An effective centroid Hamiltonian and its associated centroid dynamics for indistinguishable particles in a harmonic trap
Bibliographic record
Abstract
We show that incorporating the effects of Bose–Einstein or Fermi–Dirac quantum statistics within the centroid molecular dynamics formalism leads to additional correlations in the system due to exchange effects. In the case of Bose–Einstein statistics they appear as an additional attraction between physical particles while an additional repulsion is observed for Fermi–Dirac statistics. We show that we can account for these correlations through the effective centroid Hamiltonian. Within the approach based on the phase space centroid density, this Hamiltonian depends on centroid momenta in a nonclassical way. We illustrate the above findings using a simple model of two bosons and fermions in a harmonic potential. The average of a centroid variable along centroid trajectories based on such an effective Hamiltonian can be used to study the equilibrium properties of quantum systems. Is is also shown that the dynamics of the centroid variables derived from the quantum mechanical dynamics of the corresponding physical observables does not depend on exchange effects for a harmonic system.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.005 | 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 source (direct Gemma or distilled Codex), 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".