Pith. sign in

REVIEW 2 major objections 4 minor 54 references

Inverse determination of light-matter coupling in disordered systems from transmittance spectra

T0 review · 2 major / 4 minor · reviewed 2026-08-03 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read Inverting transmittance spectra recovers electron-photon coupling in disordered conductors, with the sharpest retrieval in multi-band systems where photon-assisted hopping opens in-gap transmission.

desk verdict A clean numerical proof-of-concept for extracting gamma from transmittance via QIP, but the single-sample case is never tested and the ergodic assumption does the heavy lifting. read the letter →

arxiv 2511.12647 v3 pith:J4UCGH3W submitted 2025-11-16 cond-mat.mes-hall cond-mat.dis-nn

Thales F. Macedo , Julián Faúndez , Antônio S. Coelho , Caio Lewenkopf , Mauro S. Ferreira , Felipe A. Pinheiro , Natanael C. Costa This is my paper · ORCID
classification cond-mat.mes-hallcond-mat.dis-nn
keywords quantuminverseproblemtransmittancelight-mattercouplingopticalcavitydisorderedsystemsAndersonmodelAubry-Andre-HarpernonequilibriumGreen'sfunctions
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper tries to establish that the electron-photon coupling strength of a disordered conductor embedded in an optical cavity can be read off from its energy-resolved transmittance spectrum alone, by minimizing a misfit function that compares the measured spectrum to a disorder-averaged model prediction. Using the Anderson model as a benchmark, the authors show that the minimum of this misfit function lands on the input coupling and disorder strength, though the minimum is broad and shallow. In the Aubry-Andre-Harper model, a multi-band system with a metal-insulator transition, the same protocol yields minima about two orders of magnitude sharper, because photon-assisted hopping produces finite transmission inside the bare spectral gaps, making the misfit far more sensitive to the coupling parameter. If this holds, transport measurements—which require no direct optical access—could serve as a spectroscopic tool for cavity quantum materials, especially in multi-band or quasiperiodic systems.

What carries the argument

The central object is the misfit function χ(Ω), the energy-window average of the squared difference between the logarithm of the true transmittance and the logarithm of the disorder-averaged model transmittance, computed from the elastic T_00 channel of the nonequilibrium Green's function formalism; the unknown Ω is {γ, W}. Minimizing χ relies on the ergodic hypothesis that one realization's window-averaged log-transmittance equals the disorder average. The mechanism that sharpens the minimum in the AAH model is photon-assisted hopping generated by the Peierls phase exp[iγ(b+b†)] in the hopping term, which opens transmission inside the bare spectral gaps.

What would settle it

Take a single, fixed disorder realization (one Anderson potential profile or one AAH phase φ) as T_true, compute χ(γ) for that one spectrum without any averaging over realizations, and check whether the minimum still sits at the known input γ; a shifted or shallow minimum indicates the ergodic hypothesis fails for realistic sample sizes. An even more direct test is to measure the transmittance of a single cavity-coupled nanowire and independently extract γ from vacuum Rabi splitting, then see whether inversion of the one transmittance trace reproduces that γ.

Watch

Extended reading notes

Core claim

The central claim is that the quantum inverse problem applied to transmittance spectra can accurately determine the light-matter coupling strength γ (and, in the Anderson model, the disorder strength W) in 1D disordered systems strongly coupled to a single-mode cavity. The authors compute the transmittance with nonequilibrium Green's functions including photon-assisted hopping via a Peierls substitution, define a misfit function χ(γ,W) as the energy-window average of the squared difference between a 'true' (synthetic) transmittance and the configurational average over ~10^3 disorder realizations, and show that the minimum of χ recovers the input parameters for both the Anderson and the Aubry

Load-bearing premise

The load-bearing premise is the ergodic hypothesis that the energy-window-averaged transmittance of a single disorder realization is the same as the disorder-averaged transmittance; the paper compares a single 'true' spectrum to a 1000-realization average, but the reported misfit curves are themselves averaged over many realizations, so the assumption that one real sample will self-average over the chosen window is never directly tested.

