Comments and Questions

I am afraid, I could not follow the main idea of the paper at all. The presentation is certainly very confusing. In section 2, the authors describe the Hamiltonian (expression 1) of non-interacting electrons on a general N X 2M rectangular strip(lattice) (Moebius or not). As mentioned, the external field phase kinetic term could accommodate the changes in the electron spin states, without the twist on the strip. (and can be introduced with the twist without the field term). More importantly, the fermion operators (denoted here by a or a-dagger) here act on the many electron states and change the (dynamic) states accordingly. After presenting this formalism, the authors go to section 3, where for N stakeholders and 2M 'activities', a "Hamiltonian"like cost function is formulated in eqn (2) (in page 11), where the a's are now (real) numbers (and no longer operators, with real eigenvalues), with some superficial similarity with Hamiltonian(1) (in page 8). How does it help to map? Is there any connection of section 3 with section 2? In any case, the optimization of the cost function in (2) can be done independently, as has been done here, essentially without any reference to electron spin statechanges: the algebra are quite different: how are the operator algebra required to deal with the Hamiltonian (1) in section 2 (which is not discussed here of course) useful for the real number algebra and optimization of the cost function (2) in section 3? There seems to be some serious flaws in the design of the paper, or I am missing perhaps something important. The presentation in the paper needs to be much more clear and straightforward before the merit of the paper can be judged.