Density of Avoided Crossings and Diabatic Representation

Round 1

Reviewer 1 Report

Obzhirov and Heller

The paper considers time-dependent dynamics of a complex quantum system, using simulations of a model for the evolution of electronic states graphene in response to thermal fluctuations of nuclear coordinates as an example. The authors discuss possible connections with the Landau-Zener process, which allows non-adiabatic transitions close to points of near-degeneracy. There is some discussion of using random matrix theory to model statistics of degeneracies in multi-parameter Hamiltonians.

The results of the dynamical simulation of the graphene model indicate that the dynamics is slower in the diabatic (as opposed to adiabatic) representation. This implies that looking at dynamics in the adiabatic basis may not actually be the efficient approach for this system (presumably the variation of the Hamiltonian is just too fast). So the emphasis on Landau-Zener and near degeneracies appears somewhat tangential.

The numerical investigation summarised in figures 2 and 3 is new, so this does qualify as a publishable contribution. but I didn't find much else that is novel here. The paper is clearly written and appears to have been carefully proof-read.

There is a very obvious omission from the cited references, introducing many of the ideas which are explored in this work. The role of Landau-Zener transitions in the response of a complex quantum system to a specified time-dependent change of parameters was addressed in

M. Wilkinson, (1988) J. Phys. A21 4021

This paper also introduces the type of parametric random matrix model which appears as equation (3) in this paper, and used these models to obtain results on near degeneracies such as equation (13). This omission should be remedied. I believe that the particular version of the parametric random matrix Hamiltonian appearing in equation (3) first appears in M. Wilkinson and E. J. Austin, (1990), J. Phys. A23 L957.

I recommend publication after adding the reference(s) mentioned above.

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Reviewer 2 Report

A file attached.

Comments for author File: Comments.pdf

Author Response

Dear Referee,

Thank you for reading our manuscript and for your comments. We are grateful for the positive evaluation. We are currently developing the ideas presented in the section 4 of our manuscript and will submit another manuscript.