The Magnus expansion for non-Hermitian Hamiltonians

The Magnus expansion offers a method to express a time-ordered exponential as an ordinary operatorial exponential. This representation has advantageous theoretical properties, while still solving the original differential equation. For any finite dimensional Hermitian Hamiltonians, the standard Magnus expansion guarantees a manifestly unitary representation. However, this property is no longer preserved if the Hamiltonian is infinite dimensional or non-Hermitian. In this work, we derive a generalized expansion that maintains the property of unitarity for all bounded finite dimensional Hamiltonians.