Quantum Bi-Hamiltonian systems, alternative Hermitian structures and Bi-Unitary transformations

TL;DR

This paper explores quantum bi-Hamiltonian systems with alternative Hermitian structures, providing conditions for their generic position and explicitly deriving the bi-unitary transformations in infinite-dimensional Hilbert spaces.

Contribution

It introduces a necessary and sufficient condition for Hermitian structures to be in generic position and explicitly characterizes the bi-unitary transformations.

Findings

Derived necessary and sufficient conditions for Hermitian structures in generic position

Explicitly obtained the transformations of the bi-unitary group

Analyzed the structure of quantum bi-Hamiltonian systems in infinite-dimensional spaces

Abstract

We discuss the dynamical quantum systems which turn out to be bi-unitary with respect to the same alternative Hermitian structures in a infinite-dimensional complex Hilbert space. We give a necessary and sufficient condition so that the Hermitian structures are in generic position. Finally the transformations of the bi-unitary group are explicitly obtained.