Editorial extensions

If this is right

  • The protocol pinpoints the input electron-photon coupling (γ=0.15) and disorder strength (W=0.5) in the Anderson model from transmittance spectra alone, with the minimum sharpening as the chain grows.
  • In the Aubry-Andre-Harper model, the misfit minima at γ=0.10 are roughly two orders of magnitude deeper than in the Anderson model, so multi-band systems with gaps are significantly better targets for inverse characterization.
  • Photon-assisted hopping opens finite transmission inside the bare gaps of a multi-band system; the mechanism is argued to be generic, so similar inversion sensitivity should hold in other multi-band cavity-QED conductors.
  • Because the Peierls coupling is general, the approach extends to higher-dimensional and multi-band disordered systems, potentially turning conductance measurements into a spectroscopic tool for extracting cavity parameters such as γ, κ, detuning, and finesse.
  • Current circuit-QED and nanowire platforms operate at coupling strengths (tens to hundreds of MHz), quality factors (~10^2–10^4), and millikelvin temperatures that fall in the range where the protocol should work, making near-term experimental tests plausible.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The gap-opening mechanism suggests that the highest-information regions of a transmittance spectrum for extracting light-matter coupling are the band edges and gaps, not the band interiors; a practical inversion would need an automated rule for locating those regions since the paper fixes the window rather than choosing it from data.
  • The ergodic assumption is only tested in ensemble-averaged misfit curves; a single-sample transmittance trace may not self-average over the chosen window, so a real-device protocol would need to validate or modify the window using the data itself.
  • The analysis restricts to the elastic T_00 channel at zero bias; at finite bias or finite temperature, inelastic T_NM channels become relevant, and it is an open question whether the sharp minimum survives—an extension that could be tested with the same Green's-function machinery.
Share X Bluesky LinkedIn Reddit HN

Signed reviews

No signed human review yet.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

2 major / 4 minor

Summary. The paper proposes an inverse-problem method to extract the electron-photon coupling strength γ and disorder strength W from transmittance spectra of 1D disordered conductors embedded in a single-mode optical cavity. The forward model uses the Peierls substitution to couple electronic hopping to a quantized cavity mode, and the transmittance is computed within the nonequilibrium Green's function formalism with a photon-number cutoff. The inversion minimizes a misfit function χ(Ω) that compares a 'true' transmittance spectrum to the disorder-averaged model prediction, and the method is benchmarked on the Anderson and Aubry-André–Harper (AAH) models using synthetic data. The authors report that the minima of χ recover the input parameters for both models, with the AAH model giving markedly sharper minima due to cavity-induced in-gap transmission. They argue the method is a practical spectroscopic tool for cavity quantum materials.

Significance. If the central claim is sound, this work would provide a transport-based route to determining cavity QED parameters in disordered conductors, complementing standard optical characterization. The forward NEGF machinery is nontrivial and carefully implemented, and the paper explicitly tests photon-number convergence and system-size dependence. The observation that multi-band AAH systems produce sharper misfit minima than single-band Anderson systems is physically interesting. However, the validation is entirely synthetic and, more importantly, the misfit function actually used in the paper is an ensemble average over many disorder realizations. The manuscript asserts but does not test the ergodic hypothesis needed to justify applying the method to a single experimental sample. This gap directly affects the central claim that parameters can be extracted 'directly from transmittance spectra' in practice.

major comments (2)
  1. [Section II.E, Eq. (12), and Figs. 4–6, 8] The reported misfit is the average χ(Ω) = (1/N_r) Σ_r χ_r(Ω) over N_r true realizations, not the misfit of a single spectrum. The ergodic hypothesis stated in Sec. II.E — that energy-window averaging over one configuration equals disorder averaging — is never tested. For both the Anderson model (where ln T(E) for a single sample is spiky) and the AAH model (where transmittance depends strongly on the global phase φ), individual χ_r(Ω) may have minima scattered away from the true parameters even if the ensemble-averaged χ(Ω) has a sharp minimum. Since a real experiment measures one sample, the authors should provide single-realization χ_r(γ,W) curves, histograms of the inferred minima, or a quantitative variance analysis. Without this, the demonstrated minima in Figs. 4, 5, 6, and 8 could be artifacts of averaging, and the central claim of extracting parameters from an experimentally meas
  2. [Section III.A, near Figs. 4 and 5] The energy-integration window [0,2t] is chosen because the text states that cavity-induced modifications to T(E) are strongest near the upper band edge and that windows near the bottom of the band yield 'very shallow minima.' This is a post hoc selection based on knowledge of where the signal lies. In an experimental setting, where γ and W are unknown, it is not clear how the window would be chosen without prior information. The paper should either test robustness of the inversion across a range of windows (including windows covering the full band) or propose a data-driven criterion for selecting E_± from the measured spectrum itself. Otherwise the claim that the method works 'directly from transmittance spectra' is weakened by an implicit dependence on model-informed window selection.
minor comments (4)
  1. [Section II.E] Eq. (12) defines χ in terms of T(E), but the text immediately says the misfit is evaluated for ln T(E). This inconsistency should be clarified, either by writing the logarithm explicitly in the equation or by explaining that Eq. (12) is schematic.
  2. [Section II.F] There is a typo: 'E− = 0 and E − = 2t' should read 'E_− = 0 and E_+ = 2t'.
  3. [Abstract and Conclusions] The phrase 'unparalleled precision' is overclaimed given that only a single value of γ_true and a few V values are tested, and the single-sample issue is unresolved. More cautious wording would better match the evidence presented.
  4. [Section IV] The experimental-feasibility discussion is qualitative and does not address the single-shot statistical issue raised above. Also, the formatting '102 to 104' should be '10^2 to 10^4'.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the transmittance-to-coupling inversion is a genuine parameter search, and the paper does not define the target observable in terms of the fitted parameter.

