Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Stability and instability towards delocalization in MBL systems   We propose a theory that describes quantitatively the (in)stability of fully
MBL systems due to ergodic, i.e. delocalized, grains, that can be for example
due to disorder fluctuations. The theory is based on the ETH hypothesis and
elementary notions of perturbation theory. The main idea is that we assume as
much chaoticity as is consistent with conservation laws. The theory describes
correctly -even without relying on the theory of local integrals of motion
(LIOM)- the MBL phase in 1 dimension at strong disorder. It yields an explicit
and quantitative picture of the spatial boundary between localized and ergodic
systems. We provide numerical evidence for this picture.
  When the theory is taken to its extreme logical consequences, it predicts
that the MBL phase is destabilised in the long time limit whenever 1)
interactions decay slower than exponentially in $d=1$ and 2) always in $d>1$.
Finer numerics is required to assess these predictions.

8
The categories of this paper are: hep-ex
13
The categories of this paper are: quant-ph
30
The categories of this paper are: q-alg
32
The categories of this paper are: atom-ph
21
The categories of this paper are: adap-org
24
The categories of this paper are: dg-ga
19
The categories of this paper are: eess
11
The categories of this paper are: hep-lat
14
The categories of this paper are: math-ph
34
The categories of this paper are: chem-ph
7
The categories of this paper are: hep-th
6
The categories of this paper are: astro-ph
3
The categories of this paper are: physics
31
The categories of this paper are: ao-sci
0
The categories of this paper are: hep-ph
2
The categories of this paper are: math