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 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.
- Research Organization:
- Brookhaven National Laboratory (BNL), Upton, NY (United States); Fermi National Accelerator Laboratory (FNAL), Batavia, IL (United States)
- Sponsoring Organization:
- USDOE Office of Science (SC), High Energy Physics (HEP); European Unions Horizon 2020
- Grant/Contract Number:
- AC02-07CH11359; SC0012704; 690575; 674896
- OSTI ID:
- 1635419
- Alternate ID(s):
- OSTI ID: 1569237; OSTI ID: 1638789
- Report Number(s):
- arXiv:1909.02009; FERMILAB-PUB-19-462-T; BNL-216160-2020-JAAM; S0370269320303968; 135592; PII: S0370269320303968
- Journal Information:
- Physics Letters. B, Journal Name: Physics Letters. B Vol. 807 Journal Issue: C; ISSN 0370-2693
- Publisher:
- ElsevierCopyright Statement
- Country of Publication:
- Netherlands
- Language:
- English
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