| # Scientific sources - Case25 |
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| ## References |
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| Rasmus Vesterager Gothelf, Christian Saugbjerg Lange, and Lars Bojer Madsen. 2025. *High-Harmonic Generation in a Crystal Driven by Quantum Light*. *arXiv*, 2502.11803. [Source](https://arxiv.org/abs/2502.11803v2). Version 2. |
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| Four-state finite-pulse intraband HHG and generated-field first/second moments, phase-space distribution-response mechanism and APP scope. Floquet structural support does not replace finite-pulse spectra or justify emitted photon statistics. |
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| ## Criterion-to-source crosswalk |
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| Locations refer to the article or named preprint/manuscript page, not a figure-file index. Source examples establish scientific identity and robust structure; the task defines required reporting, case coverage and risk-triggered validation. No original source images are reproduced. |
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| | Criteria | Source locations, scientific use and limits | |
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| | F1 | preprint pp. 3-4, Eqs. (13)-(15); p. 6, Sec. III B The Fourier band and occupied spin-momentum states generate intraband current under the supplied finite pulse. | |
| | F2, M1 | preprint pp. 4-5, Eqs. (22)-(30) The four phase-space weights have the same stated mean photon number; coherent/thermal representation and approximate positive-P Fock/BSV branches must remain distinct. | |
| | F3, O1, I1, M4, V1 | preprint pp. 5-7, Eqs. (32)-(37), Fig. 1 and Sec. III B-C Finite-pulse spectra are averages of squared state-conditioned current transforms. Floquet markers and display offsets do not replace the finite-pulse output or common physical scale. | |
| | O2, I2, M3 | preprint p. 9, Eqs. (43)-(46), Fig. 4 and following discussion The generated-field expectation excludes the driver-mode displacement and reflects the phase symmetry/anisotropy of the state weight. | |
| | O3, I3, M5 | preprint pp. 9-10, Eqs. (47)-(48), Fig. 4 and its caption Generated-field uncertainty is the variance after the stated vacuum/driver exclusions, not the mean field or a claim of photon statistics. | |
| | M2, M6 | preprint pp. 6-7, Eq. (36), Fig. 2 and Sec. III C Broad thermal/BSV radial distributions overlap nonlinear harmonic response at larger amplitudes; equal mean photon number alone does not fix spectral extent. | |
| | M7, M8, V3 | preprint pp. 9-10, Secs. IV-V and Conclusion; Appendix A Spectral and temporal claims share the same intraband input and have observable-dependent APP limits; APP does not establish emitted photon statistics or quantitative squeezing. | |
| | V2 | preprint pp. 5-7, Eqs. (32)-(37), and pp. 9-10, Eqs. (46)-(48), Sec. V Averaging level, phase-space sampling, finite-pulse treatment and APP scope can threaten specific claims. Equivalent discrimination is task-defined only for material triggered risks. | |
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| ## Formula and convention notes |
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| Source-numbered identities below are paraphrased mathematically. Explicit algebraic consequences and accepted model-conditioned representations are identified as such; they do not add a required solver, plot or validation recipe. |
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| For state weight $P(\alpha)$ and current $j_\alpha(t)$, $S(\omega)\propto\int d^2\alpha\,P(\alpha)|\int dt\,w(t)j_\alpha(t)e^{i\omega t}|^2$ (Eqs. (32)-(33), finite-pulse form Eq. (37)). This is not $|\int P\,\widetilde j_\alpha|^2$. In the periodic limit odd-order weights involve $\int P(\alpha)[\sum_lC_lJ_n(l\widetilde g_0|\alpha|)]^2d^2\alpha$ (Eq. (36)), explaining distribution-response overlap but not replacing finite-pulse evidence. |
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| Let $X_\alpha(t)=d^2j_\alpha/dt^2$ and $\langle\cdot\rangle_P=\int d^2\alpha P(\alpha)(\cdot)$. The generated field obeys $\langle E\rangle_{\rm HHG}=-4\langle X\rangle_P/(3c^3)$ and $\operatorname{Var}(E)_{\rm HHG}=16[\langle X^2\rangle_P-\langle X\rangle_P^2]/(9c^6)$ (Eqs. (46)-(48)), with driver and zero-point terms removed as specified. The plotted uncertainty is the nonnegative square root of that variance. |
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| The coherent weight is concentrated at one complex amplitude; the thermal weight is circular Gaussian. The APP Fock weight is $P_n=e^{-|\alpha|^2}|\alpha|^{2n}/(\pi n!)$, while APP BSV has the anisotropic Gaussian in Eq. (30). The APP is observable dependent, not an exact density-operator replacement for all output statistics. |
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| ## Scope of the source anchors |
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| Figure panels, displayed source coordinates, curve multipliers, numerical grids and named controls are reference examples, not compulsory submission layouts or hidden pointwise targets. Equivalent evidence must preserve the actual physical observable, case, relative scale and discriminating function. Correct data, candidate identification, causal explanation and risk resolution are separate evidential acts. Existing branch-local dependencies, applicability/N/A and descriptive Research Closure rules remain in the case rubric. |
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