Classical simulation of relativistic quantum mechanics in periodic optical structures

May combine two claims.

The oscillatory motion mimicking ZB has been observed in binary arrays written in fused silica by femtosecond laser writing, providing the first simulation in optics of ZB.

“Such an oscillatory motion has been recently observed in Ref.[38] in binary arrays written in fused silica by the femtosecond laser writing technology [5], providing the first simulation in optics of ZB.”

• cites [38] Y.V. Kartashov, V.A. Vysloukh, L. Torner, Phys. Rev. Lett. 99, 233903 (2007) sourceDisputed

  On p. 2, the paper says it predicts Rabi-like flopping in modulated waveguides; on p. 6, it says its proposed array effect could be experimentally realized. It does not report an observation in femtosecond-written fused-silica binary arrays or identify its result as a first optical simulation of ZB. (LLM, conf=0.86)

  Checked by a reasoning model — may be wrong.

  Experimental — accuracy not yet measured
• cites [5] A. Szameit, S. Nolte, J. Phys. B 43, 163001 (2010) sourceSupported

May combine two claims.

The binary waveguide array supports two minibands separated by a narrow gap of width 2σ, with dispersion curves ω±(q)=±√(σ2+4κ2cos2(qa)).

“The superlattice supports two minibands, separated by a narrow gap of width 2 σ [see Fig.1(b)], defined by the dispersion curves ω ± ( q ) = ± √ σ 2 +4 κ 2 cos 2 ( qa ), where 2 a is the lattice period and q the Bloch wave number.”

• cites [35] S. Longhi, Phys. Rev. Lett. 97, 110402 (2006) sourceDisputed

  The model description (p. 2) specifies the same hopping amplitude throughout the periodic lattice, apart from its boundary site; the waveguide construction (p. 3) describes identical wells at equal spacing beyond that boundary. That is contrary to the claimed binary superlattice. The cited paper does not give the attributed two-miniband dispersion or gap of width 2σ. (LLM, conf=0.78)

  Checked by a reasoning model — may be wrong.

  Experimental — accuracy not yet measured

• AssumptionThe authors state this as an assumption: In the binary waveguide array, the tight-binding approximation applies to light transport.

Probably not a substantial claim: may not pass S3 (load-bearing).

Several recent works have shown that optical structures in media with a complex refractive index can provide an experimentally accessible test bed to simulate in a purely classical setting non-Hermitian features rooted in the non-relativistic Schrödinger equation with a complex potential.

“Several recent works have shown that optical structures in media with a complex refractive index can provide an experimentally accessible test bed to simulate in a purely classical setting non-Hermitian features rooted in the non-relativistic Schr¨ odinger equation with a complex potential [91,92,90,93,94,95,96].”

• cites [91] S. Longhi, Phys. Rev. B 81, 075102 (2010)Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

• cites [92] S. Longhi, Phys. Rev. A 81, 022118 (2010)Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

• cites [90] S. Longhi, Opt. Lett. 35, 235 (2010) sourcePartly supported

  Split into 2 atoms — 0 confirmed, 2 partially supported, 0 disputed, 0 misattributed, 0 unverifiable. Expand the claim to see per-atom verdicts.

  Experimental — accuracy not yet measured
• cites [93] F. Dreisow, M. Heinrich, R. Keil, A. Tünnermann, S. Nolte, S. Longhi, A. Szameit, Phys. Rev. Lett. 105, 143902 (2010) sourceNot checked — no full text of the source
• cites [94] S. Longhi, Phys. Res. Int. 2010, 645106 (2010) sourceDisputed

  The Introduction describes optical structures as an accessible test bed, but Section 2 (Quantum-Optical Analogy; page unavailable) explicitly identifies this grating’s analogue as the relativistic Dirac equation and its electrostatic potential. That is contrary to attributing to this paper a simulation of non-Hermitian features of a non-relativistic Schrödinger equation with a complex potential. (LLM, conf=0.88)

  Checked by a reasoning model — may be wrong.

  Experimental — accuracy not yet measured
• cites [95] S. Longhi, Opt. Lett. 35, 1302 (2010) sourcePartly supported

  The paper’s introduction and proposed setup describe an accessible classical optical analogue using fiber Bragg gratings. But the analogue is of the relativistic Dirac oscillator; the paper describes its nonrelativistic limit as a Schrödinger equation with a quadratic potential, not a study of non-Hermitian features of a Schrödinger equation with a complex potential. The relevant passages in our copy have no page labels. (LLM, conf=0.85)

  Experimental — accuracy not yet measured
• cites [96] S. Longhi, Cent. Eur. J. Phys. 9, 110 (2011) sourcePartly supported

  Split into 2 atoms — 0 confirmed, 1 partially supported, 0 disputed, 0 misattributed, 1 unverifiable. Expand the claim to see per-atom verdicts.

  Experimental — accuracy not yet measured

May combine two claims.

Because of the non-self-adjointness of H, spectral singularities could arise in the spectrum of H, corresponding to either a zero-width resonance in the transmission/reflection spectrum of the DFB (the threshold for self-oscillation) or to perfect absorption of radiation under a suitable two-port coherent excitation of the DFB structure.

“In addition, because of the non-self-adjointness of H , spectral singularities could arise in the spectrum of H , which correspond to either a zero-width resonance in the transmission/reflection spectrum of the DFB (the threshold for self-oscillation) [94,44] or to a perfect absorption of radiation under a suitable two-port coherent excitation of the DFB structure [44,102].”

• cites [94] S. Longhi, Phys. Res. Int. 2010, 645106 (2010) sourceCould not verify

  Split into 2 atoms — 0 confirmed, 0 partially supported, 0 disputed, 0 misattributed, 2 unverifiable. Expand the claim to see per-atom verdicts.

  Experimental — accuracy not yet measured
• cites [44] F. Dreisow, M. Ornigotti, A. Szameit, M. Heinrich, R. Keil, S. Nolte, A. Tunnermann, S. Longhi, Appl. Phys. Lett. 95, 261102 (2009) sourceNot checked — no full text of the source
• cites [102] S.H. Nam, A.J. Taylor, A. Efimov, Opt. Express 18, 10120 (2010) sourceDisputed

  Split into 2 atoms — 0 confirmed, 0 partially supported, 1 disputed, 0 misattributed, 1 unverifiable. Expand the claim to see per-atom verdicts.

  Checked by a reasoning model — may be wrong.

  Experimental — accuracy not yet measured

Probably not a substantial claim: may not pass S3 (load-bearing).

