Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Efimov effect for a three-particle system with two identical fermions   We consider a three-particle quantum system in dimension three composed of
two identical fermions of mass one and a different particle of mass $m$. The
particles interact via two-body short range potentials. We assume that the
Hamiltonians of all the two-particle subsystems do not have bound states with
negative energy and, moreover, that the Hamiltonians of the two subsystems made
of a fermion and the different particle have a zero-energy resonance. Under
these conditions and for $m<m^* = (13.607)^{-1}$, we give a rigorous proof of
the occurrence of the Efimov effect, i.e., the existence of infinitely many
negative eigenvalues for the three-particle Hamiltonian $H$. More precisely, we
prove that for $m>m^*$ the number of negative eigenvalues of $H$ is finite and
for $m<m^*$ the number $N(z)$ of negative eigenvalues of $H$ below $z<0$ has
the asymptotic behavior $N(z) \sim \mathcal C(m) |\log|z||$ for $z \rightarrow
0^-$. Moreover, we give an upper and a lower bound for the positive constant
$\mathcal C(m)$.

15
The categories of this paper are: nucl-ex
35
The categories of this paper are: mtrl-th
31
The categories of this paper are: ao-sci
9
The categories of this paper are: nlin
16
The categories of this paper are: stat
33
The categories of this paper are: plasm-ph
18
The categories of this paper are: econ
10
The categories of this paper are: q-bio
21
The categories of this paper are: adap-org
1
The categories of this paper are: cs
7
The categories of this paper are: hep-th
26
The categories of this paper are: bayes-an
8
The categories of this paper are: hep-ex
29
The categories of this paper are: funct-an
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The categories of this paper are: eess
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The categories of this paper are: chao-dyn