The potential barrier at the apex of a single-wall carbon nanotube emitter is found to be strongly and nonlinearly dependent on the external applied field, due to a quantum mechanical mechanism instead of the correction of image potential in Fowler-Nordheim theory. The field enhancement factor depends on the applied field and is much smaller than that predicted by the classical theory. The field induced apex-vacuum barrier lowering is confirmed to be the essential mechanism for efficient field electron emission from capped carbon nanotubes.

The analytical expressions of the fractional parentage coefficients for the total spin states of a spinor N-boson system have been derived. Thereby an S-conserved theory for the spinor Bose-Einstein condensation has been proposed. A set of equations has been established to describe the first excited band of the condensates. Numerical solution for 23Na has been given as an example.

tions decaying as r−sd−rd. The asymptotic scaling laws are studied in the frame of a double expansion in e=4−d and r with r of order e. In d,4, the initial slip exponents u8 of the magnetization and u of the response function, are calculated up to two-loop order. The crossover between fixed points is obtained. The long-time limit of the fluctuation-dissipation ratio is found in the aging regime, and its connection to equilibrium quantities is discussed. The comparison of our results with those of other systems without long-range correlated quenched impurities is also investigated.

For spinor Bose-Einstein condensates both the total spin S and its Z component SZ should be conserved. However, in existing theories, only the conservation of SZ has been taken into account. To remedy this, here we attempt to take the conservation of both S and SZ into account. For this purpose, a total spin state with the good quantum numbers S and SZ is introduced in the trial wave function; thereby a generalized Gross-Pitaevskii equation has been derived. With this equation, the ground bands of the 23Na and 87Rb condensates have been studied, where the levels that are distinct in S split. It was found that the level density is extremely dense in the bottom of the ground band of 23Na, i.e., in the vicinity of the ground state. On the contrary, for 87Rb, the levels are extremely dense in the top of the ground band.

A quantum-mechanical simulation is carried out to investigate the charge distribution and electrostatic potential along a 1 m long (5,5) single-walled carbon nanotube under realistic field-emission experimental conditions. A single layer of carbon atoms is found sufficient to shield most of the electric field except at the tip where strong field penetration occurs. The penetration leads to a nonlinear decrease of potential barrier for emission, which is equally responsible for the low threshold voltage besides the well-known geometrical field enhancement factor.