The ergodicity landscape of quantum theories
Bibliographic record
Abstract
This paper is a physicist’s review of the major conceptual issues concerning the problem of spectral universality in quantum systems. Here, we present a unified, graph-based view of all archetypical models of such universality (billiards, particles in random media, interacting spin or fermion systems). We find phenomenological relations between the onset of ergodicity (Gaussian-random delocalization of eigenstates) and the structure of the appropriate graphs, and we construct a heuristic picture of summing trajectories on graphs that describes why a generic interacting system should be ergodic. We also provide an operator-based discussion of quantum chaos and propose criteria to distinguish bases that can usefully diagnose ergodicity. The result of this analysis is a rough but systematic outline of how ergodicity changes across the space of all theories with a given Hilbert space dimension. As a particular example, we study the SYK model and report on the transition from maximal to partial ergodicity as the disorder strength is decreased.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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".