科研之友
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摘要
We investigate the semi-classical dynamics of massless Dirac fermions in 2+1 dimensions in the presence of external electromagnetic fields. By generalizing the a matrices by two generators of the SU(2) group in the (2S+1)-dimensional representation and doing a certain scaling, we formulate an S -> 8 limit where the orbital and the spinor degrees become classical. We solve for the classical trajectories for a free particle on a cylinder and a particle in a constant magnetic field. We compare the semi-classical spectrum, obtained by Bohr-Sommerfeld quantization with the exact quantum spectrum for low values of S. For the free particle, the semi-classical spectrum is exact. For the particle in a constant magnetic field, the semi-classical spectrum reproduces all the qualitative features of the exact quantum spectrum at all S. The quantitative fit for S = 1/2 is reasonably good.
- 出版日期2012-5-11
- 单位常州工学院
