Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Corrections to Einstein's relation for Brownian motion in a tilted
  periodic potential   In this paper we revisit the problem of Brownian motion in a tilted periodic
potential. We use homogenization theory to derive general formulas for the
effective velocity and the effective diffusion tensor that are valid for
arbitrary tilts. Furthermore, we obtain power series expansions for the
velocity and the diffusion coefficient as functions of the external forcing.
Thus, we provide systematic corrections to Einstein's formula and to linear
response theory. Our theoretical results are supported by extensive numerical
simulations. For our numerical experiments we use a novel spectral numerical
method that leads to a very efficient and accurate calculation of the effective
velocity and the effective diffusion tensor.

31
The categories of this paper are: ao-sci
11
The categories of this paper are: hep-lat
16
The categories of this paper are: stat
22
The categories of this paper are: chao-dyn
15
The categories of this paper are: nucl-ex
8
The categories of this paper are: hep-ex
23
The categories of this paper are: solv-int
24
The categories of this paper are: dg-ga
36
The categories of this paper are: cmp-lg
13
The categories of this paper are: quant-ph
26
The categories of this paper are: bayes-an
30
The categories of this paper are: q-alg
34
The categories of this paper are: chem-ph
6
The categories of this paper are: astro-ph
35
The categories of this paper are: mtrl-th
10
The categories of this paper are: q-bio