Some results on the dynamics and transition probabilities for non self-adjoint hamiltonians

TL;DR

This paper explores different methods to describe quantum dynamics and transition probabilities for systems with non-self-adjoint Hamiltonians, focusing on finite-dimensional cases and proposing experiments to distinguish these approaches.

Contribution

It systematically compares various frameworks for non-self-adjoint Hamiltonians and suggests experimental tests to differentiate them.

Findings

Different inequivalent descriptions of quantum dynamics are identified.

Proposed experiments can discriminate between these descriptions.

An illustrative example from literature is analyzed in detail.

Abstract

We discuss systematically several possible inequivalent ways to describe the dynamics and the transition probabilities of a quantum system when its hamiltonian is not self-adjoint. In order to simplify the treatment, we mainly restrict our analysis to finite dimensional Hilbert spaces. In particular, we propose some experiments which could discriminate between the various possibilities considered in the paper. An example taken from the literature is discussed in detail.