On non-dissipative and dissipative qubit manifolds

TL;DR

This paper explores the geometric structures of qubit state manifolds, showing that their trajectories are geodesics on specific Riemannian or Lorentzian manifolds, in both dissipative and non-dissipative dynamics, revealing new geometric insights.

Contribution

It introduces a geometric framework for qubit dynamics using action-angle variables, highlighting the manifold structures underlying dissipative and non-dissipative evolutions.

Findings

Trajectories are geodesics on specific manifolds.

Geometry and topology of qubit manifolds are characterized.

Special physical cases reveal manifold properties.

Abstract

The trajectories of a qubit dynamics over the two-sphere are shown to be geodesics of certain Riemannian or physically-sound Lorentzian manifolds, both in the non-dissipative and dissipative formalisms, when using action-angle variables. Several aspects of the geometry and topology of these manifolds (qubit manifolds) have been studied for some special physical cases.