Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Power-law approach to steady state in open lattices of non-interacting
  electrons   We address the question of how a non-equilibrium steady state (NESS) is
reached in the Linbdladian dynamics of an open quantum system. We develop an
expansion of the density matrix in terms of the NESS-excitations, each of which
has its own (exponential) decay rate. However, when the decay rates tend to
zero for many NESS-excitations (the spectral gap of the Liouvillian is closed
in the thermodynamic limit), the long-time dynamics of the system can exhibit a
power-law behaviour. This relaxation to NESS expectation values is determined
by the density of states close to zero spectral gap and the value of the
operator in these states. We illustrate this main idea on the example of the
lattice of non-interacting fermions coupled to Markovian leads at infinite bias
voltage. The current comes towards its NESS value starting from a typical
initial state as $\tau^{-3/2}$. This behaviour is universal and independent of
the space dimension.

23
The categories of this paper are: solv-int
25
The categories of this paper are: patt-sol
19
The categories of this paper are: eess
6
The categories of this paper are: astro-ph
21
The categories of this paper are: adap-org
3
The categories of this paper are: physics
20
The categories of this paper are: acc-phys
18
The categories of this paper are: econ
31
The categories of this paper are: ao-sci
7
The categories of this paper are: hep-th
32
The categories of this paper are: atom-ph
36
The categories of this paper are: cmp-lg
22
The categories of this paper are: chao-dyn
8
The categories of this paper are: hep-ex
26
The categories of this paper are: bayes-an
37
The categories of this paper are: supr-con