Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Brownian Motion in a Classical Ideal Gas: a Microscopic Approach to
  Langevin's Equation   We present an insightful ``derivation'' of the Langevin equation and the
fluctuation dissipation theorem in the specific context of a heavier particle
moving through an ideal gas of much lighter particles. The Newton's Law of
motion ($m{\ddot x}=F$) for the heavy particle reduces to a Langevin equation
(valid on a coarser time scale) with the assumption that the lighter gas
particles follow a Boltzmann velocity distribution. Starting from the
kinematics of the random collisions we show that (1) the average force $<F>
\propto -{\dot x}$ and (2) the correlation function of the fluctuating force
$\eta= F-< F>$ is related to the strength of the average force.

8
The categories of this paper are: hep-ex
26
The categories of this paper are: bayes-an
11
The categories of this paper are: hep-lat
33
The categories of this paper are: plasm-ph
37
The categories of this paper are: supr-con
10
The categories of this paper are: q-bio
7
The categories of this paper are: hep-th
31
The categories of this paper are: ao-sci
12
The categories of this paper are: nucl-th
15
The categories of this paper are: nucl-ex
30
The categories of this paper are: q-alg
19
The categories of this paper are: eess
2
The categories of this paper are: math
17
The categories of this paper are: q-fin
27
The categories of this paper are: comp-gas
29
The categories of this paper are: funct-an