Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Scattering theory for lattice operators in dimension $d\geq 3$   This paper analyzes the scattering theory for periodic tight-binding
Hamiltonians perturbed by a finite range impurity. The classical energy
gradient flow is used to construct a conjugate (or dilation) operator to the
unperturbed Hamiltonian. For dimension $d\geq 3$ the wave operator is given by
an explicit formula in terms of this dilation operator, the free resolvent and
the perturbation. From this formula the scattering and time delay operators can
be read off. Using the index theorem approach, a Levinson theorem is proved
which also holds in presence of embedded eigenvalues and threshold
singularities.

21
The categories of this paper are: adap-org
33
The categories of this paper are: plasm-ph
23
The categories of this paper are: solv-int
25
The categories of this paper are: patt-sol
36
The categories of this paper are: cmp-lg
20
The categories of this paper are: acc-phys
11
The categories of this paper are: hep-lat
24
The categories of this paper are: dg-ga
35
The categories of this paper are: mtrl-th
8
The categories of this paper are: hep-ex
13
The categories of this paper are: quant-ph
1
The categories of this paper are: cs
30
The categories of this paper are: q-alg
32
The categories of this paper are: atom-ph
27
The categories of this paper are: comp-gas
7
The categories of this paper are: hep-th