Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Scattering of mechanical waves from the perspective of open systems and
  Feshbach projection operators   In this paper, we consider the problem of mechanical wave scattering from a
spatially finite system into an infinite surrounding environment. The goal is
to illuminate why the scattering spectrum undergoes peaks and dips at specific
locations and how these locations connect to the vibrational properties of the
scatterer. We show that these locations are not directly connected to the
eigenvalues of an operator, $H_0$, which corresponds to the finite system
isolated from its environment with fixed boundary conditions. However, they are
deeply connected to the eigenvalues of an effective operator, $H_{eff}$, which
is composed of $H_0$ and an additional coupling term. The scattering spectrum
emerges as a meromorphic expression, restricted to the real frequency axis,
whose poles are precisely the eigenvalues of $H_{eff}$. The conceptual novelty
presented here is that of open systems, which seeks to convert the infinite
dimensional scattering problem (scatterer+environment) into a finite
dimensional effective problem involving only the finite scatterer. The
numerical novelty presented here is that of the Feshbach projection operator
formalism which allows us to formally calculate $H_{eff}$ and illuminate its
relation with $H_0$. Both open systems and Feshbach formalism have a long
history in quantum mechanics but their application to mechanical waves is new.
Here, these concepts are critical to exposing the inter-relationship among the
scattering spectrum, $H_{eff}$, $H_0$, and the scattering Green's function. We
also note that concepts like Fano resonances are special cases of our analysis
-- emerging from an $H_{eff}$ some of whose complex eigenvalues overlap
(exceptional points).

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The categories of this paper are: gr-qc
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The categories of this paper are: hep-th
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-ex
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The categories of this paper are: hep-lat
30
The categories of this paper are: q-alg
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The categories of this paper are: cmp-lg
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The categories of this paper are: econ
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The categories of this paper are: alg-geom
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The categories of this paper are: mtrl-th
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The categories of this paper are: q-bio
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The categories of this paper are: math
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The categories of this paper are: astro-ph
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The categories of this paper are: adap-org
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The categories of this paper are: ao-sci
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The categories of this paper are: stat