Bibliographic record
Abstract
We consider a gas of indistinguishable bosons, confined to a ring of radius R, and interacting via a pair-wise cosine potential. This may be thought of as the quantized Hamiltonian Mean Field (HMF) model for bosons originally introduced by Chavanis as a generalization of Antoni and Ruffo’s classical model. This thesis contains three parts: In part one, the dynamics of a Bose-condensate are considered by studying a generalized Gross-Pitaevskii equation (GGPE). Quantum effects due to the quantum pressure are found to substantially alter the system’s dynamics, and can serve to inhibit a pathological instability for repulsive interactions. The non-commutativity of the large-N , long-time, and classical limits is discussed. In part two, we consider the GGPE studied above and seek static solutions. Exact solutions are identified by solving a non-linear eigenvalue problem which is closely related to the Mathieu equation. Stationary solutions are identified as solitary waves (or solitons) due to their small spatial extent and the system’s underlying Galilean invariance. Asymptotic series are developed to give an analytic solution to the non- linear eigenvalue problem, and these are then used to study the stability of the solitary wave mentioned above. In part three, the exact solutions outlined above are used to study quantum fluctuations of gapless excitations in the HMF model’s symmetry broken phase. It is found that this phase is destroyed at zero temperature by large quantum fluctuations. This demonstrates that mean-field theory is not exact, and can in fact be qualitatively wrong, for long-range interacting quantum systems, in contrast to conventional wisdom.
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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 | 0.000 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 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".