Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Scale Invariant Effective Hamiltonians for a Graph with a Small Compact
  Core   We consider a compact metric graph of size $\varepsilon$, and attach to it
several edges (leads) of length of order one (or of infinite length). As
$\varepsilon$ goes to zero, the graph $\mathcal{G}^\varepsilon$ obtained in
this way looks like the star-graph formed by the leads joined in a central
vertex. On $\mathcal{G}^\varepsilon$ we define an Hamiltonian $H^\varepsilon$,
properly scaled with the parameter $\varepsilon$. We prove that there exists a
scale invariant effective Hamiltonian on the star-graph that approximates
$H^\varepsilon$ (in a suitable norm resolvent sense) as $\varepsilon\to0$. The
effective Hamiltonian depends on the spectral properties of an auxiliary
$\varepsilon$-independent Hamiltonian defined on the compact graph obtained by
setting $\varepsilon = 1$. If zero is not an eigenvalue of the auxiliary
Hamiltonian, in the limit $\varepsilon\to0$, the leads are decoupled.

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The categories of this paper are: cs
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The categories of this paper are: hep-th
3
The categories of this paper are: physics
15
The categories of this paper are: nucl-ex
29
The categories of this paper are: funct-an
35
The categories of this paper are: mtrl-th
36
The categories of this paper are: cmp-lg
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The categories of this paper are: chao-dyn
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The categories of this paper are: q-fin
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The categories of this paper are: q-bio
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The categories of this paper are: dg-ga
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The categories of this paper are: econ
30
The categories of this paper are: q-alg
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The categories of this paper are: alg-geom
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The categories of this paper are: comp-gas
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The categories of this paper are: patt-sol