Zitterbewegung refers to the trembling motion of a freely moving relativistic quantum particle that arises from interference between the positive and negative energy states of the spinor wavefunction.

“Zitterbewegung (ZB) refers to the trembling motion of a freely moving relativistic quantum particle that arises from the interference between the positive (electron) and negative (positron) energy states of the spinor wavefunction [25,47].”

• cites [46] S. Longhi, Opt. Lett. 34, 2736 (2009) sourceCould not verify

  The paper’s discussion of optical analogues concerns molecular vibrational wave packets and crossings between potential surfaces (section labeled “Stefano Longhi”; page not provided). Searches for Zitterbewegung and for Dirac particles, electron–positron states, and their interference found no passage addressing the cited definition. (LLM, conf=0.76)

  Experimental — accuracy not yet measured
• cites [25] S. Longhi, Phys. Rev. B 80, 235102 (2009)Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

• cites [47] A. Szameit, F. Dreisow, M. Heinrich, R. Keil, S. Nolte, A. Tunnermann, S. Longhi, Phys. Rev. Lett. 104, 150403 (2010)Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

May combine two claims.

An exact expression for 〈ξ〉(z) can be derived and reads Eq.(4).

“Under such an assumption, an exact expression for 〈 ξ 〉 ( z ) can be derived and reads [35]”

• cites [35] S. Longhi, Phys. Rev. Lett. 97, 110402 (2006) sourceCould not verify

  Our copy derives an exact decay law for the site-occupation amplitude c₁(t) (p. 4), but no passage found gives an exact expression for 〈ξ〉(z). I searched for 〈ξ〉, mean position, and an expectation value as a function of propagation distance. The paper refers to its Eq. (4) as a decay-rate equation (p. 5), but the equation itself is not decoded in our copy. (LLM, conf=0.76)

  Experimental — accuracy not yet measured

May combine two claims.

This explains the inhibition of KT and the transition to the Sauter's regime.

“This explains the inhibition of KT and the transition to the Sauter's regime [50].”

• cites [50] S. Longhi, J. Phys. B 44, 051001 (2011) sourceCould not verify

  The discussion on pp. 4–8 concerns Josephson oscillations, self-trapping, and correlated pair tunneling in a Bose–Hubbard waveguide model. Searches for KT, Klein tunneling, and Sauter’s regime found no passage addressing inhibition of KT or a transition to Sauter’s regime. (LLM, conf=0.76)

  Experimental — accuracy not yet measured

Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

Electron-positron pair production due to the instability of the QED vacuum in an external electric field is a prediction of Dirac theory and its experimental observation is still lacking.

“Electron-positron pair production due to the instability of the quantum electrodynamics (QED) vacuum in an external electric field is another remarkable prediction of Dirac theory and regarded as one of the most intriguing nonlinear phenomena in QED, whose experimental observation is still lacking (see, for instance, [52, 53]).”

• cites [52] S. Longhi, Phys. Rev. A 83, 043835 (2011)Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

• cites [53] K.S. Novoselov, A.K. Geim, S.V. Morozov, D. Jiang, M.I. Katsnelson, I.V. Grigorieva, S.V. Dubonos, A.A. Firsov, Nature (London) 438, 197 (2005) sourceCould not verify

  The paper’s ‘Two-Dimensional Gas of Massless Dirac Fermions in Graphene’ section discusses graphene’s electron- and hole-like states and quantum Hall effect, not electron–positron pair production. Searches for QED-vacuum instability, pair creation in an electric field, and experimental observation found no passage addressing the claim. Page numbers are unavailable in our copy. (LLM, conf=0.75)

  Experimental — accuracy not yet measured

May combine two claims.

Klein tunneling arises from the existence of negative-energy solutions of the Dirac equation and requires a potential step height ΔV of the order of twice the rest energy mc2 of the electron.

“Such a transparency effect, originally predicted by Klein [26] and referred to as Klein tunneling (KT), arises from the existence of negative-energy solutions of the Dirac equation and requires a potential step height ∆V of the order of twice the rest energy mc 2 of the electron [49].”

• cites [26] G. Della Valle, S. Longhi, Opt. Lett. 35, 673 (2010) sourceNot checked — no full text of the source
• cites [49] S. Longhi, Opt. Lett. 36, 819 (2011) sourceCould not verify

  The discussion of dynamical trapping (pp. 1–3) concerns light in modulated waveguide lattices; its negative quasienergies are those of Floquet states, not negative-energy solutions of the Dirac equation. Searches for Klein tunneling, the Dirac equation, and a potential step of roughly twice the electron rest energy found no passage addressing the attributed claim. (LLM, conf=0.76)

  Experimental — accuracy not yet measured

May combine two claims.

Sauter showed that to observe barrier transparency the potential increase ΔV ≃ eEl should occur over a distance l of the order or smaller than the Compton wavelength λC, the transmission probability rapidly decaying toward zero for a smoother potential increase.

“Sauter showed that to observe barrier transparency the potential increase ∆V ≃ eEl should occur over a distance l of the order or smaller than the Compton wavelength λ C = ¯ h/ ( mc ), the transmission probability rapidly decaying toward zero for a smoother potential increase [49,50,51].”

• cites [50] S. Longhi, J. Phys. B 44, 051001 (2011) sourceCould not verify

  Split into 2 atoms — 0 confirmed, 0 partially supported, 0 disputed, 0 misattributed, 2 unverifiable. Expand the claim to see per-atom verdicts.

  Experimental — accuracy not yet measured
• cites [49] S. Longhi, Opt. Lett. 36, 819 (2011) sourceCould not verify

  Split into 2 atoms — 0 confirmed, 0 partially supported, 0 disputed, 0 misattributed, 2 unverifiable. Expand the claim to see per-atom verdicts.

  Experimental — accuracy not yet measured
• cites [51] S. Longhi, Phys. Rev. A 83, 034102 (2011)Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

Classified as probably not a substantial claim.

The DO model is obtained from the free Dirac equation by introducing an external potential via a non-minimal coupling.

“The DO model is obtained from the free Dirac equation by the introduction of the external potential via a non-minimal coupling [57,59,63].”

