Scientific Sources — Case12
References
Tao-Yuan Du, Zhong Guan, Xiao-Xin Zhou, and Xue-Bin Bian. 2016. Enhanced high-order harmonic generation from periodic potentials in inhomogeneous laser fields. Physical Review A, 94, 023419. Source
Enhanced high-order harmonic generation from periodic potentials in inhomogeneous laser fields
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 | Du et al. (2016), article pp.023419-1-2, Eqs.(1)-(7), paragraph choosing the k=0 valence-top state: specified periodic SAE model and xE+epsilonx^2E interaction. Inhomogeneity is the stated interaction, not a separately substituted force law. |
| F3 | Du et al. (2016), article p.023419-2, Eq.(8) and following Fourier paragraph: current-derived harmonic spectrum. Equivalent radiation forms require consistent frequency/boundary mapping. |
| O1, O2, I1, M1, M2 | Du et al. (2016), article p.023419-2, Fig.2(a-c), caption and two-plateau paragraph: matched epsilon=0,0.0002,0.0005 total spectra and selective high-energy enhancement rather than common scaling. |
| O3, I2, M3, M4, M5 | Du et al. (2016), article pp.023419-3-4, Fig.3, Fig.5(c,d), Fig.6 and transition-probability paragraphs: small lower-band versus much larger higher-band change and coupling to the valence state. The article does not define a unique projected-current cross-term allocation; task accepts functionally equivalent causal evidence. |
| O4, I3, M6 | Du et al. (2016), article p.023419-3, Fig.4(a,b) full response and Fig.4(c,d) interband illustrations: inhomogeneity changes emission/pathway structure. The caption does not assign the nonzero map an unambiguous epsilon from the two scan values; grade a candidate-declared case, not guessed panel identity. |
| M7 | Du et al. (2016), article pp.023419-2-3, Fig.2(b,c) odd/even spectra, broken-symmetry paragraph and Fig.4 time-frequency discussion: pathway changes and parity-permitted supporting structure. |
| M8, V1, V2 | Du et al. (2016), article pp.023419-1,4-5, one-dimensional SAE model and summary; bounded selectivity and triggered numerical/physical-alternative treatment are task obligations, not absolute-yield or universal experimental-efficiency requirements. |
Formula and convention notes
For F2-F3/M3-M5, article pp.023419-1-2, Eqs.(1)-(3),(8), If acceleration is used, Ehrenfest evolution for this stated Hamiltonian gives $\dot{\langle p\rangle}=-\langle V'(x)\rangle-E(t)[1+2\epsilon\langle x\rangle]$ (subject to any separately accounted boundary/mask effects). Substituting $1+\epsilon x$ as the force while retaining this Hamiltonian is not equivalent. Band population evidence may use $n_b(t)=\langle\psi(t)|P_b|\psi(t)\rangle$ with declared projectors. Source Fig.6 compares $|\langle\varphi_{n_0}|x|\varphi_n\rangle|^2$ and $|\langle\varphi_{n_0}|x^2|\varphi_n\rangle|^2$; these illustrate a mechanism, not a mandatory decomposition or permission to add component spectral powers.
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.