| # 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](https://doi.org/10.1103/PhysRevB.107.075135) |
|
|
| 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), |
| $$H=\tfrac12\begin{pmatrix}\varepsilon&\Omega\\\Omega&-\varepsilon\end{pmatrix},\quad |
| \Omega=2Fd(K_t),\quad\lambda=\sqrt{\varepsilon^2+\Omega^2},\quad K_t=K+A(t),$$ |
| $$u(K,t)=\frac i2\int_{-\infty}^t\Omega(K_{t'},t')e^{-i\int_{t'}^t\lambda(K_\tau,\tau)d\tau}dt' |
| =e^{-i\int^t\lambda d\tau}v(K,t).$$ |
| 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. |
|
|