full rationale

The central inversion is a non-trivial misfit minimization. The paper defines chi(Omega) as the squared deviation between a given T_true(E) and the configurationally averaged model prediction <T(E;Omega)> (Eq. 12), then searches the (gamma,W) domain. Recovering gamma_true/W_true from spectra generated at those values is a standard self-consistency test of an inverse procedure, not an identity or renaming: no equation in the paper reduces the recovered gamma to the input gamma by construction, and the misfit minimum is not imposed by the definition of chi. The QIP method is inherited from Refs. [25,26], whose authors overlap with the present paper, and the AAH phase-boundary information is cited from Ref. [40] by the same group; however, these are published, externally checkable results used as tools rather than as unverified uniqueness constraints, and the present work adds an independent numerical demonstration for the cavity-coupled Anderson and AAH models. The paper's weaker point is the ergodic hypothesis of Sec. II.E: the reported chi minima are averages over N_r realizations, so the single-sample behavior that an experiment would face is not demonstrated. This is a robustness/correctness limitation, not circularity, and the manuscript itself acknowledges related limitations (photon loss, device disorder) in Sec. IV and the Conclusions. Because no load-bearing step equates the prediction to its inputs by definition, the circularity score is 0.

Assumptions & free parameters 3 free parameters · 6 assumptions · 0 invented entities

The central claim rests on modeling assumptions about the cavity (single lossless mode, dipole approximation, no coupling in leads) and on the ergodic hypothesis that lets a single spectrum be compared to an ensemble average. The hand-chosen energy window and photon cutoff are pragmatic numerical choices that affect the reliability of the inversion. No new physical entities are introduced.

free parameters (3)
  • Energy integration window [E-,E+] = [0, 2t]
    Chosen post hoc because cavity effects are strongest near the top of the band; the paper states that windows near the bottom produce shallow minima and ineffective inversion.
  • Photon-number cutoff N_ph = 5
    Chosen based on convergence test at gamma=0.2 (relative error ~1%); assumed valid for smaller gamma.
  • Use of ln T in the misfit = logarithmic misfit
    Chosen to enhance the misfit response for localized states; it changes the shape of chi and is not derived from first principles.
assumptions (6)
  • domain assumption NEGF/Landauer-Büttiker formalism applies to the coupled electron-photon system with the photon sector treated exactly via cutoff (Eqs. 9-10).
    The transmission T_00 is assumed to give the full conductance at T=0; virtual photon processes are included via dressed Green's functions (Sec. II.D).
  • domain assumption Electron-photon coupling vanishes in the leads; lead self-energies are diagonal in photon number (Eq. 8).
    Sec. II.D explicitly assumes coupling only in the central region; if leads couple to the cavity, the self-energy structure changes.
  • domain assumption Single-mode dipole approximation for the cavity with uniform vector potential; Peierls substitution with phase gamma(b+b†), neglecting other modes and UV cutoff (Eqs. 3-5).
    Sec. II.C; relies on lambda_EM >> a and a macroscopically effective single mode per Ref. 45.
  • domain assumption Ergodic hypothesis: single-configuration energy-window average equals configuration average (Sec. II.E).
    Justifies comparing one 'true' realization to <T(E;Omega)> over 1000 configurations; central to the QIP.
  • domain assumption Cavity is closed: photon loss kappa = 0; effects of kappa and master-equation dynamics are beyond scope (Sec. IV).
    Experimental transmittance includes loss; the paper's model does not.
  • standard math Baker-Campbell-Hausdorff and standard matrix inversion are used to build the Hamiltonian in the |j,N> basis.
    Sec. II.C.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Inverse determination of light-matter coupling in disordered systems from transmittance spectra." pith.science (2026). https://pith.science/paper/J4UCGH3W

