Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Reaction-diffusion dynamics in a Fibonacci chain: Interplay between
  classical and quantum behavior   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-$\tau$" 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
$A+A\rightarrow 0$ and $A+A\rightarrow A$ 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 $\rho(t)=\frac{c}{\sqrt{8\pi}}(Dt)^{-\Delta}$, where $D$ is a
non-universal diffusion constant, $\Delta=1/2$ is superuniversal, and $c$ is
universal and can be obtained exactly in terms of the fusion tree structure.
Specifically, $c=\frac{2\varphi}{\varphi+1}$ and
$c=\frac{2(4\varphi+3)}{5(\varphi+1)}$ for the all-$\tau$ and completely random
configuration respectively, where $\varphi=\frac{\sqrt{5}+1}{2}$ is the golden
ratio. We also study the two-point correlation functions.

17
The categories of this paper are: q-fin
26
The categories of this paper are: bayes-an
22
The categories of this paper are: chao-dyn
32
The categories of this paper are: atom-ph
1
The categories of this paper are: cs
20
The categories of this paper are: acc-phys
15
The categories of this paper are: nucl-ex
21
The categories of this paper are: adap-org
35
The categories of this paper are: mtrl-th
37
The categories of this paper are: supr-con
12
The categories of this paper are: nucl-th
0
The categories of this paper are: hep-ph
25
The categories of this paper are: patt-sol
31
The categories of this paper are: ao-sci
11
The categories of this paper are: hep-lat
23
The categories of this paper are: solv-int