Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Anomalous transport and phonon renormalization in a chain with
  transverse and longitudinal vibrations   We study thermal transport in a chain of coupled atoms, which can vibrate in
longitudinal as well as transverse directions. The particles interact through
anharmonic potentials upto cubic order. The problem is treated quantum
mechanically. We first calculate the phonon frequencies self-consistently
taking into account the anharmonic interactions. We show that for all the
modes, frequencies must have linear dispersion with wave-vector $q$ for small
$q$ irrespective of their bare dispersions. We then calculate the phonon
relaxation rates $\Gamma_i(q)$, where $i$ is the polarization index of the
mode, in a self-consistent approximation based on second order perturbation
diagrams. We find that the relaxation rate for the longitudinal phonon,
$\Gamma_x(q) \propto q^{3/2}$, while that for the transverse phonon
$\Gamma_y(q) \propto q^2$. The consequence of these results on the thermal
conductivity $\kappa(N)$ of a chain of $N$ particles is that $\kappa(N) \propto
N^{1/2}$.

5
The categories of this paper are: gr-qc
36
The categories of this paper are: cmp-lg
1
The categories of this paper are: cs
0
The categories of this paper are: hep-ph
30
The categories of this paper are: q-alg
21
The categories of this paper are: adap-org
19
The categories of this paper are: eess
26
The categories of this paper are: bayes-an
35
The categories of this paper are: mtrl-th
11
The categories of this paper are: hep-lat
16
The categories of this paper are: stat
29
The categories of this paper are: funct-an
14
The categories of this paper are: math-ph
8
The categories of this paper are: hep-ex
37
The categories of this paper are: supr-con
15
The categories of this paper are: nucl-ex