@misc{pith2026251112647,
  author       = {Pith},
  title        = {Pith review of: Inverse determination of light-matter coupling in disordered systems from transmittance spectra},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/J4UCGH3W}},
  note         = {Machine review of arXiv:2511.12647}
}
read the original abstract

We investigate quantum inverse problems in one-dimensional (1D) electronic disordered systems strongly coupled to optical cavities. More specifically, we consider the Anderson and the Aubry-Andre-Harper models connected to electronic reservoirs and embedded in a single-mode optical cavity. The light-matter interaction enables photon-assisted hopping processes that significantly modify the transmittance spectrum. Within the nonequilibrium Green's function formalism, we implement an inversion-based approach capable of accurately extracting the electron-photon coupling strength directly from transmittance spectra. While cavity coupling acts as a minor perturbation within the Anderson model, yielding broad yet precise parameter estimates, its influence is markedly different in the Aubry-Andr\'e-Harper model. The latter exhibits a sharp metal-insulator transition in 1D, thus resulting in more pronounced cavity-induced spectral changes. This renders even more accurate inverse solutions, offering unparalleled precision in the characterization of low-dimensional disordered systems. Altogether, our results demonstrate that the quantum inverse problem provides a robust diagnostic tool for quantum materials, particularly effective for systems exhibiting metal-insulator transitions.

Figures

Figures reproduced from arXiv: 2511.12647 by the authors.

Figure 1
Figure 1. FIG. 1. (a) Schematic illustration of an 1D chain embedded in [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2. Relative error for the integrated transmittance [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3. Disorder-averaged logarithm of the transmittance, [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figures from the paper (3 more)
Figure 6
Figure 6. Figure 6: FIG. 6. Contour map of the averaged misfit function [PITH_FULL_IMAGE:figures/full_fig_p007_6.png]
Figure 8
Figure 8. Figure 8: FIG. 8. Averaged misfit function [PITH_FULL_IMAGE:figures/full_fig_p008_8.png]
Figure 9
Figure 9. Figure 9: FIG. 9. Logarithm of the transmittance, ln[ [PITH_FULL_IMAGE:figures/full_fig_p009_9.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

54 extracted references · 1 linked inside Pith

  1. [1]

    Ritsch, P

    H. Ritsch, P. Domokos, F. Brennecke, and T. Esslinger, Cold atoms in cavity-generated dynamical optical poten- tials, Rev. Mod. Phys.85, 553 (2013)

    2013

  2. [2]

    Schlawin, A

    F. Schlawin, A. Cavalleri, and D. Jaksch, Cavity- mediated electron-photon superconductivity, Phys. Rev. Lett.122, 133602 (2019)

    2019

  3. [3]

    Schlawin, D

    F. Schlawin, D. M. Kennes, and M. A. Sentef, Cavity quantum materials, Appl. Phys. Rev.9, 011312 (2022)

    2022

  4. [4]

    Orgiu, J

    E. Orgiu, J. George, J. A. Hutchison, E. Devaux, J. F. Dayen, B. Doudin, F. Stellacci, C. Genet, J. Schachen- mayer, C. Genes, G. Pupillo, P. Samor ` ı, and T. W. Ebbe- sen, Conductivity in organic semiconductors hybridized with the vacuum field, Nat. Mater.14, 1123 (2015)

    2015

  5. [5]

    L´ eonard, A

    J. L´ eonard, A. Morales, P. Zupancic, T. Esslinger, and T. Donner, Supersolid formation in a quantum gas break- ing a continuous translational symmetry, Nature543, 87 (2017)

    2017

  6. [6]

    L´ eonard, A

    J. L´ eonard, A. Morales, P. Zupancic, T. Donner, and T. Esslinger, Monitoring and manipulating Higgs and Goldstone modes in a supersolid quantum gas, Science 358, 1415 (2017)

    2017

  7. [7]

    Landig, L

    R. Landig, L. Hruby, N. Dogra, M. Landini, R. Mottl, T. Donner, and T. Esslinger, Quantum phases from com- peting short-and long-range interactions in an optical lat- tice, Nature532, 476 (2016)

