Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An investigation of equilibration in small quantum systems: the example
  of a particle in a 1D random potential   We investigate the equilibration of a small isolated quantum system by means
of its matrix of asymptotic transition probabilities in a preferential basis.
The trace of this matrix is shown to measure the degree of equilibration of the
system launched from a typical state, from the standpoint of the chosen basis.
This approach is substantiated by an in-depth study of the example of a
tight-binding particle in one dimension. In the regime of free ballistic
propagation, the above trace saturates to a finite limit, testifying good
equilibration. In the presence of a random potential, the trace grows linearly
with the system size, testifying poor equilibration in the insulating regime
induced by Anderson localization. In the weak-disorder situation of most
interest, a universal finite-size scaling law describes the crossover between
the ballistic and localized regimes. The associated crossover exponent 2/3 is
dictated by the anomalous band-edge scaling characterizing the most localized
energy eigenstates.

19
The categories of this paper are: eess
13
The categories of this paper are: quant-ph
6
The categories of this paper are: astro-ph
30
The categories of this paper are: q-alg
8
The categories of this paper are: hep-ex
27
The categories of this paper are: comp-gas
14
The categories of this paper are: math-ph
16
The categories of this paper are: stat
7
The categories of this paper are: hep-th
32
The categories of this paper are: atom-ph
21
The categories of this paper are: adap-org
18
The categories of this paper are: econ
37
The categories of this paper are: supr-con
31
The categories of this paper are: ao-sci
35
The categories of this paper are: mtrl-th
1
The categories of this paper are: cs