• cites [57] A.H. Castro Neto, F. Guinea, N.M. Peres, K.S. Novoselov, A.K. Geim, Rev. Mod. Phys. 81, 109 (2009) sourceCould not verify

  The paper’s “B. Dirac fermions” section derives a massless Dirac-like description of electrons in graphene, but does not describe the DO model. A further search for “Dirac oscillator” and “non-minimal coupling” found no passage explaining the claimed construction; the coupling example retrieved uses minimal coupling instead. (LLM, conf=0.72)

  Experimental — accuracy not yet measured
• cites [59] J. Schliemann, D. Loss, R.M. Westervelt, Phys. Rev. Lett. 94, 206801 (2005) sourceCould not verify

  The discussion of semiconductor wave packets (p. 1) mentions the free Dirac equation and external potentials, but does not describe a Dirac oscillator (DO) model or non-minimal coupling. Searches for those terms and for the claimed construction found no passage addressing it. (LLM, conf=0.76)

  Experimental — accuracy not yet measured
• cites [63] M. Johanning, A.F. Varón, C. Wunderlich, J. Phys. B 42, 154009 (2009) sourceCould not verify

  The discussion of Dirac simulations in section 6.4.1 describes a free-particle Dirac Hamiltonian, while section 6.4.3 adds a potential step to simulate the Klein paradox. Neither passage addresses the Dirac oscillator (DO) model or says that it is obtained through non-minimal coupling; searches for both terms found no such passage in our copy. Page numbers were not available. (LLM, conf=0.70)

  Experimental — accuracy not yet measured

Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

Relativistic extensions of the Kronig-Penney model have been discussed by several authors, and the impact of relativity on band structure and localization, such as shrinkage of bulk bands with increasing band number, has been highlighted.

“Relativistic extensions of the Kronig-Penney model (also referred to as the Dirac-Kronig-Penney model) have been discussed by several authors (see, for instance, [65,66,67,68,69,70, 71,72,73,74,75,76] and references therein), and the impact of relativity on the band structure and localization, such as shrinkage of the bulk bands with increasing band number, have been highlighted on many occasions.”

• cites [65] S.L. Zhu, B.G. Wang, L.M. Duan, Phys. Rev. Lett. 98, 260402 (2007)Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

• cites [66] T.M. Rusin, W. Zawadzki, Phys. Rev. D 82, 125031 (2010) sourceCould not verify

  The Introduction (p. 2) describes a study of relativistic electrons in a magnetic field, and the Discussion (p. 13) addresses Landau levels and Zitterbewegung. Searches for the Kronig–Penney model and for bulk-band shrinkage found no passage in our copy addressing the attributed claim. (LLM, conf=0.76)

  Experimental — accuracy not yet measured
• cites [67] K.L. Wang, T. Liu, M. Feng, K. Wang, Phys. Rev. A 82, 064501 (2010)Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

• cites [68] Q. Zhang, J.B. Gong, C.H. Oh, Phys. Rev. A 81, 023608 (2010)Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

• cites [69] D. Braun, Phys. Rev. A 82, 013617 (2010) sourceCould not verify

  The paper’s discussion of relativistic motion and localization (p. 1) concerns a cold-atom simulator, while its discussion of energy levels (p. 4) concerns a harmonically trapped atom. Searches for the Kronig–Penney model and for bulk-band shrinkage found no passage addressing the attributed claim. (LLM, conf=0.78)

  Experimental — accuracy not yet measured
• cites [70] J. Casanova, J.J. Garcia-Ripoll, R. Gerritsma, C.F. Roos, E. Solano, Phys. Rev. A 82, 020101 (2010) sourceCould not verify

  The paper’s introduction (p. 1) and conclusions (p. 4) describe a trapped-ion simulation of the Dirac equation with potentials and relativistic scattering. Searches for the Kronig–Penney model, band structure, localization, and shrinking bulk bands found no passage addressing those claims. (LLM, conf=0.75)

  Experimental — accuracy not yet measured
• cites [71] J.I. Cirac, P. Maraner, J.K. Pachos, Phys. Rev. Lett. 105, 190403 (2010) sourceCould not verify

  The paper’s discussion of its optical-lattice model (pp. 1–2) describes a low-energy Dirac dispersion, but does not identify the model as a relativistic Kronig–Penney extension. Searches for Kronig–Penney, localization, and shrinking bulk bands found no passage addressing those claims. (LLM, conf=0.77)

  Experimental — accuracy not yet measured
• cites [72] K. Huang, Am. J. Phys. 20, 479 (1952) sourceNot checked — no full text of the source
• cites [73] O. Klein, Z. Phys. 53, 157 (1929) sourceNot checked — no full text of the source
• cites [74] A.F. Young, P. Kim, Nat. Phys. 5, 222 (2009) sourceCould not verify

  The main text discusses relativistic tunnelling through graphene p–n junctions and a Berry-phase effect associated with its Dirac band structure. Searches for “Kronig-Penney,” “Dirac-Kronig-Penney,” and shrinking bulk bands found no passage in our copy addressing those claims. The supplied passages have no page numbers. (LLM, conf=0.76)

  Experimental — accuracy not yet measured

Probably not a substantial claim: may not pass S3 (load-bearing).

Dynamic pair production is closely related to phenomena like Rabi oscillations of the Dirac sea.

“Dynamic pair production is closely related to such intriguing phenomena like Rabi oscillations of the Dirac sea (see, for instance, [53]).”

• cites [53] K.S. Novoselov, A.K. Geim, S.V. Morozov, D. Jiang, M.I. Katsnelson, I.V. Grigorieva, S.V. Dubonos, A.A. Firsov, Nature (London) 438, 197 (2005) sourceCould not verify

  The graphene paper discusses massless Dirac carriers, quantum Hall effects, and magnetic-field oscillations (main text; page unavailable). Searches for “Rabi oscillations of the Dirac sea” and for pair production in a time-dependent field found no passage relating dynamic pair production to Rabi oscillations. (LLM, conf=0.75)

  Experimental — accuracy not yet measured

Probably not a substantial claim: may not pass S3 (load-bearing).

Earlier studies raised a debate about the existence of Dirac surface states, i.e. relativistic surface Tamm states which disappear in the nonrelativistic limit.

“In earlier studies, the Dirac-Kronig-Penney model also attracted some attention and caused a lively debate about the existence of so-called Dirac surface states, i.e. relativistic surface Tamm states which disappear in the nonrelativistic limit [66,70,77,78,79,80,81,82].”

