Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Many-Body-Localization Transition : sensitivity to twisted boundary
  conditions   For disordered interacting quantum systems, the sensitivity of the spectrum
to twisted boundary conditions depending on an infinitesimal angle $\phi$ can
be used to analyze the Many-Body-Localization Transition. The sensitivity of
the energy levels $E_n(\phi)$ is measured by the level curvature $K_n=E_n"(0)$,
or more precisely by the Thouless dimensionless curvature $k_n=K_n/\Delta_n$,
where $\Delta_n$ is the level spacing that decays exponentially with the size
$L$ of the system. For instance $\Delta_n \propto 2^{-L}$ in the middle of the
spectrum of quantum spin chains of $L$ spins, while the Drude weight $D_n=L
K_n$ studied recently by M. Filippone, P.W. Brouwer, J. Eisert and F. von Oppen
[arxiv:1606.07291v1] involves a different rescaling. The sensitivity of the
eigenstates $\vert \psi_n(\phi) > $ is characterized by the susceptibility
$\chi_n=-F_n"(0)$ of the fidelity $F_n =\vert < \psi_n(0) \vert \psi_n(\phi)
>\vert $. Both observables are distributed with probability distributions
displaying power-law tails $P_{\beta}(k) \simeq A_{\beta} \vert k
\vert^{-(2+\beta)} $ and $Q(\chi) \simeq B_{\beta} \chi^{-\frac{3+\beta}{2}} $,
where $\beta$ is the level repulsion index taking the values $\beta^{GOE}=1$ in
the ergodic phase and $\beta^{loc}=0$ in the localized phase. The amplitudes
$A_{\beta}$ and $B_{\beta}$ of these two heavy tails are given by some moments
of the off-diagonal matrix element of the local current operator between two
nearby energy levels, whose probability distribution has been proposed as a
criterion for the Many-Body-Localization transition by M. Serbyn, Z. Papic and
D.A. Abanin [Phys. Rev. X 5, 041047 (2015)].

5
The categories of this paper are: gr-qc
7
The categories of this paper are: hep-th
3
The categories of this paper are: physics
30
The categories of this paper are: q-alg
0
The categories of this paper are: hep-ph
10
The categories of this paper are: q-bio
27
The categories of this paper are: comp-gas
26
The categories of this paper are: bayes-an
20
The categories of this paper are: acc-phys
33
The categories of this paper are: plasm-ph
28
The categories of this paper are: alg-geom
22
The categories of this paper are: chao-dyn
14
The categories of this paper are: math-ph
2
The categories of this paper are: math
16
The categories of this paper are: stat
29
The categories of this paper are: funct-an