Kvantmekanisk sammanflätning i nukleon-nukleonspridning
Typ
Examensarbete för kandidatexamen
Bachelor Thesis
Bachelor Thesis
Program
Publicerad
2023
Författare
ABRAHAMSSON, LUCAS
CAVALLIN, ALMA
HANEBRING, LISE
HANSEN, HAMPUS
KARLSSON ÖHMAN, ERIK
LEO
Modellbyggare
Tidskriftstitel
ISSN
Volymtitel
Utgivare
Sammanfattning
The following report studies the quantum entanglement phenomenon analytically and numerically. Spe cifically, the degree to which the scattering operators S and M entangle a neutron and a proton with
respect to spin during a scattering process is investigated. The M matrix is computed analytically, using
a low-energy approximation considering only s-waves, as well as numerically.
This study differentiates itself from prior research by investigating entanglement based on the M ope rator instead of the S operator. The numerical calculation of M is possible without making the s-wave
approximation, thus resulting in a more realistic model where it is possible to analyze higher energies
and the scattering angle dependence.
Numerical calculations are performed using provided code, and the convergence of the calculations with
respect to partial waves and sampling points is analyzed. Entanglement measures are calculated nume rically using various methods, including Monte Carlo integration, which is implemented in Python. Two
entanglement measures are presented and compared, and the entanglement power is then used to inve stigate entanglement in nucleon-nucleon scattering. The study establishes that there is no combination
of kinetic energy and scattering angle that yields a fully entangled final state in spin space for all pos sible initial states. Similarly, there is no combination of kinetic energy and scattering angle that yields a
non-entangled final state for all possible initial states.
The entanglement power of the analytic S and M operators is investigated. It is found that the entang lement power for M converges to a non-zero value in the low-energy limit, which is also observed in
the numerical results. The entanglement power of the analytically derived M matrix is compared with
the numerically calculated one and shows good agreement for energies up to a few MeV. The analytical
expression of M establishes that no entanglement occurs in the interaction at very low energies if the
nucleons initially have parallel spins. This is also verified in the numerical results for specific initial states.
Beskrivning
Ämne/nyckelord
entanglement, scattering, nucleon, strong force, Nijmegen potential, partial waves, two-nucleon system, entanglement power