介质中回旋共振的相对论量子理论

The long-term cyclotron dynamics of relativistic wave packets: spontaneous collapse and revival

In this work we study the effects of collapse and revival as well as {\it Zitterbewegung} (ZB) phenomenon, for the relativistic electron wave packets, which are a superposition of the states with quantum numbers sharply peaked around some level $n_0$ of the order of few tens. The probability densities as well as average velocities of the packet center and the average spin components were calculated analytically and visualized. Our computations demonstrate that due to dephasing of the states for times larger than the cyclotron period the initial wave packet (which includes the states with the p…

Relativistic and non-relativistic quantum Brownian motion in an anisotropic dissipative medium

Using a minimal-coupling-scheme we investigate the quantum Brownian motion of a particle in an anisotropic-dissipative-medium under the influence of an arbitrary potential in both relativistic and non-relativistic regimes. A general quantum Langevin equation is derived and explicit expressions for quantum-noise and dynamical variables of the system are obtained. The equations of motion for the canonical variables are solved explicitly and an expression for the radiation-reaction of a charged particle in the presence of a dissipative-medium is obtained. Some examples are given to elucidate the …

A Canonical Relativistic Approach to Quantize Electromagnetic Field in the Presence of Moving Magneto-Dielectric Media

A canonical relativistic formulation is introduced to quantize electromagnetic field in the presence of a polarizable and magnetizable moving medium. The medium is modeled by a continuum of four vectors in a phenomenological way. The covariant wave equation for the vector potential and the covariant constitutive equation of the medium are obtained as the Euler- Lagrange equations using the Lagrangian of the total system. A tensor of the third rank which couples the electromagnetic field with the medium is introduced and the susceptibility tensor of the medium is obtained in terms of the coupli…

相对论不变随机介质中的粒子动力学

Particle dynamics in a relativistic invariant stochastic medium

研究了粒子在由相对论不变随机性质定义的介质中运动的动力学。为此，介质施加在粒子上的力由平稳随机变量定义为粒子固有时间的函数。得到了单个一维粒子的运动方程，并进行了数值求解。给出了粒子在随机运动过程中漂移动量的守恒定律。此外，两个相互排斥的粒子的总线动量的平均值守恒也符合库仑相互作用。因此，结果表明在所研究的系统中实现了一种随机Noether定理。可能的应用程序的随机表示的量子力学先进。

Finite temperature Cherenkov radiation in the presence of a magnetodielectric medium

A canonical approach to Cherenkov radiation in the presence of a magnetodielectric medium is presented in classical, nonrelativistic and relativistic quantum regimes. The equations of motion for the canonical variables are solved explicitly for both positive and negative times. Maxwell and related constitute equations are obtained. In the large-time limit, the vector potential operator is found and expressed in terms of the medium operators. The energy loss of a charged particle, emitted in the form of radiation, in finite temperature is calculated. A Dirac equation concerning the relativistic…

Trembling motion of relativistic electrons in a magnetic field

Zitterbewegung (ZB, the trembling motion) of free relativistic electrons in a vacuum in the presence of an external magnetic field is calculated. It is shown that the motion of an electron wave packet has intraband frequency components, corresponding to the classical cyclotron motion, and several interband frequency components corresponding to the Zitterbewegung. For a two-dimensional situation, the presence of a magnetic field makes the ZB motion stationary, i.e. not decaying in time. We show how to simulate the ZB in a magnetic field using trapped ions and laser excitations in the spirit of …