Fibonacci Fast Convergence for Neutrino Oscillations in Matter

TL;DR

This paper introduces a Fibonacci sequence-based exponential convergence scheme for approximating neutrino oscillations in matter, improving computational efficiency in diagonalizing the Hamiltonian.

Contribution

It presents a novel rotation-based approximation method with Fibonacci convergence for neutrino oscillation Hamiltonians, enhancing existing approximation schemes.

Findings

Convergence rate follows Fibonacci sequence.

Optimal strategy involves vacuum rotation and pivot selection.

Method potentially applicable to other systems.

Abstract

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.