arXiv subjects
Publications and source records attributed to Cai-Dong Xiong.
A relativistic quantum-mechanical description of guided waves is given, based on which we present an alternative way to describe and interpret the propagation of electromagnetic wave packets through an undersized waveguide. In particular, we show that the superluminal phenomenon of evanescent modes is actually a known conclusion in quantum field theory, and it preserves a quantum-mechanical causality.
Time operator can be introduced by three different approaches: by pertaining it to dynamical variables; by quantizing the classical expression of time; taken as the restriction of energy shift generator to the Hilbert space of a physical system.
Relativistic free-motion time-of-arrival theory for massive spin-1/2 particles is systematically developed. Contrary to the nonrelativistic time-of-arrival operator studied thoroughly in previous literatures, the relativistic time-of-arrival operator possesses self-adjoint extensions because of the particle-antiparticle symmetry. The nonrelativistic limit of our theory is in agreement with the nonrelativistic time-of-arrival theory.
The usual quantum mechanics describes the mass eigenstates. To describe the proper-time eigenstates, a duality theory of the usual quantum mechanics was developed. The time interval is treated as an operator on an equal footing with the space interval, and the quantization of the space-time intervals between events is obtained. As a result, one can show that there exists a zero-point time interval.
Much experimental evidence of superluminal phenomena has been available by electromagnetic wave propagation experiments, with the results showing that the phase time do describe the barrier traversal time. Based on the extrapolated phase time approach and numerical methods, we show that, in contrary to the ordinary Bessel waves of real argument, the group velocities of modified Bessel waves are superluminal, and obtain the following results: 1) the group velocities increase with the increase of propagation distance, which is similar to the evanescent plane-wave cases; 2) for large wave numbers, the group velocities fall off as the wave numbers increase, which is similar to the evanescent plane-wave cases; 3) for small wave numbers, the group velocities increase with the increase of wave numbers, this is different from the evanescent plane-wave cases.
Traditionally, the theory related to the spatial angular momentum has been studied completely, while the investigation in the generator of Lorentz boost is inadequate. In this paper we show that the generator of Lorentz boost has a nontrivial physical significance, it endows a charged system with an electric moment, and has an important significance for the electrical manipulations of electron spin in spintronics. An alternative treatment and interpretation for the traditional Darwin term and spin-orbit coupling are given.
In this article, we show that in the level of quantum mechanics, a photon position operator with commuting components can be obtained in a more natural way; in the level of quantum field theory, the photon position operator corresponds to the center of the photon number. It is most interesting for us to show that, a photon inside a waveguide can be localized in the same sense that a massive particle can be localized in free space, and just as that it is impossible to localize a massive particle with a greater precision than its Compton wavelength, one can also arrival at a similar conclusion: it is impossible to localize a photon inside a waveguide with a greater precision than its equivalent Compton wavelength, which owing to evanescent-wave or photon-tunneling phenomena.