Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Impact of mode regularization for quasinormal mode perturbation theories   We give insight into the critical problem of an open resonator that is
subject to a perturbation outside of its cavity region. We utilize the
framework of quasinormal modes (QNMs), which are the natural mode solutions to
the open boundary problem with complex eigenfrequencies. We first highlight
some fundamental problems with currently adopted formulas using QNM
perturbation theory, when perturbations are added outside the resonator
structure and present a first potential step for solving this problem connected
to a regularization of the QNMs. We then show an example for a full
three-dimensional plasmonic resonator of arbitrary shape and complex dispersion
and loss, clearly displaying the divergent nature of the first-order mode
change predicted from QNM perturbation theory. Subsequently, we concentrate on
the illustrative case of a one-dimensional dielectric barrier, where analytical
QNM solutions are possible. We inspect the change of the mode frequency as
function of distance between the cavity and another smaller barrier structure.
The results obtained from a few QNM expansion are compared with exact
analytical solutions from a transfer matrix approach. We show explicitly how
regularization prevents a problematic spatial divergence for QNM perturbations
in the far field, though eventually higher-order effects and multimodes can
also play a role in the full scattering solution, and retaining a pure discrete
QNM picture becomes questionable in such situations, since the input-output
coupling ultimately involves reservoir modes.

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The categories of this paper are: gr-qc
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: econ
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The categories of this paper are: solv-int
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The categories of this paper are: dg-ga
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The categories of this paper are: cmp-lg
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The categories of this paper are: ao-sci
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The categories of this paper are: supr-con
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The categories of this paper are: funct-an
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The categories of this paper are: stat
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The categories of this paper are: nucl-ex
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The categories of this paper are: acc-phys
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The categories of this paper are: q-fin
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The categories of this paper are: chao-dyn