Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Time auto-correlation function and Green-Kubo formula: A study on
  disordered harmonic chain   We have considered heat conduction in a one-dimensional mass disordered
harmonic chain of $N$ particles connected to two Langevin type reservoirs at
different temperatures. An exact expression for the boundary heat
current-current auto-correlation function in the non-equilibrium steady state
(NESS) is obtained in terms of non-equilibrium phonon Green's functions. The
time integral of the correlation function gives expected result, both in
non-equilibrium as well as equilibrium cases. Using the form of this
correlation function we show that asymptotic system size dependence of current
fluctuation in NESS for a mass disordered harmonic chain is $N^{-\alpha}$ for
different boundary conditions. For free and fixed boundary conditions we get
$\alpha=1/2$ and 3/2 respectively, while for pinned case the fluctuation decays
exponentially with system size.

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The categories of this paper are: hep-ph
36
The categories of this paper are: cmp-lg
3
The categories of this paper are: physics
37
The categories of this paper are: supr-con
21
The categories of this paper are: adap-org
6
The categories of this paper are: astro-ph
14
The categories of this paper are: math-ph
18
The categories of this paper are: econ
33
The categories of this paper are: plasm-ph
30
The categories of this paper are: q-alg
16
The categories of this paper are: stat
28
The categories of this paper are: alg-geom
29
The categories of this paper are: funct-an
15
The categories of this paper are: nucl-ex
5
The categories of this paper are: gr-qc
32
The categories of this paper are: atom-ph