# Positive Hamiltonians can give purely exponential decay

## TL;DR

This paper demonstrates that Hamiltonians bounded below, previously thought incapable of exponential decay, can indeed produce such decay when focusing on subsystems rather than the entire system.

## Contribution

It challenges the belief that only unbounded Hamiltonians can yield exponential decay by showing bounded Hamiltonians can do so in subsystems.

## Key findings

- Bounded Hamiltonians can produce exponential decay in subsystems.
- Purely exponential decay is not necessarily unphysical.
- The focus on subsystems alters decay behavior understanding.

## Abstract

It is commonly claimed that only Hamiltonians with a spectrum unbounded both above and below can give purely exponential decay. Because such Hamiltonians have no ground state, they are considered unphysical. Here we show that Hamiltonians which are bounded below can give purely exponential decay. This is possible when, instead of looking at the global survival probability, one considers a subsystem only. We conclude that purely exponential decay might not be as unphysical as previously thought.