# Hilbert space partitioning for non-Hermitian Hamiltonians: From off-resonance to Zeno subspaces

## TL;DR

This paper investigates how non-Hermitian Hamiltonians can lead to Hilbert space partitioning, resulting in dynamical confinement, which can be interpreted as Zeno effects or a combination of phenomena depending on system parameters.

## Contribution

It provides a detailed analysis of Hilbert space partitioning in non-Hermitian Hamiltonians and clarifies the conditions under which Zeno effects or complex dynamics occur.

## Key findings

- Dynamical confinement depends on the complex phases of Hamiltonian diagonal terms.
- Larger moduli are required for confinement when the phase approaches π/2.
- Partitioning can be interpreted as Zeno effect or a mix of phenomena.

## Abstract

Effective non-Hermitian Hamiltonians describing decaying systems are derived and analyzed in connection with the occurrence of possible Hilbert space partitioning, resulting in a confinement of the dynamics. In some cases, this fact can be interpreted properly as Zeno effect or Zeno dynamics, according to the dimension of the subspace one focuses on; in some other cases, the interpretation is more complicated and traceable back to a mix of Zeno phenomena and lack of resonance. Depending on the complex phases of the diagonal terms of the Hamiltonian, the system reacts in different ways, requiring larger moduli for the dynamical confinement to occur when the complex phase is close to $\pi/2$.