Non-Hermitian-Hamiltonian-induced unitarity and optional physical inner products in Hilbert space

TL;DR

This paper explores how relaxing isotropy in Hilbert space geometry within quasi-Hermitian quantum mechanics can extend the parameter range for unitary evolution, demonstrated through solvable models.

Contribution

It introduces a method to enlarge the domain of unitary evolution by weakening Hilbert space isotropy, tested on simplified metrics and solvable models.

Findings

Enlarged parameter domain for unitarity in quasi-Hermitian systems

Weakening isotropy aids in maintaining unitarity

Validated approach with exactly solvable models

Abstract

In the framework of quasi-Hermitian quantum mechanics it is shown that a weakening of the isotropy of the Hilbert-space geometry can help us to enlarge the domain of the parameters at which the evolution is unitary. The idea is tested using a simplified subset of eligible metrics and two exactly solvable models.