cases/case11/sources.md

Scientific Sources — Case11

References

A. Thorpe, N. Boroumand, A. M. Parks, E. Goulielmakis, and T. Brabec. 2023. High harmonic generation in solids: Real versus virtual transition channels. Physical Review B, 107, 075135. Source

High harmonic generation in solids: Real versus virtual transition channels

Criterion-to-source crosswalk

Article page identifiers below are journal pages, not PDF viewer indices. Supplemental pages are explicitly marked. The crosswalk distinguishes direct source facts, mathematical entailments and task-defined evidence duties. Original images and PDFs are referenced only; none are reproduced.

Criteria	Source locations, scientific use and limits
F1, F2	Thorpe et al. (2023), article pp.075135-2-4, Eqs.(1)-(19), Fig.2 caption: moving-K two-band exact density matrix, instantaneous adiabatic diagonalization, second-order expansion and dressed-gap SFAF; exact propagation is distinct from FVB.
F3, M3	Thorpe et al. (2023), article pp.075135-4-5, Eqs.(20)-(25): filtering complex amplitude v into low-frequency resonant and complementary virtual parts; mixed population term belongs to the nonresonant definition.
F4	Thorpe et al. (2023), article pp.075135-3,5-6, Eqs.(19),(24),(25), Fig.5 and high-field interference discussion: coherent current combination before Fourier power. Candidate spectral-density/fluence equivalents are allowed under common conventions.
O1, I1, M1	Thorpe et al. (2023), article p.075135-4, Fig.2(a) and comparison paragraph: semiconductor exact/SFAF agreement and interband predominance. Fig.3 on p.075135-5 is auxiliary channel evidence, not a substitute for the dielectric family.
O2, I2, M2	Thorpe et al. (2023), article p.075135-4, Fig.2(b) and following material/Stark discussion: long-pulse dielectric exact/SFAF comparison, changed high-order balance and optional FVB disagreement.
O3, I3	Thorpe et al. (2023), article pp.075135-5-6, Fig.5(a,b), Eqs.(20)-(25): short-pulse F0=0.005 dielectric, interband-dominated total with small intraband terms.
O4, M7, M4	Thorpe et al. (2023), article pp.075135-5-6, Fig.5(c,d): F0=0.012 dielectric, high-order resonant interband dominance and comparable nonresonant intraband contribution suppressing the coherent total. Signed interference follows from amplitudes, not component-power addition.
M5, M6	Thorpe et al. (2023), article pp.075135-4-6, Fig.2(a,b), Fig.5(a-d) and dynamic-Stark paragraphs: material and field redistribute real/virtual channels. Adequacy conclusions require the actual submitted case/harmonic evidence.
V1, V2	Thorpe et al. (2023), article pp.075135-2,6-7, no-electron-hole-interaction premise and Sec.IV scope/dephasing discussion. Positive model boundaries and triggered alternatives are task duties; additional dephasing/real-material simulation is not compulsory.

Formula and convention notes

For F1-F3/M3/M6, article pp.075135-2-5, Eqs.(2)-(4),(18)-(23), $$u(K,t)=\frac{i}{2}{\int }_{-\mathrm{\infty }}^t\mathrm{\Omega }(K_{t^{\mathrm{\prime }}},t^{\mathrm{\prime }})e^{-i{\int }_{t^{\mathrm{\prime }}}^t\lambda (K_{\tau },\tau )d\tau }d{t}^{\mathrm{\prime }}=e^{-i{\int }^t\lambda d\tau }v(K,t)\mathrm{.}u(K,t)=\backslash frac\; i2\backslash int\_\{-\backslash infty\}^t\backslash Omega(K\_\{t\text{'}\},t\text{'})e^\{-i\backslash int\_\{t\text{'}\}^t\backslash lambda(K\_\backslash tau,\backslash tau)d\backslash tau\}dt\text{'}\; =e^\{-i\backslash int^t\backslash lambda\; d\backslash tau\}v(K,t).$$ The resonant filter is $G_r(\omega)=1$ for $|\omega|\le\omega_0/2$ and zero otherwise; $v_i=\mathcal F^{-1}[G_i\widetilde v]$, $G_{nr}=1-G_r$. Existing mixed-population and current formulas below retain their full signs. Filtering $|v|^2$, current power or harmonic bins is a different object. The dressed gap cannot be replaced by $\varepsilon$ and still labelled SFAF; that optional replacement is FVB.

Scope of the source anchors

The locators identify scientific objects and mechanisms, not compulsory figure layouts, solver settings, exact grids, pointwise tolerances or a fixed evidence package. Canonical examples may be replaced by functionally equivalent evidence subject to the rubric. Source readback verifies the candidate's science; it cannot supply missing candidate presentation, identification or inference. Reporting, applicability/N/A and descriptive Research Closure duties remain those stated in the rubric and task.