• cites [66] T.M. Rusin, W. Zawadzki, Phys. Rev. D 82, 125031 (2010) sourceCould not verify

  The Introduction (p. 1) and Discussion (p. 14) address Zitterbewegung and a controversy about electron motion, not Dirac-Kronig-Penney surface states. Searches for “Dirac surface states,” “Tamm states,” and their disappearance in the nonrelativistic limit found no passage addressing the claim. (LLM, conf=0.75)

  Experimental — accuracy not yet measured
• cites [70] J. Casanova, J.J. Garcia-Ripoll, R. Gerritsma, C.F. Roos, E. Solano, Phys. Rev. A 82, 020101 (2010) sourceCould not verify

  The introduction (p. 1) discusses debate about relativistic effects such as the Klein paradox, and the discussion of potentials (pp. 2–3) addresses Klein tunneling. Searches for Dirac surface states, surface Tamm states, and the Dirac-Kronig-Penney model found no passage addressing the claimed debate or whether such states disappear in the nonrelativistic limit. (LLM, conf=0.76)

  Experimental — accuracy not yet measured
• cites [77] R. Gerritsma, B.P. Lanyon, G. Kirchmair, F. Zähringer, C. Hempel, J. Casanova, J.J. García-Ripoll, E. Solano, R. Blatt, C.F. Roos, Phys. Rev. Lett. 106, 060503 (2011) sourceCould not verify

  The paper discusses the Klein paradox and relativistic scattering from electrostatic potentials (pp. 1–3). Searches for Dirac-Kronig-Penney models, surface Tamm states, and their nonrelativistic limit found no passage addressing the claimed debate. (LLM, conf=0.76)

  Experimental — accuracy not yet measured
• cites [78] R. Gerritsma, G. Kirchmair, F. Zähringer, E. Solano, R. Blatt, C.F. Roos, Nature (London) 463, 68 (2010) sourceCould not verify

  The paper discusses a debate about the existence of Zitterbewegung (p. 1) and its disappearance in the nonrelativistic limit (p. 2). Searches for Dirac-Kronig-Penney, surface Tamm states, and the claimed surface-state debate found no passage addressing them. (LLM, conf=0.76)

  Experimental — accuracy not yet measured
• cites [79] F.D.M. Haldane, S. Raghu, Phys. Rev. Lett. 100, 013904 (2008)Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

• cites [80] R.A. Sepkhanov, Ya.B. Bazaliy, C.W.J. Beenakker, Phys. Rev. A 75, 063813 (2007) sourceCould not verify

  The Introduction discusses transmission at a photonic Dirac point, and Section II discusses the Dirac equation for Bloch states; neither addresses Dirac-Kronig-Penney surface states. Searches for “relativistic surface Tamm states” and the alleged debate found no passage about their existence or disappearance in the nonrelativistic limit. (LLM, conf=0.74)

  Experimental — accuracy not yet measured
• cites [81] O. Peleg, G. Bartal, B. Freedman, O. Manela, M. Segev, D.N. Christodoulides, Phys. Rev. Lett. 98, 103901 (2007) sourceNot checked — no full text of the source
• cites [82] O. Bahat-Treidel, O. Peleg, M. Segev, Opt. Lett. 33, 2251 (2008) sourceNot checked — no full text of the source

May combine two claims.

As the wave packets belonging to the two minibands refract at different angles, they separate each other after some propagation distance; such a splitting is precisely the signature of e+e- pair production.

“Note that, as the wave packets belonging to the two minibands refract at different angles, they separate each other after some propagation distance. Such a splitting is precisely the signature of e + e -pair production, as discussed in [56].”

• cites [56] C.W.J. Beenakker, Rev. Mod. Phys. 80, 1337 (2008) sourceCould not verify

  The Introduction (p. 2) describes Klein tunneling as analogous to tunneling into a Dirac sea of antiparticles, and the negative-refraction discussion (pp. 14–15) describes electron trajectories. Neither passage says that wave packets from two minibands separate or that such splitting is a signature of electron–positron pair production. Searches for pair production, pair creation, and wave-packet separation found no passage making that connection. (LLM, conf=0.76)

  Experimental — accuracy not yet measured

May combine two claims.

The space dependence of the particle mass describes interaction with a scalar Lorentz potential, and the substitution p_x → p_x - i f(x) σ_z corresponds to a non-minimal coupling essential to describe the relativistic DO.

“The space dependence of the particle mass m is known to describe the particle interaction with a scalar Lorentz potential, whereas the substitution p x → p x -if ( x ) σ z corresponds to a non-minimal coupling which is essential to describe the relativistic DO (see, for instance, [63]).”

• cites [63] M. Johanning, A.F. Varón, C. Wunderlich, J. Phys. B 42, 154009 (2009) sourceCould not verify

  Section 6.1 discusses simulating the Dirac Hamiltonian with trapped ions, but does not describe a position-dependent particle mass as a scalar Lorentz potential or the stated momentum substitution as non-minimal coupling. Searches for “Dirac oscillator,” “scalar Lorentz potential,” and “non-minimal coupling” found no passage addressing those claims in our copy. (LLM, conf=0.72)

  Experimental — accuracy not yet measured

Probably not a substantial claim: may not pass S3 (load-bearing).

Dynamic pair creation was originally proposed by Brezin and Itzykson for oscillating spatially homogeneous fields.

“The other mechanism, namely dynamic pair creation, was originally proposed by Brezin and Itzykson [55] for oscillating spatially homogeneous fields”

• cites [55] M.I. Katsnelson, K.S. Novoselov, A.K. Geim, Nat. Phys. 2, 620 (2006) sourceCould not verify

  The discussion of the Klein paradox (p. 2) concerns tunnelling through a potential barrier and mentions pair production only in other contexts. Searches for Brezin and Itzykson, dynamic pair creation, and oscillating spatially homogeneous fields found no passage in our copy addressing the claimed proposal. (LLM, conf=0.76)

  Experimental — accuracy not yet measured

Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

There are two distinct transition mechanisms for pair production: the Schwinger mechanism induced by an ultrastrong static electric field, and dynamic pair creation induced by time-varying electric fields.

“There are basically two distinct transition mechanisms: the Schwinger mechanism, induced by an ultrastrong static electric field, and dynamic pair creation, induced by time-varying electric fields.”

• cites [54] S.Y. Zhou, G.-H. Gweon, J. Graf, A.V. Fedorov, C.D. Spataru, R.D. Diehl, Y. Kopelevich, D.-H. Lee, S.G. Louie, A. Lanzara, Nat. Phys. 2, 595 (2006) sourceCould not verify

  The Abstract passages discuss Dirac fermions and electronic dispersion in graphite, not pair production. Searches for the Schwinger mechanism and for dynamic pair creation in time-varying electric fields found no passage addressing either proposed mechanism; page numbers are unavailable in our copy. (LLM, conf=0.76)

  Experimental — accuracy not yet measured
• cites [55] M.I. Katsnelson, K.S. Novoselov, A.K. Geim, Nat. Phys. 2, 620 (2006) sourcePartly supported

  The Abstract (p. 2) links enormous electric fields required for the Klein paradox to examples of positron and particle–antiparticle production. It does not identify this as the Schwinger mechanism or discuss dynamic pair creation under time-varying fields, so it does not support the claimed distinction between two mechanisms. (LLM, conf=0.78)

  Experimental — accuracy not yet measured

May combine two claims.

