SciPost logo

SciPost Submission Page

Semiconductor Electron-Phonon Equations: a Rung Above Boltzmann in the Many-Body Ladder

by Gianluca Stefanucci, Enrico Perfetto

This Submission thread is now published as

Submission summary

Authors (as registered SciPost users): Gianluca Stefanucci
Submission information
Preprint Link: scipost_202311_00010v2  (pdf)
Date accepted: 2024-03-04
Date submitted: 2024-01-12 13:25
Submitted by: Stefanucci, Gianluca
Submitted to: SciPost Physics
Ontological classification
Academic field: Physics
  • Condensed Matter Physics - Theory
Approach: Theoretical


Starting from the {\em ab initio} many-body theory of electrons and phonons, we go through a series of well defined simplifications to derive a set of coupled equations of motion for the electronic occupations and polarizations, nuclear displacements as well as phononic occupations and coherences. These are the semiconductor electron-phonon equations (SEPE), sharing the same scaling with system size and propagation time as the Boltzmann equations. At the core of the SEPE is the {\em mirrored} Generalized Kadanoff-Baym ansatz (GKBA) for the Green's functions, an alternative to the standard GKBA which we show to lead to unstable equilibrium states. The SEPE treat coherent and incoherent degrees of freedom on equal footing, widen the scope of the semiconductor Bloch equations and Boltzmann equations, and reduce to them under additional simplifications. The new features of the SEPE pave the way for first-principles studies of phonon squeezed states and coherence effects in time-resolved absorption and diffraction experiments.

List of changes

List of changes

1) We have realized that the full HSEX contribution can be included in Eq.(61). With the new definitions in Eqs.(62) and (63) the purely electronic SEPE becomes equivalent to the time-dependent HSEX approximation for vanishing scattering terms.

2) Brief discussions have been added following the suggestions of the Referees, see our reply to points 2, 4, 5, 8, 10, and 11 of Referee 1 and points 1, 6, 7, and 9 of Referee 2

3) Addition of Appendix C "H-theorem for coupled electron-phonon systems"

Published as SciPost Phys. 16, 073 (2024)

Reports on this Submission

Report 2 by Claudio Verdozzi on 2024-2-26 (Invited Report)

  • Cite as: Claudio Verdozzi, Report on arXiv:scipost_202311_00010v2, delivered 2024-02-26, doi: 10.21468/SciPost.Report.8620


1) This work introduces a new approach (SEPE) to the optical response of semiconductors
2) The approach provide an unified perspective of methods like the Bethe Salpether equation, the Boltzmann equation, the Bloch equations.
3) At the same time, it offers an equal footing account of the coherent and incoherent dynamics of phonons, and the influence of these (via renormalization of the quasi-particle energies) on the
4) A proof of the Boltzmann's H-theorem is given


No particular weaknesses


Following the indications of the editor and the referees,
in the revised paper the authors have introduced a number of changes which
have further improved the overall readability of the manuscript (which was in fact already quite readable), and helped to clarify a number of specific points.

In particular, my previous observations and requests of change are satisfactorily addressed in the new version. I thus have only two remarks about the latter, concerning i) the MGKBA and ii) the introduction of the proof of the Boltzmann’s H-theorem fo the e-ph systems.

With respect to i), there is now a reference in Sect. 5.1 to previous work [60].
I think it might be preferable to refer to [60] already in the introduction to the paper, for a broader historical context for MGKBA.

Concerning ii), I found the proof of the H-theorem quite interesting. My suggestion here is that it might be appropriate for readability to state more explicitly that the total entropy of the e-ph system is written as S_e+S_ph in the context of the Boltzmann equation formulation (in general, in the presence of interactions, eqs.104 too would take a more general form).

Aside from these two minor points (and the possible related small changes by the authors), I recommend that the paper is published in the present form.

Requested changes

Two minor optional changes, see above

  • validity: top
  • significance: top
  • originality: top
  • clarity: high
  • formatting: excellent
  • grammar: excellent

Author:  Gianluca Stefanucci  on 2024-02-27  [id 4327]

(in reply to Report 2 by Claudio Verdozzi on 2024-02-26)

We thank the reviewer for his/her suggestions. In the resubmitted version we have changed the manuscript accordingly.

Report 1 by Dino Novko on 2024-1-30 (Invited Report)


I thank the authors for providing a detailed explanations on my comments and questions. I fully support the publication of the new and improved version of the manuscript.

  • validity: top
  • significance: high
  • originality: high
  • clarity: high
  • formatting: excellent
  • grammar: excellent

Login to report or comment