    2016

  8. [8]

    Klinder, H

    J. Klinder, H. Keßler, M. R. Bakhtiari, M. Thorwart, and A. Hemmerich, Observation of a superradiant Mott insulator in the Dicke-Hubbard model, Phys. Rev. Lett. 115, 230403 (2015)

    2015

Show all 54 references
  1. [9]

    V. D. Vaidya, Y. Guo, R. M. Kroeze, K. E. Ballantine, A. J. Koll´ ar, J. Keeling, and B. L. Lev, Tunable-range, photon-mediated atomic interactions in multimode cav- ity QED, Phys. Rev. X8, 011002 (2018)

    2018

  2. [10]

    Budden, T

    M. Budden, T. Gebert, M. Buzzi, G. Jotzu, E. Wang, T. Matsuyama, G. Meier, Y. Laplace, D. Pontiroli, M. Ricc` o, F. Schlawin, D. Jaksch, and A. Cavalleri, Evi- dence for metastable photo-induced superconductivity in K3C60, Nat. Phys.17, 611 (2021)

    2021

  3. [11]

    Appugliese, J

    F. Appugliese, J. Enkner, G. L. Paravicini-Bagliani, M. Beck, C. Reichl, W. Wegscheider, G. Scalari, C. Ciuti, and J. Faist, Breakdown of topological protection by cav- ity vacuum fields in the integer quantum Hall effect, Sci- ence375, 1030 (2022)

    2022

  4. [12]

    Hagenm¨ uller, J

    D. Hagenm¨ uller, J. Schachenmayer, S. Sch¨ utz, C. Genes, and G. Pupillo, Cavity-enhanced transport of charge, Phys. Rev. Lett.119, 223601 (2017)

    2017

  5. [13]

    Svintsov, G

    D. Svintsov, G. Alymov, Z. Devizorova, and L. Martin- Moreno, One-dimensional electron localization in semi- conductors coupled to electromagnetic cavities, Phys. Rev. B109, 045432 (2024)

    2024

  6. [14]

    Hagenm¨ uller, S

    D. Hagenm¨ uller, S. Sch¨ utz, J. Schachenmayer, C. Genes, and G. Pupillo, Cavity-assisted mesoscopic transport of fermions: Coherent and dissipative dynamics, Phys. Rev. B97, 205303 (2018). 12

    2018

  7. [15]

    X.-Y. Lu, X. Liu, Q.-L. Tian, H. Wang, J.-J. Wang, and L.-X. Yan, Finesse measurement for high-power op- tical enhancement cavity, Chinese Physics B33, 014205 (2023)

    2023

  8. [16]

    K. S. Menghrajani, A. B. Vasista, W. J. Tan, P. A. Thomas, F. Herrera, and W. L. Barnes, Molecular strong coupling and cavity finesse, The Journal of Physical Chemistry Letters15, 7449 (2024)

    2024

  9. [17]

    J. D. Fischbach, S. Gladyshev, A. C. Valero, M. Ny- man, T. Weiss, and C. Rockstuhl, Resonant states re- veal strong light-matter coupling in nanophotonic cavi- ties, arXiv:2511.03468 (2025)

    2025 arXiv

  10. [18]

    M. S. Rider, E. C. Johnson, D. Bates, W. P. Wardley, R. H. Gordon, R. D. J. Oliver, S. P. Armes, G. J. Leggett, and W. L. Barnes, Strong coupling in molecular systems: a simple predictor employing routine optical measure- ments, Nanophotonics13, 2453 (2024)

    2024

  11. [19]

    Lalanne, W

    P. Lalanne, W. Yan, K. Vynck, C. Sauvan, and J.-P. Hugonin, Light interaction with photonic and plasmonic resonances, Laser Photonics Rev.12, 1700113 (2018)

    2018

  12. [20]

    Hertzog, M

    M. Hertzog, M. Wang, J. Mony, and K. B¨ orjesson, Strong light–matter interactions: a new direction within chem- istry, Chem. Soc. Rev.48, 937 (2019)

    2019

  13. [21]

    A. F. Kockum, A. Miranowicz, S. D. Liberato, S. Savasta, and F. Nori, Ultrastrong coupling between light and mat- ter, Nat. Rev. Phys.1, 19 (2019)

    2019

  14. [22]

