Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Few-body states of bosons interacting with a heavy quantum impurity   We consider the problem of a fixed impurity coupled to a small number $N$ of
non-interacting bosons. We focus on impurity-boson interactions that are
mediated by a closed-channel molecule, as is the case for tuneable interatomic
interactions in cold-atom experiments. We show that this two-channel model can
be mapped to a boson model with effective boson-boson repulsion, which enables
us to solve the three-body ($N=2$) problem analytically and determine the
trimer energy for impurity-boson scattering lengths $a>0$. By analysing the
atom-dimer scattering amplitude, we find a critical scattering length $a^*$ at
which the atom-dimer scattering length diverges and the trimer merges into the
dimer continuum. We furthermore calculate the tetramer energy exactly for $a>0$
and show that the tetramer also merges with the continuum at $a^*$. Indeed,
since the critical point $a^*$ formally resembles the unitary point $1/a = 0$,
we find that all higher-body bound states (involving the impurity and $N>1$
bosons) emerge and disappear at both of these points. We show that the behavior
at these 'multi-body resonances' is universal, since it occurs for any model
with an effective three-body repulsion involving the impurity. Thus, we see
that the fixed-impurity problem is strongly affected by a three-body parameter
even in the absence of the Efimov effect.

16
The categories of this paper are: stat
37
The categories of this paper are: supr-con
14
The categories of this paper are: math-ph
25
The categories of this paper are: patt-sol
8
The categories of this paper are: hep-ex
6
The categories of this paper are: astro-ph
15
The categories of this paper are: nucl-ex
11
The categories of this paper are: hep-lat
27
The categories of this paper are: comp-gas
5
The categories of this paper are: gr-qc
28
The categories of this paper are: alg-geom
35
The categories of this paper are: mtrl-th
22
The categories of this paper are: chao-dyn
18
The categories of this paper are: econ
20
The categories of this paper are: acc-phys
24
The categories of this paper are: dg-ga