Reaction-diffusion dynamics in a Fibonacci chain: Interplay between classical and quantum behavior
Bibliographic record
Abstract
We study the reaction-diffusion dynamics of Fibonacci anyons in a one-dimensional lattice. Due to their non-Abelian nature, besides the position degree of freedom (DOF), these anyons also have a nonlocal internal DOF, which can be characterized by a fusion tree. We first consider a pure-reaction dynamics associated with the internal DOF, which is of intrinsically quantum origin, with either an ``all-$\ensuremath{\tau}$'' or ``completely random'' initial fusion tree. These two fusion trees are unstable and likely stable steady states for the internal DOF, respectively. We obtain the decay rate of the anyon number for these two cases exactly. Still using these two initial fusion trees, we study the full reaction-diffusion dynamics and find an interesting interplay between classical and quantum behaviors: These two fusion trees are still respectively unstable and likely stable steady states of the internal DOF, while the dynamics of the position DOF can be mapped to a hybrid classical $A+A\ensuremath{\rightarrow}0$ and $A+A\ensuremath{\rightarrow}A$ reaction-diffuson dynamics, with the relative reaction rates of these two classical dynamics determined by the state of the nonlocal internal DOF. In particular, the anyon density at late times are given by $\ensuremath{\rho}(t)=\frac{c}{\sqrt{8\ensuremath{\pi}}}{(Dt)}^{\ensuremath{-}\mathrm{\ensuremath{\Delta}}}$, where $D$ is a nonuniversal diffusion constant, $\mathrm{\ensuremath{\Delta}}=1/2$ is superuniversal, and $c$ is universal and can be obtained exactly in terms of the fusion tree structure. Specifically, $c=\frac{2\ensuremath{\varphi}}{\ensuremath{\varphi}+1}$ and $c=\frac{2(4\ensuremath{\varphi}+3)}{5(\ensuremath{\varphi}+1)}$ for the all-$\ensuremath{\tau}$ and completely random configuration respectively, where $\ensuremath{\varphi}=\frac{\sqrt{5}+1}{2}$ is the golden ratio. We also study the two-point correlation functions.
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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 | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.003 | 0.001 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.000 | 0.001 |
| 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".