.

Findings

Modified weak value definition for non-Hermitian systems

Explicit computation of metric operators in the model

Numerical validation with a bound state scattering example

Abstract

"Weak measurements" -- involving a weak unitary interaction between a quantum system and a meter followed by a projective measurement -- are investigated when the system has a non-Hermitian Hamiltonian. We show in particular how the standard definition of the "weak value" of an observable must be modified. These studies are undertaken in the context of bound state scattering theory, a non-Hermitian formalism for which the Hilbert spaces involved are unambiguously defined and the metric operators can be explicitly computed. Numerical examples are given for a model system.