Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quantum impurity in a Luttinger liquid: Exact solution of the
  Kane-Fisher model   A Luttinger Liquid coupled to a quantum impurity describes a large number of
physical systems. The Hamiltonian consists of left- and right-moving fermions
interacting among themselves via a density-density coupling and scattering off
a localised transmitting and reflecting impurity. We solve exactly the
Hamiltonian by means of an incoming-outgoing scattering Bethe basis which
properly incorporates all scattering processes. A related model, the
Weak-Tunnelling model, wherein the impurity is replaced by a tunnel junction,
is solved by the same method. The consistency of the construction is
established through a generalised Yang-Baxter relation. Periodic boundary
conditions are imposed and the resulting Bethe Ansatz equations are derived by
means of the Off Diagonal Bethe Ansatz approach. We derive the spectrum of the
model for all coupling constant regimes and calculate the impurity free energy.
We discuss the low energy behaviour of the systems for both repulsive and
attractive interactions.

25
The categories of this paper are: patt-sol
12
The categories of this paper are: nucl-th
17
The categories of this paper are: q-fin
31
The categories of this paper are: ao-sci
27
The categories of this paper are: comp-gas
1
The categories of this paper are: cs
7
The categories of this paper are: hep-th
23
The categories of this paper are: solv-int
3
The categories of this paper are: physics
30
The categories of this paper are: q-alg
35
The categories of this paper are: mtrl-th
10
The categories of this paper are: q-bio
37
The categories of this paper are: supr-con
29
The categories of this paper are: funct-an
9
The categories of this paper are: nlin
22
The categories of this paper are: chao-dyn