The main statement of composite fermion theory is that the strongly correlated electrons at a magnetic field B ( or filling factor \ nu ) turn into weakly interacting composite fermions at a magnetic field B ^ * ( or composite fermion filling factor \ nu ^ * ).
12.
A properly designed NMR probe will maximize both the observe factor, which is the ratio of the sample volume being observed by the RF coil to the total sample volume required for analysis, and the filling factor, the ratio of the sample volume being observed by the RF coil to the coil volume.
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Electrons form Landau levels in a magnetic field, and the number of filled Landau levels is called the filling factor, given by the expression \ nu = \ rho \ phi _ 0 / B . Composite fermions form Landau-like levels in the effective magnetic field B ^ *, which are called composite fermion Landau levels or \ Lambda levels.
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Here \ Psi ^ { \ rm FQHE } _ { \ nu } is the wave function of interacting electrons at filling factor \ nu; \ Psi ^ { \ rm IQHE } _ { \ nu ^ * } is the wave function for weakly interacting electrons at \ nu ^ *; N is the number of electrons or composite fermions; z _ j = x _ j + iy _ j is the coordinate of the j th particle; and P is an operator that projects the wave function into the lowest Landau level.
15.
If we ignore the jellium and mutual Coulomb repulsion between the electrons as a zeroth order approximation, we have an infinitely degenerate lowest Landau level ( LLL ) and with a filling factor of 1 / n, we'd expect that all of the electrons would lie in the LLL . Turning on the interactions, we can make the approximation that all of the electrons lie in the LLL . If \ psi _ 0 is the single particle wavefunction of the LLL state with the lowest orbital angular momentum, then the Laughlin ansatz for the multiparticle wavefunction is
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