In the one-particle Dirac theory of vacuum decay, a simple picture of pair production is represented by the time evolution of an initially negative-energy Gaussian wave packet under the influence of an oscillating electric field; when the e+e- pair is produced, a droplet is separated from the wave packet and moves opposite to the initial one, and the droplet is a positive-energy state representing

“In the framework of the one-particle Dirac theory of vacuum decay, a simple picture of pair production is represented by the time evolution of an initially negative-energy Gaussian wave packet, representing an electron in the Dirac sea, under the influence of an oscillating electric field [56]. When the e + e -pair is produced, a droplet is separated from the wave packet and moves opposite to the”

• cites [56] C.W.J. Beenakker, Rev. Mod. Phys. 80, 1337 (2008) sourceCould not verify

  Split into 2 atoms — 0 confirmed, 0 partially supported, 0 disputed, 0 misattributed, 2 unverifiable. Expand the claim to see per-atom verdicts.

  Experimental — accuracy not yet measured

Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

The Schwinger mechanism is basically a tunneling process through a classically forbidden region, bearing a close connection to Klein tunneling.

“The Schwinger mechanism [54] is basically a tunneling process through a classically forbidden region, bearing a close connection to Klein tunneling discussed in the previous section.”

• cites [54] S.Y. Zhou, G.-H. Gweon, J. Graf, A.V. Fedorov, C.D. Spataru, R.D. Diehl, Y. Kopelevich, D.-H. Lee, S.G. Louie, A. Lanzara, Nat. Phys. 2, 595 (2006) sourceCould not verify

  The paper’s Abstract reports an experimental observation of Dirac fermions in graphite, not an account of the Schwinger mechanism. Searches for tunneling through a classically forbidden region and its connection to Klein tunneling found no passage addressing the claim. (LLM, conf=0.77)

  Experimental — accuracy not yet measured

Probably not a substantial claim: may not pass S3 (load-bearing).

The relativistic extension of the Tamm model is defined by the potential Eq. (28).

“The relativistic extension of the Tamm model is defined by the potential (see, for instance, [70,80])”

• cites [70] J. Casanova, J.J. Garcia-Ripoll, R. Gerritsma, C.F. Roos, E. Solano, Phys. Rev. A 82, 020101 (2010) sourceCould not verify

  The discussion of covariant potentials (p. 1) describes potentials in the Dirac equation, but does not identify one as a relativistic extension of the Tamm model. Searches for “Tamm model” and “Eq. (28)” found no passage addressing that specific attribution. (LLM, conf=0.72)

  Experimental — accuracy not yet measured
• cites [80] R.A. Sepkhanov, Ya.B. Bazaliy, C.W.J. Beenakker, Phys. Rev. A 75, 063813 (2007) sourceCould not verify

  The passages on boundary matching and transfer matrices (§3.5–3.8) and transmission probability (§4.9) do not define a Tamm-model potential. Searches for “Tamm model,” its relativistic extension, and potential (28) found no passage addressing the claim. (LLM, conf=0.75)

  Experimental — accuracy not yet measured

Classified as probably not a substantial claim.

Eq. (26) defines the dispersion relation of the relativistic Kronig-Penney model.

“Equation (26) defines the dispersion relation of the relativistic Kronig-Penney model, which has been investigated by several authors (see, for instance, [65,67,70]).”

• cites [65] S.L. Zhu, B.G. Wang, L.M. Duan, Phys. Rev. Lett. 98, 260402 (2007)Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

• cites [67] K.L. Wang, T. Liu, M. Feng, K. Wang, Phys. Rev. A 82, 064501 (2010)Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

• cites [70] J. Casanova, J.J. Garcia-Ripoll, R. Gerritsma, C.F. Roos, E. Solano, Phys. Rev. A 82, 020101 (2010) sourceCould not verify

  The citation appears to support the statement that the relativistic Kronig–Penney model has been investigated. Our copy instead discusses trapped-ion simulations of Dirac potentials (p. 1) and Klein scattering and confinement (p. 3); searches for Kronig–Penney, its dispersion relation, and periodic band structure found no passage addressing that model. (LLM, conf=0.75)

  Experimental — accuracy not yet measured

May combine two claims.

A special case of the Dirac-Kronig-Penney model is V0 = π/2; the resulting superstructure FBG comprises a periodic sequence of π phase slips, which has been proposed and demonstrated to realize slowing down of optical pulses.

“A special case of the Dirac Kronig Penney model corresponds to case V 0 = π/ 2. In this case, the resulting superstucture FBG comprises a periodic sequence of π phase slips, which has been proposed and demonstrated to realize slowing down of optical pulses [83].”

• cites [83] T. Ochiai, M. Onoda, Phys. Rev. B 80, 155103 (2009) sourceCould not verify

  The Introduction (p. 1) and Summary (p. 8) describe a two-dimensional honeycomb photonic crystal and its edge states. Searches for the Dirac–Kronig–Penney model, V0 = π/2, fiber Bragg gratings, π phase slips, and optical-pulse slowing found no passage addressing the attributed claim. (LLM, conf=0.76)

  Experimental — accuracy not yet measured

Probably not a substantial claim: may not pass S3 (load-bearing).

Many works have remarked that the Hermiticity of the underlying Hamiltonian can be relaxed and a consistent quantum theory can be constructed for a broader class of Hamiltonians, in particular those possessing parity-time (PT) symmetry.

“Indeed, many works have remarked that the Hermiticity of the underlying Hamiltonian can be relaxed, and that a a consistent quantum theory can be constructed for a broader class of Hamiltonians [85,86,87,88], in particular those possessing parity-time ( PT ) symmetry.”

