Bibliographic record
Abstract
We consider a quantum system composed of a small part, having finitely many degrees of freedom, interacting with a free, spatially infinitely extended Bose gas. An equilibrium state for the uncoupled system is given by the product state where the small part is in the Gibbs state at some temperature T> 0, and the Bose gas is in a state where a spatially homogeneous Bose-Einstein Condensate is immersed in black body radiation at the same temperature T. An interaction between the two subsystems is specified by a coupled dynamics. The interaction strength is measured by the size of a coupling constant. We show that the equilibrium state of the uncoupled system is stable: any initial state close to it, evolving according to the interacting dynamics, converges to it, in the successive limits of large time and small coupling constant. We deduce the stability result from properties of structure and regularity of eigenvectors of the generator of the dynamics, called the Liouville operator. Among our technical results is a Virial Theorem for Liouville type operators which has new applications to systems with and without a condensate. Supported by a CRM-ISM postdoctoral fellowship in conjunction with McGill University;
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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) | 0.002 | 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".