Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Many-body Systems Interacting via a Two-body Random Ensemble: average
  energy of each angular momentum   In this paper, we discuss the regularities of energy of each angular momentum
$I$ averaged over all the states for a fixed angular momentum (denoted as
$\bar{E}_I$'s) in many-body systems interacting via a two-body random ensemble.
It is found that $\bar{E}_I$'s with $I \sim I_{min}$ (minimum of $I$) or
$I_{max}$ have large probabilities (denoted as ${\cal P}(I)$) to be the lowest,
and that ${\cal P}(I)$ is close to zero elsewhere. A simple argument based on
the randomness of the two-particle cfp's is given. A compact trajectory of the
energy $\bar{E}_I$ vs. $I(I+1)$ is found to be robust. Regular fluctuations of
the $P(I)$ (the probability of finding $I$ to be the ground state) and ${\cal
P}(I)$ of even fermions in a single-$j$ shell and boson systems are found to be
reverse, and argued by the dimension fluctuation of the model space. Other
regularities, such as why there are 2 or 3 sizable ${\cal P}(I)$'s with $I\sim
I_{min}$ and ${\cal P}(I) \ll {\cal P}(I_{max})$'s with $I\sim I_{max}$, why
the coefficients $C$ defined by $<\bar{E}_I >$=$CI(I+1)$ is sensitive to the
orbits and not sensitive to particle number, are found and studied for the
first time.

33
The categories of this paper are: plasm-ph
31
The categories of this paper are: ao-sci
23
The categories of this paper are: solv-int
29
The categories of this paper are: funct-an
6
The categories of this paper are: astro-ph
16
The categories of this paper are: stat
36
The categories of this paper are: cmp-lg
4
The categories of this paper are: cond-mat
17
The categories of this paper are: q-fin
19
The categories of this paper are: eess
35
The categories of this paper are: mtrl-th
32
The categories of this paper are: atom-ph
14
The categories of this paper are: math-ph
30
The categories of this paper are: q-alg
13
The categories of this paper are: quant-ph
24
The categories of this paper are: dg-ga