    E. Baum, A. Broman, T. Clarke, N. C. Costa, J. Mucciac- cio, A. Yue, Y. Zhang, V. Norman, J. Patton, M. Radu- laski, and R. T. Scalettar, Effect of emitters on quantum state transfer in coupled cavity arrays, Phys. Rev. B105, 195429 (2022)

    2022

  15. [23]

    Saxena, A

    A. Saxena, A. Manna, R. Trivedi, and A. Majumdar, Re- alizing tight-binding hamiltonians using site-controlled coupled cavity arrays, Nat. Commun.14, 5260 (2023)

    2023

  16. [24]

    Patton, V

    J. Patton, V. A. Norman, E. C. Mann, B. Puri, R. T. Scalettar, and M. Radulaski, Polariton creation in cou- pled cavity arrays with spectrally disordered emitters, Mater. Quantum. Technol4, 025401 (2024)

    2024

  17. [25]

    Mukim, F

    S. Mukim, F. P. Amorim, A. R. Rocha, R. B. Muniz, C. Lewenkopf, and M. S. Ferreira, Disorder information from conductance: A quantum inverse problem, Phys. Rev. B102, 075409 (2020)

    2020

  18. [26]

    Mukim, C

    S. Mukim, C. Lewenkopf, and M. Ferreira, Spatial map- ping of disordered 2d systems: The conductance sudoku, Carbon188, 360 (2022)

    2022

  19. [27]

    F. R. Duarte, F. Matusalem, D. Grasseschi, A. R. Rocha, L. Seixas, C. J. S. de Matos, S. Mukim, and M. S. Fer- reira, Decoding disorder signatures of AuCl 3 and vacan- cies in MoS2 films: from synthetic to experimental inver- sion, J. Phys. Condens. Matter36, 495901 (2024)

    2024

  20. [28]

    Mukim, M

    S. Mukim, M. E. Kucukbas, S. R. Power, and M. S. Fer- reira, Edge disorder and magnetism in graphene nanorib- bons: an inverse modelling approach, J. Phys. Condens. Matter37, 185302 (2025)

    2025

  21. [29]

    P. W. Anderson, Absence of diffusion in certain random lattices, Phys. Rev.109, 1492 (1958)

    1958

  22. [30]

    Abrahams, P

    E. Abrahams, P. W. Anderson, D. C. Licciardello, and T. V. Ramakrishnan, Scaling theory of localization: Ab- sence of quantum diffusion in two dimensions, Phys. Rev. Lett.42, 673 (1979)

    1979

  23. [31]

    P. A. Lee and T. V. Ramakrishnan, Disordered electronic systems, Rev. Mod. Phys.57, 287 (1985)

    1985

  24. [32]

    P. G. Harper, Single band motion of conduction electrons in a uniform magnetic field, Proc. Phys. Soc. A68, 874 (1955)

    1955

  25. [33]

    Aubry and G

    S. Aubry and G. Andr´ e, Analyticity breaking and Ander- son localization in incommensurate lattices, Ann. Israel Phys. Soc3, 18 (1980)

    1980

  26. [34]

    Meir and N

    Y. Meir and N. S. Wingreen, Landauer formula for the current through an interacting electron region, Phys. Rev. Lett.68, 2512 (1992)

    1992

  27. [35]

    Haug and A

    H. Haug and A. Jauho,Quantum Kinetics in Transport and Optics of Semiconductors, Springer Series in Solid- State Sciences (Springer Berlin Heidelberg, 2007)

    2007

  28. [36]

    Datta,Electronic Transport in Mesoscopic Systems (Cambridge University Press, Cambridge, 1997)

    S. Datta,Electronic Transport in Mesoscopic Systems (Cambridge University Press, Cambridge, 1997)

    1997

  29. [37]

    Markos, Numerical analysis of the Anderson localiza- tion, Acta Phys

    P. Markos, Numerical analysis of the Anderson localiza- tion, Acta Phys. Slovaca56, 561 (2006)

    2006

  30. [38]

    G. A. Dom ´ ınguez-Castro and R. Paredes, The Aubry–Andr´ e model as a hobbyhorse for under- standing the localization phenomenon, Eur. J. Phys.40, 045403 (2019)

    2019

  31. [39]

    S. N. Evangelou and J.-L. Pichard, Critical quantum chaos and the one-dimensional Harper model, Phys. Rev. Lett.84, 1643 (2000)

    2000

  32. [40]

