Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A relativistically exact Eikonal equation for optical fibers with
  application to adiabatically deforming ring interferometers   We derive the relativistically exact Eikonal equation for ring
interferometers undergoing deformations. For ring interferometers that undergo
slow deformation we describe the two leading terms in the adiabatic expansion
of the phase shift. The leading term is independent of the refraction index $n$
and is given by a line integral generalizing results going back to Sagnac
\cite{sagnac1913,wang2004,Ori} for non-deforming interferometers to all orders
in {$\beta=|\mathbf{v}|/c$}. In the non-relativistic limit {this term} is
$O(\beta)$. The next term in the adiabaticity has the form of a double
integral, it is of order $\beta^0$ and depends on the refractive index $n$. It
accounts for non-reciprocity due to changing circumstances in the fiber. The
adiabatic correction is often comparable to the Sagnac term. In particular,
this is the case in Fizeau's interferometer. Besides providing a mathematical
framework that puts all ring interferometers under a single umbrella, our
results generalize and strengthen results of \cite{Ori, shupe} to fibers with
chromatic dispersion.

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The categories of this paper are: nucl-th
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The categories of this paper are: gr-qc
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The categories of this paper are: q-fin
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The categories of this paper are: astro-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: bayes-an
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The categories of this paper are: quant-ph
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The categories of this paper are: adap-org
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The categories of this paper are: hep-th
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The categories of this paper are: cmp-lg
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The categories of this paper are: q-bio
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The categories of this paper are: chem-ph
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The categories of this paper are: q-alg
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The categories of this paper are: dg-ga
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The categories of this paper are: comp-gas
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The categories of this paper are: hep-lat