cases/case09/sources.md

Scientific Sources — Case09

References

Zhong Guan, Xiao-Xin Zhou, and Xue-Bin Bian. 2016. High-order-harmonic generation from periodic potentials driven by few-cycle laser pulses. Physical Review A, 93, 033852. Source

High-order-harmonic generation from periodic potentials driven by few-cycle laser pulses

Mengxi Wu, Shambhu Ghimire, David A. Reis, Kenneth J. Schafer, and Mette B. Gaarde. 2015. High-harmonic generation from Bloch electrons in solids. Physical Review A, 91, 043839. Source

Secondary periodic Bloch/Houston method and physical-equivalence boundary, not a required auxiliary implementation.

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	Guan et al. (2016), article pp.033852-1-2, Eqs.(1)-(7), Fig.1(a-d), paragraph choosing k=0 in band 2: B-spline generalized metric and physical initial-state identity, not finite-box ordinal.
F3	Guan et al. (2016), article p.033852-2, Eq.(8), and p.033852-3 Fourier/window paragraph: laser-induced current and spectrum. Gauge/derivative equivalence requires actual observable mapping, not appearance alone.
F4, O4, M5, M6, V1	Guan et al. (2016), article pp.033852-2-4, Fig.1(a,b), Fig.2 and Fig.4(a,b), Sec.III.A comparison to Bloch/Houston expansions: static bands plus driven response comparisons. Distinct failure-mode sensitivity and case/range-specific reliability conclusions are task-defined; no named auxiliary method is compulsory. Secondary standard-method support: Wu et al. (2015), article pp.043839-2,6, Secs.II-III, Fig.4(a-c), Eqs.(22),(23) and Fig.5: matched physical k=0 valence initial state, Houston/Bloch equivalence and band-truncation limitations.
O1, I1, M1	Guan et al. (2016), article p.033852-3, Fig.2 and two-plateau paragraph: first plateau and roughly five-orders-weaker second plateau, with cutoff scales near harmonic orders 40 and 120; bands 2/3 and higher-band pathways differ.
O2, O3, I2, I3, M2, M3, M4	Guan et al. (2016), article pp.033852-2-4, Eqs.(9)-(12), Fig.4(a,b): same-band/intraband low-order contribution and different-band/interband higher-first-plateau dominance at Case-B intensity. Current components combine coherently; their powers do not simply add.
M7, V2	Guan et al. (2016), article pp.033852-1-4, SAE model boundary, Sec.III.A numerical-stability comparison and last p.033852-4 model-potential qualification. Reconciling material disagreements and bounded reliability claims are task-defined, not universal experimental equivalence.

Formula and convention notes

For F1-F3/O3/M2-M4, article p.033852-2, Eqs.(4),(6)-(12), a nonorthogonal B-spline representation obeys $iS\dot C=H(t)C$, with norm $C^\dagger SC$. For physical band projectors $P_b$, $$j_{\mathrm{i}\mathrm{n}\mathrm{t}\mathrm{r}\mathrm{a}}=-\frac{e}{m}\sum _b⟨\psi \mathrm{\mid }{P}_b\widehat{p}{P}_b\mathrm{\mid }\psi ⟩,j_{\mathrm{i}\mathrm{n}\mathrm{t}\mathrm{e}\mathrm{r}}=-\frac{e}{m}\sum _{b\mathrm{\ne }{b}^{\mathrm{\prime }}}⟨\psi \mathrm{\mid }{P}_b\widehat{p}{P}_{b^{\mathrm{\prime }}}\mathrm{\mid }\psi ⟩,j=j_{\mathrm{i}\mathrm{n}\mathrm{t}\mathrm{r}\mathrm{a}}+j_{\mathrm{i}\mathrm{n}\mathrm{t}\mathrm{e}\mathrm{r}}\mathrm{.}j\_\{\backslash rm\; intra\}=-\backslash frac\; em\backslash sum\_b\backslash langle\backslash psi|P\_b\backslash hat\; pP\_b|\backslash psi\backslash rangle,\backslash quad\; j\_\{\backslash rm\; inter\}=-\backslash frac\; em\backslash sum\_\{b\backslash ne\; b\text{'}\}\backslash langle\backslash psi|P\_b\backslash hat\; pP\_\{b\text{'}\}|\backslash psi\backslash rangle,\backslash quad\; j=j\_\{\backslash rm\; intra\}+j\_\{\backslash rm\; inter\}.$$ Thus $|\widetilde j|^2=|\widetilde j_{\rm intra}|^2+|\widetilde j_{\rm inter}|^2+2\Re(\widetilde j_{\rm intra}\widetilde j_{\rm inter}^*)$. In a different gauge the current and projectors must be transformed consistently. Equivalent methods must preserve the same physical k=0 band-2 state and causal content; matching a finite-box ordinal, swapping component names, or comparing two implementations sharing the relevant error class does not establish equivalence or independent reliability.

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.