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')