cases/case34/task.md

Quantum-informed trajectory modelling of strong-field photoelectron spectra

Background and physical system

Semiclassical trajectory models provide an interpretable account of continuum electron motion, but their predictive value depends on how the outgoing wavepacket is represented as trajectory input. Investigate whether a quantum-informed trajectory description can give a quantitatively credible account of strong-field ionization while retaining a semiclassical description of continuum dynamics.

Work in atomic units with the one-dimensional single-electron potential

$$V(x)=-\frac{1}{\sqrt{x^2+a^2}},a=1,V(x)=-\backslash frac\{1\}\{\backslash sqrt\{x^2+a^2\}\},\backslash qquad\; a=1,$$

and initialize the electron in its field-free ground state. The laser field is defined by

$$A(t)=(-1{)}^{n+1}\frac{F_0}{\omega }{\sin }^2\text{\hspace{0.17em}⁣}\left(\frac{\omega t}{2n}\right)\sin (\omega t+\varphi ),0\le t\le t_f=\frac{2\pi n}{\omega },A(t)=(-1)^\{n+1\}\backslash frac\{F\_0\}\{\backslash omega\}\; \backslash sin^2\backslash !\backslash left(\backslash frac\{\backslash omega\; t\}\{2n\}\backslash right)\; \backslash sin(\backslash omega\; t+\backslash phi),\; \backslash qquad\; 0\backslash leq\; t\backslash leq\; t\_f=\backslash frac\{2\backslash pi\; n\}\{\backslash omega\},$$

with $A(t)=0$ outside the pulse and $F(t)=-dA/dt$. Use

$$n=4,F_0=0.0757,\omega =0.057,\varphi =0.n=4,\backslash qquad\; F\_0=0.0757,\backslash qquad\; \backslash omega=0.057,\backslash qquad\; \backslash phi=0.$$

Research problem

Assess whether a semiclassical two-step model with quantum input gives a defensible account of the final photoelectron momentum distribution for this target and pulse when judged against both a conventional one-dimensional semiclassical two-step (SCTS) calculation and an independently converged direct TDSE result. Determine which information carried by the quantum input is material to the agreement or disagreement you establish, and delimit the physical and numerical scope supported by your calculated evidence.

How you derive the model, organize the comparisons and construct evidence for the final judgment is for you to decide. Base the conclusion on your own calculated final photoelectron signal; qualitative resemblance by itself does not establish model validity.

Model identity and scope

In the quantum-input model, the trajectory input is the complex position--momentum amplitude obtained from a Gaussian-window Gabor representation of the newly outgoing wavefunction removed by an absorbing boundary. Classical trajectories evolve in the stated laser and soft-core fields. Their asymptotic momentum contributions are combined coherently, with the task-specific semiclassical trajectory phase and the finite postpulse potential contribution retained. These conditions define the commissioned model; deriving a consistent computable realization remains part of the task.

All discretization, TDSE extraction, absorbing-boundary, Gabor-window, sampling, propagation, asymptotic-matching, momentum-binning, normalization and display choices not fixed above are yours. State choices that materially affect your claims and provide evidence sufficiently reliable and reconstructible to support them. A declared common scale may be used; absolute yield is not a grading target unless independently established by your calculation.

Do not add multielectron, three-dimensional, relativistic, focal-volume, macroscopic-propagation or detector-response physics to the required production model. Clearly separated extensions are permitted but cannot replace the stated commission.

Submission and resources

Submit one self-contained scientific report and an auditable offline calculation package containing the task-specific derivation, code, numerical data underlying all material claims, a provenance note listing every offline source or software document actually consulted and the method basis for items supplied from general knowledge, and concise run and environment information. No fixed file tree, filename scheme, panel count or complete exploration history is required.

Resource limits are supplied exclusively by the accompanying resource_limits.json. Its fixed CPU allocation, candidate-active wall time, network boundary are binding. No separate aggregate CPU-hour limit applies. Greater computational expense receives no additional credit.

Reference and integrity policy

This examination is conducted without network access or live literature retrieval. You may rely on your existing general scientific knowledge and, if any are explicitly supplied with the examination, on those offline materials or software documentation. Record every such source actually consulted. For formulas, methods, constants, or conventions used from general knowledge rather than a consulted source, state enough of the method basis, definition, value, units, and convention to make the calculation auditable; do not invent a citation. You are not required to identify or prove a publication date or to retrieve literature during the examination.

The hidden target article and its identifying metadata, figures or captions, supplementary material, author code or data, target-specific reproduction code, solution or scoring material, online solutions, and worked reproductions of this case must not be used. All submitted scientific figures and numerical data must be generated by your own implementation of the stated problem.

See submission requirements for the common submission entry points.