Classical and Quantum Evolution in a Simple Coherent Neutrino Problem

TL;DR

This study compares mean-field and many-body quantum evolutions in a simple neutrino oscillation model, revealing their agreement in the infinite-spin limit and exploring quantum information measures' relation to dynamics.

Contribution

It provides an exact solution for the quantum many-body evolution in a simplified neutrino model, extending beyond mean-field approximations and analyzing quantum information properties.

Findings

Mean-field and many-body solutions agree in the infinite-spin limit.

Symmetries enable solving large quantum systems efficiently.

Quantum information measures relate to dynamical behavior.

Abstract

The extraordinary neutrino flux produced in extreme astrophysical environments like the early universe, core-collapse supernovae and neutron star mergers may produce coherent quantum neutrino oscillations on macroscopic length scales. The Hamiltonian describing this evolution can be mapped into quantum spin models with all-to-all couplings arising from neutrino-neutrino forward scattering. To date many studies of these oscillations have been performed in a mean-field limit where the neutrinos time evolve in a product state. In this paper we examine a simple two-beam model evolving from an initial product state and compare the mean-field and many-body evolution. The symmetries in this model allow us to solve the real-time evolution for the quantum many-body system for hundreds or thousands of spins, far beyond what would be possible in a more general case with an exponential number ($2^N$) of quantum states. We compare mean-field and many-body solutions for different initial product states and ratios of one- and two-body couplings, and find that in all cases in the limit of infinite spins the mean-field (product state) and many-body solutions coincide for simple observables. This agreement can be understood as a consequence of the fact that the typical initial condition represents a very local but dense distribution about a mean energy in the spectrum of the Hamiltonian. We explore quantum information measures like entanglement entropy and purity of the many-body solutions, finding intriguing relationships between the quantum information measures and the dynamical behavior of simple physical observables.