• cites [85] O. Bahat-Treidel, O. Peleg, M. Grobman, N. Shapira, T. Pereg-Barnea, M. Segev, Phys. Rev. Lett. 104, 063901 (2010) sourceCould not verify

  The paper discusses effective Hamiltonians for deformed honeycomb lattices (Abstract, pp. 3–4), not whether Hermiticity can be relaxed to construct a consistent quantum theory. Searches for PT symmetry and relaxed Hermiticity found no passage addressing that claim. (LLM, conf=0.78)

  Experimental — accuracy not yet measured
• cites [86] O. Bahat-Treidel, O. Peleg, M. Segev, H. Buljan, Phys. Rev. A 82, 013830 (2010) sourceCould not verify

  The Abstract (p. 1) concerns nonlinear wave dynamics in honeycomb lattices, and the conclusion (p. 9) concerns the breakdown of the Dirac approximation. Searches for relaxed Hermiticity, consistent quantum theory, and parity-time (PT) symmetry found no passage in our copy addressing the attributed claim. (LLM, conf=0.75)

  Experimental — accuracy not yet measured
• cites [87] D.Ö. Güney, D.A. Meyer, Phys. Rev. A 79, 063834 (2009) sourceCould not verify

  The Introduction (p. 2) and Conclusion (p. 7) discuss negative refraction, the Klein paradox, and optical simulations. Searches for PT symmetry, non-Hermitian Hamiltonians, and relaxing Hermiticity found no passage in our copy addressing the attributed claim. (LLM, conf=0.75)

  Experimental — accuracy not yet measured
• cites [88] L.-G. Wang, Z.-G. Wang, J.-X. Zhang, S.-Y. Zhu, Opt. Lett. 34, 1510 (2009) sourceCould not verify

  The Abstract (p. 1) and discussion (p. 2) concern optical Dirac points and an analogy with graphene; the conclusion (p. 7) concerns light transport in metamaterials. Searches for relaxed Hermiticity and PT-symmetric Hamiltonians found no passage addressing whether they permit a consistent quantum theory. (LLM, conf=0.78)

  Experimental — accuracy not yet measured

Probably not a substantial claim: may not pass S3 (load-bearing).

Non-Hermitian Hamiltonians are often found in reduced descriptions of open Hermitian quantum systems, with applications to atomic, molecular and condensed-matter physics.

“Non-Hermitian Hamiltonians are also very often found in reduced descriptions of open Hermitian quantum systems, with important applications to atomic, molecular and condensed-matter physics [89].”

• cites [89] L.-G. Wang, Z.-G. Wang, S.-Y. Zhu, Europhys. Lett. 86, 47008 (2009) sourceCould not verify

  The paper’s passages on optical pulses near a Dirac point and its discussion of Zitterbewegung in other physical systems do not address non-Hermitian Hamiltonians as reduced descriptions of open Hermitian quantum systems. Searches for that formulation and for the claimed atomic, molecular, and condensed-matter applications found no supporting passage in our copy. (LLM, conf=0.76)

  Experimental — accuracy not yet measured

Classified as probably not a substantial claim.

Under assumptions of negligible group velocity dispersion and perfect phase matching in the no-pump-depletion approximation, the sum-frequency generation process is described by two coupled wave equations.

“Assuming that group velocity dispersion is negligible and assuming perfect phase matching, in the no-pumpdepletion approximation the sum-frequency generation process in described by the two coupled wave equations”

• AssumptionThe authors state this as an assumption: In the nonlinear frequency conversion process, group velocity dispersion is negligible.
• AssumptionThe authors state this as an assumption: Perfect phase matching holds in the nonlinear frequency conversion process.
• AssumptionThe authors state this as an assumption: The no-pump-depletion approximation holds for the sum-frequency generation process.
• AssumptionThe authors state this as an assumption: At the input plane z=0, the nonlinear crystal is excited by a strong and nearly continuous-wave pump field at frequency ω1 and by a weak and short signal pulse at frequency ω2 with temporal profile g(t).

May combine two claims.

ZB vanishes for either the far-relativistic (m→0) and the weak-relativistic (m→∞) limits: in the first case the amplitude of ZB diverges but the oscillation frequency ωZB goes to zero, whereas in the latter case the frequency of ZB diverges but its amplitude vanishes.

“Therefore, ZB vanishes for either the farrelativistic ( m → 0) and the weak-relativistic ( m →∞ ) limits: in the first case the amplitude of ZB diverges, but the oscillation frequency ω ZB goes to zero, whereas in the latter case the frequency of ZB diverges but its amplitude vanishes (see, for instance, [48]).”

• cites [48] G. Della Valle, S. Longhi, J. Phys. B 43, 051002 (2010)Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

May combine two claims.

For a beam envelope centered at k=0, at leading order 〈ξ〉(z) ≃ 〈ξ〉(0)+v0 z +(κ/2σ) sin(2σz), i.e. the amplitude and frequency of ZB are given by Eq.(5).

“For ˆ G ( k ) centered at k = 0, at leading order Eq.(4) yields 〈 ξ 〉 ( z ) ≃ 〈 ξ 〉 (0)+ v 0 z +( κ/ 2 σ ) sin(2 σz ), i.e. the amplitude and frequency of ZB are given by”

Probably not a substantial claim: may not pass S3 (load-bearing).

Fig.4(d) depicts typical transmission spectra in three FBGs with different chirp rates, realized to operate near the λ=1.5 μm wavelength of optical communications.

“This is shown in Fig.4(d), which depicts typical transmission spectra in three FBGs with different chirp rates, realized to operate near the λ = 1 . 5 µ m wavelength of optical communications (for more details see [39]).”

• cites [39] K. Shandarova, C.E. Ruter, D. Kip, K.G. Makris, D.N. Christodoulides, O. Peleg, M. Segev, Phys. Rev. Lett. 102, 123905 (2009) sourceNot checked — no full text of the source

May combine two claims.

For a sharp potential step a transmission window is opened inside the bandgap of the periodic grating, whereas for a smooth potential step tunneling is prevented and the transmission window inside the gap vanishes.

“In fact, for a sharp potential step a transmission window is opened inside the bandgap of the periodic grating, whereas for a smooth potential step tunneling is prevented [according to the diagram of Fig.4(c)] and the transmission window inside the gap vanishes.”

May combine two claims.

For a sharp discontinuity of media properties, beam transmission is not complete, and some light is reflected like in a Fresnel discontinuity between two different dielectric media.

“However, owing to the sharp discontinuity of media properties, beam transmission is not complete, and some light is reflected like in a Fresnel discontinuity between two different dielectric media.”

May combine two claims.

The input wave packet is mostly composed by Bloch modes belonging to the lowest miniband of the array, i.e. it belongs to the Dirac sea (the negative-energy branch of the Dirac equation).

“The input wave packet is mostly composed by Bloch modes belonging to the lowest miniband of the array, i.e. it belongs to the Dirac sea (the negative-energy branch of the Dirac equation).”

