Collective neutrino oscillations in non-spherical geometry
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The rich phenomenology of collective neutrino oscillations has been studied only in one-dimensional or spherically symmetric systems. Motivated by the non-spherical example of coalescing neutron stars, presumably the central engines of short gamma-ray bursts, we use the Liouville equation to formulate the problem for general source geometries. Assuming the neutrino ensemble displays self-maintained coherence, the problem once more becomes effectively one-dimensional along the streamlines of the overall neutrino flux. This approach for the first time provides a formal definition of the ``single-angle approximation'' frequently used for supernova neutrinos and allows for a natural generalization to non-spherical geometries. We study the explicit example of a disk-shaped source as a proxy for coalescing neutron stars.
14 pages, 6 eps figures
14 pages, 6 eps figures