Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Statistical diagonalization of a random biased Hamiltonian: the case of
  the eigenvectors   We present a non perturbative calculation technique providing the mixed
moments of the overlaps between the eigenvectors of two large quantum
Hamiltonians: $\hat{H}_0$ and $\hat{H}_0+\hat{W}$, where $\hat{H}_0$ is
deterministic and $\hat{W}$ is random. We apply this method to recover the
second order moments or Local Density Of States in the case of an arbitrary
fixed $\hat{H}_0$ and a Gaussian $\hat{W}$. Then we calculate the fourth order
moments of the overlaps in the same setting. Such quantities are crucial for
understanding the local dynamics of a large composite quantum system. In this
case, $\hat{H}_0$ is the sum of the Hamiltonians of the system subparts and
$\hat{W}$ is an interaction term. We test our predictions with numerical
simulations.

2
The categories of this paper are: math
37
The categories of this paper are: supr-con
24
The categories of this paper are: dg-ga
8
The categories of this paper are: hep-ex
20
The categories of this paper are: acc-phys
14
The categories of this paper are: math-ph
11
The categories of this paper are: hep-lat
29
The categories of this paper are: funct-an
6
The categories of this paper are: astro-ph
25
The categories of this paper are: patt-sol
26
The categories of this paper are: bayes-an
1
The categories of this paper are: cs
31
The categories of this paper are: ao-sci
23
The categories of this paper are: solv-int
9
The categories of this paper are: nlin
33
The categories of this paper are: plasm-ph