Chaos and dynamical instability in a closed kicked system
Bibliographic record
Abstract
Quantum-classical correspondence plays an important role in understanding the emergence of classical chaos from underlying quantum mechanics. However, the transition from quantum to classical is not straightforward. Here we study a well-known \nclosed-kicked spin system with a chaotic classical limit. The quantum dynamics takes the form of stroboscopic unitary kicks acting on a single spin system. By mapping it to a programmable quantum circuit, we show that NISQ devices can be a potential testbed for simulating quantum chaos. The results suggest that entanglement can be considered a signature of classical chaos even in the deep quantum regime. Extending the work to arbitrary spins and focusing on special Hamiltonian parameters, we then show that the system may acquire temporal periodicity. These temporal periodicities do not depend on the initial state. Throughout such periodic evolutions, no initial quantum state fully explores Hilbert space as either a state vector or phase space as a quasi-probability distribution despite the classical limit being chaotic. Because these state-independent temporal periodicities are present in all dimensions, their existence represents a universal violation of the correspondence principle. We also consider the stability of this periodic behavior \n as a function of the degree of chaos in the classical model. Our study suggests that even in the semi-classical regime, there are specific parameter values for which a quantum system never behaves classically or displays signatures of chaos.
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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) | 0.001 | 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".