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 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".