May combine two claims.

The negative (positron) energy spectrum of the DO is not obtained from the positive (electron) energy spectrum by sign reversal (δ → -δ); the positron branch has an additional bound state with energy δ = -m0.

“Note that the negative (positron) energy spectrum of the DO is not obtained from the positive (electron) energy spectrum by sign reversal ( δ →-δ ), the positron branch possessing an additional bound state with energy δ = -m 0 .”

Probably not a substantial claim: may not pass S3 (load-bearing).

Fig.5 shows the behavior of the transition probability P after interaction with a single-cycle pulse, as obtained by numerical simulations of the Dirac equation for κ=2, σ=1.817, Λ=0.6676, momentum q=π/(4a), and increasing values of field amplitude Φ0.

“As an example, Fig.5 shows the behavior of the transition probability P , after the interaction with a single-cycle pulse, as obtained by numerical simulations of the Dirac equation for κ = 2, σ = 1 . 817, Λ = 0 . 6676, momentum q = π/ (4 a ) ,and for increasing values of the the field amplitude Φ 0 .”

Classified as probably not a substantial claim.

The detailed beam evolution of an initial Gaussian wave packet along a waveguide array with single-cycle modulated axis, corresponding to conditions A, B and C of Fig.5, is depicted in the insets.

“The detailed beam evolution of an initial Gaussian wave packet along a waveguide array with single-cycle modulated axis, corresponding to the three conditions A,B and C of Fig.5, are depicted in the insets of the figure.”

Probably not a substantial claim: may not pass S3 (load-bearing).

The physical relevance of ZB in relativistic quantum mechanics is controversial because it arises in the single-particle picture of the Dirac equation but not in quantum field theory.

“Moreover, the physical relevance of ZB in relativistic quantum mechanics is a rather controversial issue, because such an effect arises in the framework of the single-particle picture of the Dirac equation, but not in quantum field theory.”

Classified as probably not a substantial claim. May combine two claims.

For a free electron, the Dirac equation predicts ZB to have an extremely small amplitude of the order of the Compton wavelength about 10^-12 m and an extremely high frequency about 10^21 Hz, making such an effect experimentally inaccessible.

“For a free electron, the Dirac equation predicts the ZB to have an extremely small amplitude (of the order of the Compton wavelength ≃ 10 -12 m) and an extremely high frequency ( ≃ 10 21 Hz), making such an effect experimentally inaccessible.”

Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

Examples of optical analogues include spatial and temporal photonic analogues of Zitterbewegung, Klein tunneling, vacuum decay and pair-production, the Dirac oscillator, the relativistic Kronig-Penney model, and optical realizations of non-Hermitian extensions of relativistic wave equations.

“Examples include spatial and temporal photonic analogues of the Zitterbewegung of a relativistic electron, Klein tunneling, vacuum decay and pair-production, the Dirac oscillator, the relativistic Kronig-Penney model, and optical realizations of non-Hermitian extensions of relativistic wave equations.”

May combine two claims.

Optical analogues of relativistic quantum phenomena can be based on either spatial light transport in engineered photonic lattices or temporal pulse propagation in Bragg grating structures.

“In this work a brief overview of a few optical analogues of relativistic quantum phenomena, based on either spatial light transport in engineered photonic lattices or on temporal pulse propagation in Bragg grating structures, is presented.”

Probably not a substantial claim: may not pass S3 (load-bearing).

In optics, several proposals of KT analogs have been suggested in the past few years.

“In optics, several proposals of KT analogs have been suggested as well in the past few years, as discussed in the introduction section.”

May combine two claims.

As the refractive index modulation of the grating, i.e. the mass term m in the Dirac equation (16), is decreased, the stop band region shrinks and the limit of a massless Dirac equation is attained.

“As the refractive index modulation of the grating, i.e. the mass term m in the Dirac equation (16), is decreased, the stop band region shrinks and the limit of a massless Dirac equation (similar to the one describing the dynamics of electrons in graphene near a Dirac point) is attained.”

May combine two claims.

The temporal evolution of the spinor wave function ψ for the Dirac particle is mapped into the spatial evolution of the envelopes A2 and A3 for signal and sum-frequency pulses, whereas the spatial coordinate of the Dirac particle is mapped into the retarded time η of the optical pulses.

“Therefore, the temporal evolution of the spinor wave function ψ for the Dirac particle is mapped into the spatial evolution of the envelopes A 2 and A 3 for signal and sum-frequency pulses, respectively, whereas the spatial coordinate of the Dirac particle is mapped into the retarded time η of the optical pulses.”

May combine two claims.

For a sharp potential step at the interface ξ=0, the electron and positron energy bands are overlapped, and the beam does not need to cross any forbidden region, i.e. KT occurs.

“For a sharp potential step [Fig.3(b)] at the interface ξ = 0 the electron and positron energy bands are overlapped, and the beam does not need to cross any forbidden region, i.e. KT occurs.”

Probably not a substantial claim: may not pass S3 (load-bearing).

Light transport in honeycomb photonic lattices, the so-called photonic graphene, has a band structure that mimics the one of graphene.

“An important optical set up is provided by light transport in honeycomb photonic lattices, the cocalled photonic graphene, whose band structure mimics the one of graphene [33].”

• cites [33] T. Schwartz, G. Bartal, S. Fishman, M. Segev, Nature 446, 55 (2007) sourceNot checked — no full text of the source

May combine two claims.

The required field for relativistic KT corresponds to the critical field for e+e- pair production in vacuum, and its value is extremely strong making the observation of relativistic KT for electrons very challenging.

“The required field corresponds to the critical field for e + e -pair production in vacuum, and its value is extremely strong making the observation of relativistic KT for electrons very challenging.”

May combine two claims.

Within the two-level model, pair production generally occurs as a multiphoton resonance process enforced by energy conservation, with effects such as Rabi oscillations of the quantum vacuum.

“Within the two-level model, pair production generally occurs as a multiphoton resonance process enforced by energy conservation, with interesting effects such as Rabi oscillations of the quantum vacuum.”

• AssumptionThe authors state this as an assumption: The two-level model applies to pair creation in a spatially homogeneous and time-dependent field.

Classified as probably not a substantial claim.

In the framework of one-particle Dirac theory, the pair production process can be viewed as the transition of an electron of the Dirac sea occupying a negative-energy state into a final positive-energy state, leaving a vacancy (positron) in the negative-energy state.

