import sys
sys.path.append('../code')
from init_mooc_nb import *
init_notebook()
MoocVideo("Ndf2Z84g1R0", src_location="2.3-intro")
question = ("Consider an isolated system with N=7 pairs of Majoranas, and an even total fermion parity. "
"What is the ground state degeneracy of the system?")
answers = ["Trick question - it is not possible to get N=7 pairs of Majorana modes with even parity.",
"2^7.",
"2^6.",
"14",
"The system has an energy gap, so it cannot be degenerate."]
explanation = ("N pairs of Majoranas means a Hilbert space with dimension 2^7, "
"out of which half have even total parity and half have odd total parity. "
"So the degeneracy at fixed even parity is 2^6.")
MoocMultipleChoiceAssessment(question, answers, correct_answer=2, explanation=explanation)
question = ("Consider a system with only one pair of Majorana modes, thus with just two degenerate states with different fermion parity. "
"What happens when we exchange the pair of Majorana modes, starting from a given fermion parity eigenstate?")
answers = ["The fermion parity of the state flips.",
"Nothing happens.",
"The system wave-function picks up a phase that depends on the fermion parity.",
"You end up in a superposition of the two states."]
explanation = ("The total fermion parity cannot change, "
"but the two states can pick up a different phase. "
"This is indeed what happens since the operator $U$ describing the exchange depends on fermion parity.")
MoocMultipleChoiceAssessment(question, answers, correct_answer=2, explanation=explanation)
MoocVideo("V3e9r4S8GHs", src_location="2.3-summary")
MoocDiscussion('Questions', 'Non-Abelian statistics of Majorana modes')