Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Fermi Edge Singularities and Backscattering in a Weakly Interacting 1D
  Electron Gas   The photon-absorption edge in a weakly interacting one-dimensional electron
gas is studied, treating backscattering of conduction electrons from the core
hole exactly. Close to threshold, there is a power-law singularity in the
absorption, $I(\epsilon) \propto \epsilon^{-\alpha}$, with $\alpha = 3/8 +
\delta_+/\pi - \delta_+^2/2\pi^2$ where $\delta_+$ is the forward scattering
phase shift of the core hole. In contrast to previous theories, $\alpha$ is
finite (and universal) in the limit of weak core hole potential. In the case of
weak backscattering $U(2k_F)$, the exponent in the power-law dependence of
absorption on energy crosses over to a value $\alpha = \delta_+/\pi -
\delta_+^2/2\pi^2$ above an energy scale $\epsilon^* \sim
[U(2k_F)]^{1/\gamma}$, where $\gamma$ is a dimensionless measure of the
electron-electron interactions.

30
The categories of this paper are: q-alg
36
The categories of this paper are: cmp-lg
11
The categories of this paper are: hep-lat
6
The categories of this paper are: astro-ph
22
The categories of this paper are: chao-dyn
25
The categories of this paper are: patt-sol
16
The categories of this paper are: stat
7
The categories of this paper are: hep-th
33
The categories of this paper are: plasm-ph
37
The categories of this paper are: supr-con
10
The categories of this paper are: q-bio
21
The categories of this paper are: adap-org
2
The categories of this paper are: math
31
The categories of this paper are: ao-sci
35
The categories of this paper are: mtrl-th
29
The categories of this paper are: funct-an