“In intuitive terms and in the framework of oneparticle Dirac theory, the pair production process can be simply viewed as the transition of an electron of the Dirac sea occupying a negative-energy state into a final positive-energy state, leaving a vacancy (positron) in the negative-energy state.”

Classified as probably not a substantial claim.

A photonic realization of the DO based on light propagation in structured FBGs has been proposed.

“In a recent work [40], a photonic realization of the DO, based on light propagation in structured FBGs, has been proposed.”

• cites [40] E. Paspalakis, Opt. Commun. 258, 31 (2006) sourceNot checked — no full text of the source

• AssumptionRests on an assumption: The DO model in relativistic quantum mechanics and particle physics remains far from any experimental consideration.

May combine two claims.

Light propagation in a FBG with a periodic sequence of phase slips simulates the relativistic Kronig-Penney model, and the band structure of the Dirac-Kronig-Penney model is mapped into the spectral transmission (alternation of stop/transmission bands) of the FBG.

“Light propagation in a FBG with a periodic sequence of phase slips was shown to simulate the relativistic Kronig-Penney model, the band structure of which being mapped into the spectral transmission of the FBG.”

• Also stated in: § 6 Photonic realization of the relativistic Kronig-Penney model and relativistic surface Tamm states · p. 10 · plain

  “The band structure of the Dirac-KronigPenney model is simply mapped into the alternation of stop/transmission bands observed in spectrally-resolved transmission measurements of the FBG.”

• cites [41] S. Longhi, G. Della Valle, M. Ornigotti, P. Laporta, Phys. Rev. B 76, 201101(R) (2007)Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

May combine two claims.

The disappearance of δ-barrier effects when V0 is an integer multiple of π is due to the phase slips being integer multiples of 2π, so the grating has no phase defects and mimics a one-dimensional free relativistic Dirac particle.

“The circumstance that the effects of the δ barriers disappear in the Dirac-Kronig-Penney model when V 0 is an integer multiple π is simply due to the fact that, under such a condition, the phase slips are integer multiplies of 2 π , and thus the grating has no phase defects and mimics the dynamics of a one-dimensional free relativistic Dirac particle.”

May combine two claims.

Spatial or temporal light transport in engineered photonic lattices and Bragg grating structures can simulate the Zitterbewegung of a relativistic electron, Klein tunneling, vacuum decay and pair-production, the Dirac oscillator, the relativistic Kronig-Penney model, and certain non-Hermitian extensions of the Dirac equations, including superluminal (tachyonic) wave equations.

“Spatial or temporal light transport in engineered photonic lattices and Bragg grating structures can simulate the Zitterbewegung of a relativistic electron, Klein tunneling, vacuum decay and pair-production, the Dirac oscillator, the relativistic Kronig-Penney model, and certain non-Hermitian extensions of the Dirac equations, including superluminal (tachyonic) wave equations.”

• AssumptionRests on an assumption: The DO model in relativistic quantum mechanics and particle physics remains far from any experimental consideration.
• AssumptionRests on an assumption: Physical realizations of non-Hermitian extensions of relativistic wave equations remain mostly unexplored.

Probably not a substantial claim: may not pass S3 (load-bearing).

In Ref. [44], optical simulations of non-Hermitian wave equations have been proposed, based on light propagation in distributed-feedback (DFB) optical structures with controlled gain and/or loss regions.

“In Ref.[44], optical simulations of non-Hermitian wave equations have been proposed, which are based on light propagation in distributed-feedback (DFB) optical structures with controlled gain and/or loss regions.”

• cites [44] F. Dreisow, M. Ornigotti, A. Szameit, M. Heinrich, R. Keil, S. Nolte, A. Tunnermann, S. Longhi, Appl. Phys. Lett. 95, 261102 (2009) sourceNot checked — no full text of the source

• AssumptionRests on an assumption: Physical realizations of non-Hermitian extensions of relativistic wave equations remain mostly unexplored.

May combine two claims.

If V0 is an integer multiple of π, all band gaps disappear and the dispersion relation reduces to that of a relativistic free particle, as if the δ-barriers were absent.

“In particular, if V 0 is an integer multiple of π , all band gaps disappear and the dispersion relation reduces to the one of a relativistic free particle [Eq.(16) with V ( z ) = 0], as if the δ -barriers were absent.”

Probably not a substantial claim: may not pass S3 (load-bearing). May combine two claims.

Since H is non-Hermitian, its spectrum is generally complex-valued; however, it could happen that, in spite of non-Hermiticity, the energy spectrum remains real-valued, like in PT symmetric Hamiltonians in the unbroken symmetry phase.

“Since H is non-Hermitian, its spectrum is generally complex-valued, however it could happen that, in spite of non-Hermiticity, the energy spectrum remains real-valued, like in PT symmetric Hamiltonians in the unbroken symmetry phase.”

Classified as probably not a substantial claim.

A photonic realization of the relativistic Kronig-Penney model and relativistic surface Tamm states has been proposed, based on light propagation in superstructure FBGs with phase defects.

“In Ref.[41], a photonic realization of the relativistic Kronig-Penney model and relativistic surface Tamm states has been proposed, which is based on light propagation in superstructure FBGs with phase defects.”

• cites [41] S. Longhi, G. Della Valle, M. Ornigotti, P. Laporta, Phys. Rev. B 76, 201101(R) (2007)Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

May combine two claims.

A remarkable property of such an equation, in addition to enabling a kind of superluminal propagation, is the possibility to make a DFB structure fully transparent.

“A remarkable property of such an equation, in addition to enable a kind of superluminal propagation, is the possibility to make a DFB structure fully transparent, as recently discussed in Ref.[105].”

• cites [105] E. Schrödinger, Sitz. Preuss. Akad. Wiss. Phys.-Math. Kl. 24, 418 (1930)Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

Probably not a substantial claim: may not pass S3 (load-bearing).

Examples of non-Hermitian Dirac Hamiltonians showing two different kinds of spectral singularities were discussed in Ref. [44] assuming a pure index grating (h real-valued) for either PT-invariant and PT-non-invariant DFB structures.

“Examples of non-Hermitian Dirac Hamiltonians showing such a two different kinds of spectral singularities were discussed in Ref.[44] assuming a pure index grating (i.e. h ( x ) real-valued) for either PT -invariant and PT -non-invariant DFB structures.”

• cites [44] F. Dreisow, M. Ornigotti, A. Szameit, M. Heinrich, R. Keil, S. Nolte, A. Tunnermann, S. Longhi, Appl. Phys. Lett. 95, 261102 (2009) sourceNot checked — no full text of the source