Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Time delay matrix at the spectrum edge and the minimal chaotic cavities   Using the concept of minimal chaotic cavities, we give the distribution of
the proper delay times of $Q=-i\hbar S^\dagger \frac{\partial S}{\partial E}$
at the spectrum edge with a scattering matrix $S$ belonging to circular
ensembles CE. The three classes of symmetry ($\beta=1$, 2 and 4) will be
analyzed to show how it differs from the distribution obtained in the bulk of
the spectrum. In this new class of universality at the spectrum edge, more
attention will be given to the Wigner time $\tau_w=tr(Q)$ and its distribution
will be given analytically in the case of 2 modes scattering. The results will
be presented exactly at all the Fermi energies without any approximation. All
this will be tested numerically with an excellent precision.

28
The categories of this paper are: alg-geom
33
The categories of this paper are: plasm-ph
5
The categories of this paper are: gr-qc
15
The categories of this paper are: nucl-ex
12
The categories of this paper are: nucl-th
34
The categories of this paper are: chem-ph
22
The categories of this paper are: chao-dyn
23
The categories of this paper are: solv-int
35
The categories of this paper are: mtrl-th
16
The categories of this paper are: stat
29
The categories of this paper are: funct-an
31
The categories of this paper are: ao-sci
9
The categories of this paper are: nlin
26
The categories of this paper are: bayes-an
25
The categories of this paper are: patt-sol
0
The categories of this paper are: hep-ph