Classical and quantum evolution in a simple coherent neutrino problem
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 (2N) 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.
- Research Organization:
- Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)
- Sponsoring Organization:
- USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR); USDOE Office of Science (SC), Nuclear Physics (NP)
- Grant/Contract Number:
- SC0020970; SC0017803; AC52-06NA25396; 89233218CNA000001
- OSTI ID:
- 2325267
- Alternate ID(s):
- OSTI ID: 1868305
- Report Number(s):
- LA-UR-21-32145; PRVDAQ; 083020
- Journal Information:
- Physical Review. D., Journal Name: Physical Review. D. Vol. 105 Journal Issue: 8; ISSN 2470-0010
- Publisher:
- American Physical SocietyCopyright Statement
- Country of Publication:
- United States
- Language:
- English
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