The Klein paradox arises when considering the problem of tunneling a relativistic particle through a high potential barrier . When solving the Dirac equation, the probability of a particle passing through a potential barrier whose height is greater than the doubled resting energy of the particle and whose spatial width is less than the Compton wavelength of the particle [1] tends to unity, regardless of the height of the barrier [2] .
This paradox has a general physical character and is observed in nuclear physics, solid state physics (electron – hole excitations in graphene), and cosmology [1] .
The generally accepted explanation of the paradox lies in the plane of quantum field theory . So, the Dirac equation does not describe the motion of an individual particle, but the evolution in time of a quantum field, in which antiparticles will also be present. Therefore, in the presence of strong fields, pairs will be generated and newly born particles can also arise behind the barrier [1] .
The 75-year-old paradox was considered numerically in 2004 in a paper [3] by physicists from the University of Illinois . Using computer simulation in quantum field theory, it was shown that the electron is completely reflected from the barrier, and electron- positron pairs are created in the barrier.
Notes
- ↑ 1 2 3 Andreev A.V. Eighty years of the Klein paradox // Radioelectronics. Nanosystems. Information Technology. 2010. T. 2. No. 1-2. S. 3-43.
- ↑ Klein O. Die reflexion von elektronen an einem potentialsprung nach der relativistischen dynamik von Dirac // Z. Phys., 1929, 53, 157-165.
- ↑ Krekora P. et al. The Klein paradox in spatial and temporal resolution. Phys. Rev. Lett. 92 , 040406 (2004)