Fibonacci fast convergence for neutrino oscillations in matter

Understanding neutrino oscillations in matter requires a non-trivial diagonalization of the Hamiltonian. As the exact solution is very complicated, many approximation schemes have been pursued. Here we show that one scheme, systematically applying rotations to change to a better basis, converges exp...

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Bibliographic Details
Published in:Physics letters. B 2020-08, Vol.807 (C), p.135592, Article 135592
Main Authors: Denton, Peter B., Parke, Stephen J., Zhang, Xining
Format: Article
Language:English
Subjects:
PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
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Summary:Understanding neutrino oscillations in matter requires a non-trivial diagonalization of the Hamiltonian. As the exact solution is very complicated, many approximation schemes have been pursued. Here we show that one scheme, systematically applying rotations to change to a better basis, converges exponentially fast wherein the rate of convergence follows the Fibonacci sequence. We find that the convergence rate of this procedure depends very sensitively on the initial choices of the rotations as well as the mechanism of selecting the pivots. We then apply this scheme for neutrino oscillations in matter and discover that the optimal convergence rate is found using the following simple strategy: first apply the vacuum (2-3) rotation and then use the largest off-diagonal element as the pivot for each of the following rotations. The Fibonacci convergence rate presented here may be extendable to systems beyond neutrino oscillations.
ISSN:0370-2693
1873-2445
DOI:10.1016/j.physletb.2020.135592