High-order adiabatic representations of quantum systems through a perturbative construction of dynamical invariants
Bibliographic record
Abstract
A perturbative series is derived for the systematic construction of a dynamical invariant (Lewis invariant) for a time-dependent Hamiltonian which is characterized by a time-scale parameter $\ensuremath{\tau}$, as appears in the usual formulation of the adiabatic theorem. The derivations make efficient use of the quantum averaging method, and the perturbative series obtained permits the construction of the invariant in successive orders in $ϵ\ensuremath{\sim}1/\ensuremath{\tau}$, corresponding to high-order adiabatic approximations. The series can be considered and resummed analytically to all orders, yielding an exact invariant for an harmonic oscillator linearly driven by an external field. For a nondegenerate two-level system, approximate invariants have been obtained up to the fifth order and illustrate how the adiabatic approximations of increasing orders successively approach the exact dynamics. The construct is applicable also to Floquet Hamiltonians and, in this context, it furnishes high-order adiabatic representations for the time evolution of Floquet states associated with a material system in an aperiodic laser pulse. We illustrate in particular how an exact Floquet dynamical invariant, defining exact adiabatic transports of Floquet states, is obtained for a laser-driven harmonic vibrational mode.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".