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 positive energy only) loses the spatial localization so that the evolution can no longer be described classically. However, at the half-revival time $t=T_R/2$ its reshaping takes place firstly. The behavior of the wave packet containing the states of both energy bands (with $E_n>0$ and $E_n<0$) is more complicated. At short times of a few classical periods such packet splits into two parts which rotate with cyclotron frequency in the opposite directions and meet each other every one-half of the cyclotron period. At these moments their wave functions have significant overlap that leads to ZB. At the time of fractional revival each of two sub-packets is decomposed into few packets-fractions. However, at $t=T_R$ each of the two sub-packets (with positive or negative energy) restores at various points of the cyclotron orbit, that makes it impossible reshaping of initial wave packet entirely unlike the wave packet which consists of states with energies $E_n>0$ only. Obtained results can be useful for the description of electromagnetic radiation and absorption in relativistic plasma on astrophysics objects, where super high magnetic field has the value of the order $10^8-10^9$T, as well as for interpretation of experiments with trapped ions

Space-time evolution of Dirac wave packets

In this work we study the dynamics of free 3D relativistic Gaussian wave packets with different spin polarization. We analyze the connection between the symmetry of initial state and the dynamical characteristics of moving particle. The corresponding solutions of Dirac equation having different types of symmetry were evaluated analytically and numerically and after that the electron probability densities, as well as, the spin densities were visualized. The average values of velocity of the packet center and the average spin were calculated analytically, and the parameters of transient Zitterbewegung in different directions were obtained. These results can be useful for the interpretation of future experiments with trapped ions.Comment: 10 pages, 7 figure

Influence of the Processes of Fluffing the Flax Stem Strips on the Structural Parameters of the Layer

Introduction. The efficiency of separating long flax fiber from the flax straw largely depends on the structural parameters of the layer of flax stems. Modern fluffers for flax strips create random distortions and intersection of the layer of flax stems under the pick-up drum. These disadvantages of existing machines are minimized in an experimental fluffer, in which a layer of flax stems moves over the pick-up drum with a kinematic mode indicator equal to one. Aim of the Article. The study is aimed at finding means and methods for preserving the structural parameters of the layer of flax stems when fluffing flax straw strips. Materials and Methods. Experimental studies were carried out according to existing and newly developed methods, and the analysis of flax fiber was carried out according to the current GOST standards. The experiments were carried out on the flax strips formed by the LC-4A flax harvester. After grass sprouted through the strips of flax stems, they were fluffed with the serial machine VL-3 and an experimental fluffer. For each variant, the necessary measurements of the main structural parameters of the stem strip and collection of samples for analysis were made before the unit passed and after fluffering the flax stem strip. The results of measurements and processing of samples were processed using the methods of mathematical statistics. Results. It was found that macro-bends of the original and processed flax strips were in all the experiments. At the same time, the range of changes in the curvature of the flax strip outside the cutoff frequencies expanded 2.3 times under the influence of the working tools of the serial tedder VL-3. The randomness of these pulsations was caused by an increase in the distortion and elongation of the flax stems in the strip by 6.0° and 6.9%, respectively. At the same time, the experimental fluffer produced the smallest changes in the structural parameters of the flax stem layer. The technological evaluation of the flax straw confirmed the advantages of the experimental fluffer in comparison with the serial VL-3, which has an average production of long fiber higher by 0.65% and 0.5 units of number. Discussion and Conclusion. The analysis of the obtained results indicates the practicability of fluffing flax strips by picking up and moving the stems from above the pick-up drum with its kinematic mode index equal to one

Quantum states and linear response in dc and electromagnetic fields for charge current and spin polarization of electrons at Bi/Si interface with giant spin-orbit coupling

An expansion of the nearly free-electron model constructed by Frantzeskakis, Pons and Grioni [Phys. Rev. B {\bf 82}, 085440 (2010)] describing quantum states at Bi/Si(111) interface with giant spin-orbit coupling is developed and applied for the band structure and spin polarization calculation, as well as for the linear response analysis for charge current and induced spin caused by dc field and by electromagnetic radiation. It is found that the large spin-orbit coupling in this system may allow resolving the spin-dependent properties even at room temperature and at realistic collision rate. The geometry of the atomic lattice combined with spin-orbit coupling leads to an anisotropic response both for current and spin components related to the orientation of the external field. The in-plane dc electric field produces only the in-plane components of spin in the sample while both the in-plane and out-of-plane spin components can be excited by normally propagating electromagnetic wave with different polarizations.Comment: 10 pages, 9 figure

Experimental study of the decay KL0→π0ννˉK_L^0\to\pi^0\nu\bar{\nu}

The first dedicated search for the rare neutral-kaon decay $K_L^0\to\pi^0\nu\bar{\nu}$ has been carried out in the E391a experiment at the KEK 12-GeV proton synchrotron. The final upper limit of 2.6 $\times 10^{-8}$ at the 90% confidence level was set on the branching ratio for the decay.Comment: 23 pages, 27 figures, accepted for publication as a regular article in Physical Review

Search for the decay KL0→3γK_L^0 \rightarrow 3\gamma

We performed a search for the decay $K_L^0 \rightarrow 3\gamma$ with the E391a detector at KEK. In the data accumulated in 2005, no event was observed in the signal region. Based on the assumption of $K_L^0 \rightarrow 3\gamma$ proceeding via parity-violation, we obtained the single event sensitivity to be $(3.23\pm0.14)\times10^{-8}$, and set an upper limit on the branching ratio to be $7.4\times10^{-8}$ at the 90% confidence level. This is a factor of 3.2 improvement compared to the previous results. The results of $K_L^0 \rightarrow 3\gamma$ proceeding via parity-conservation were also presented in this paper