Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Two interacting particles in a random potential: mapping onto one
  parameter localization theories without interaction   We consider two models for a pair of interacting particles in a random
potential: (i) two particles with a Hubbard interaction in arbitrary dimensions
and (ii) a strongly bound pair in one dimension. Establishing suitable
correpondences we demonstrate that both cases can be described in terms
familiar from theories of noninteracting particles. In particular, these two
cases are shown to be controlled by a single scaling variable, namely the pair
conductance $g_2$. For an attractive or repulsive Hubbard interaction and
starting from a certain effective Hamiltonian we derive a supersymmetric
nonlinear $\sigma$ model. Its action turns out to be closely related to the one
found by Efetov for noninteracting electrons in disordered metals. This enables
us to describe the diffusive motion of the particle pair on scales exceeding
the one-particle localization length $L_1$ and to discuss the corresponding
level statistics. For tightly bound pairs in one dimension, on the other hand,
we follow early work by Dorokhov and exploit the analogy with the transfer
matrix approach to quasi 1d conductors. Extending our study to M particles we
obtain a M-particle localization length scaling like the Mth power of the
one-particle localization length.

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The categories of this paper are: hep-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: physics
7
The categories of this paper are: hep-th
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The categories of this paper are: q-fin
25
The categories of this paper are: patt-sol
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The categories of this paper are: hep-lat
19
The categories of this paper are: eess
2
The categories of this paper are: math
18
The categories of this paper are: econ
16
The categories of this paper are: stat
24
The categories of this paper are: dg-ga
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The categories of this paper are: cs
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The categories of this paper are: gr-qc
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The categories of this paper are: comp-gas
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The categories of this paper are: solv-int