Short-time behavior of a system ruled by non-Hermitian time-dependent Hamiltonians

TL;DR

This paper derives the short-time survival probability for systems with non-Hermitian time-dependent Hamiltonians, enabling analysis of phenomena like the quantum Zeno effect amidst decay processes.

Contribution

It provides a second-order perturbative expression for short-time behavior of non-Hermitian systems, facilitating new insights into quantum dynamics with decay.

Findings

Predicts quantum Zeno effect in decaying systems

Derives second-order perturbative formula for survival probability

Applicable to quantum technology scenarios

Abstract

The short-time behavior of the survival probability of a system governed by a time-dependent non-Hermitian Hamiltonian is derived using to the second order perturbative approach. The resulting expression allows for the analysis of some situations which could be of interest in the field of quantum technology. For example, it becomes possible to predict a quantum Zeno effect even in the presence of decay processes.