    T. F. Macedo, J. Fa´ undez, R. R. dos Santos, N. C. Costa, and F. A. Pinheiro, Multifractal critical phase driven by coupling quasiperiodic systems to electromagnetic cavi- ties, Phys. Rev. B112, 174202 (2025)

    2025

  33. [41]

    Peierls, Zur theorie des diamagnetismus von leitungse- lektronen, Zeitschrift f¨ ur Physik80, 763 (1933)

    R. Peierls, Zur theorie des diamagnetismus von leitungse- lektronen, Zeitschrift f¨ ur Physik80, 763 (1933)

    1933

  34. [42]

    M. P. Marder,Condensed Matter Physics, 2nd ed. (John Wiley & Sons, Hoboken, NJ, 2010)

    2010

  35. [43]

    Cresti, Convenient Peierls phase choice for periodic atomistic systems under magnetic field, Phys

    A. Cresti, Convenient Peierls phase choice for periodic atomistic systems under magnetic field, Phys. Rev. B 103, 045402 (2021)

    2021

  36. [44]

    J. Li, D. Golez, G. Mazza, A. J. Millis, A. Georges, and M. Eckstein, Electromagnetic coupling in tight-binding models for strongly correlated light and matter, Phys. Rev. B101, 205140 (2020)

    2020

  37. [45]

    J. Li, L. Schamriß, and M. Eckstein, Effective theory of lattice electrons strongly coupled to quantum electromag- netic fields, Phys. Rev. B105, 165121 (2022)

    2022

  38. [46]

    Mikami, S

    T. Mikami, S. Kitamura, K. Yasuda, N. Tsuji, T. Oka, and H. Aoki, Brillouin-wigner theory for high-frequency expansion in periodically driven systems: Application to floquet topological insulators, Phys. Rev. B93, 144307 (2016)

    2016

  39. [47]

    Datta,Quantum Transport: Atom to Transistor (2005)

    S. Datta,Quantum Transport: Atom to Transistor (2005)

    2005

  40. [48]

    Hern´ andez, V

    A. Hern´ andez, V. M. Apel, F. A. Pinheiro, and C. H. Lewenkopf, Quantum electronic transport: Linear and nonlinear conductance from the Keldysh approach, Phys- ica A385, 148 (2007)

    2007

  41. [49]

    M. R. Delbecq, V. Schmitt, F. D. Parmentier, N. Roch, J. J. Viennot, G. F` eve, B. Huard, C. Mora, A. Cottet, and T. Kontos, Coupling a quantum dot, fermionic leads, and a microwave cavity on a chip, Phys. Rev. Lett.107, 256804 (2011)

    2011

  42. [50]

    G.-W. Deng, D. Wei, S.-X. Li, J. Johansson, W.-C. Kong, H.-O. Li, G. Cao, M. Xiao, G.-C. Guo, F. Nori, H.-W. Jiang, and G.-P. Guo, Coupling two distant double quan- tum dots with a microwave resonator, Nano Lett.15, 6620 (2015)

    2015

  43. [51]

    G.-W. Deng, D. Zhu, X.-H. Wang, C.-L. Zou, J.-T. Wang, H.-O. Li, G. Cao, D. Liu, Y. Li, M. Xiao, G.-C. Guo, K.- L. Jiang, X.-C. Dai, and G.-P. Guo, Strongly coupled nanotube electromechanical resonators, Nano Lett.16, 13 5456 (2016)

    2016

  44. [52]

    T. R. Hartke, Y.-Y. Liu, M. J. Gullans, and J. R. Petta, Microwave detection of electron-phonon interactions in a cavity-coupled double quantum dot, Phys. Rev. Lett. 120, 097701 (2018)

    2018

  45. [53]

    Jiang, T.-Y

    S.-L. Jiang, T.-Y. Jiang, Y.-Q. Xu, R. Wu, T.-Y. Hao, S.-K. Ye, R.-R. Cai, B.-C. Wang, H.-O. Li, G. Cao, and G.-P. Guo, Coupling and characterization of a Si/SiGe triple quantum dot array with a microwave resonator, Chinese Physics B33, 090311 (2024)

    2024

  46. [54]

    K. D. Petersson, L. W. McFaul, M. D. Schroer, M. Jung, J. M. Taylor, A. A. Houck, and J. R. Petta, Circuit quan- tum electrodynamics with a spin qubit, Nature490, 380 (2012)

    2012

Pith tools

Reviewed August 3, 2026 · model on record in the stance chip above.