Spectral density, memory function, and mean relaxation time for resonant subsystem-reservoir interactions
Bibliographic record
Abstract
We show that the projection operators P usually employed to derive the Nakajima–Zwanzig master equation are non-Hermitian. As a consequence the operator QLQ which governs the dynamics of subsystem-reservoir interactions (here Q=1−P and L is the Liouville operator) is also non-Hermitian and possesses a complex temperature-dependent spectrum of resonances. We use the self-consistent Born approximation to derive a formula for the spectral density of QLQ. From this spectral density we calculate the memory function and mean relaxation time of subsystem-reservoir correlations. These formulas are compared with numerical results obtained from the spin–spin-bath model to test their accuracy. The memory function and mean relaxation time are essential ingredients for the SRA (statistical resonance approximation) theory of microscopic dissipation and decoherence. We show that the SRA master equation preserves positivity when the memory function derived in this paper is employed.
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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".