Wave packet dynamics in a monolayer graphene

The dynamics of charge particles described by Gaussian wave packet in monolayer graphene is studied analytically and numerically. We demonstrate that the shape of wave packet at arbitrary time depends on correlation between the initial electron amplitudes $\psi_1(\vec r,0)$ and $\psi_2(\vec r,0)$ on the sublattices $A$ and $B$ correspondingly (i.e. pseudospin polarization). For the transverse pseudospin polarization the motion of the center of wave packet occurs in the direction perpendicular to the average momentum ${\vec p_0}=\hbar \vec{k_0}$. Moreover, in this case the initial wave packet splits into two parts moving with opposite velocities along ${\vec p_0}$. If the initial direction of pseudospin coincides with average momentum the splitting is absent and the center of wave packet is displaced at $t>0$ along the same direction. The results of our calculations show that all types of motion experience {\it zitterbewegung}. Besides, depending on initial polarization the velocity of the packet center may have the constant component $v_c=uf(a)$, where $u\approx 10^8 cm/s$ is the Fermi velocity and $f(a)$ is a function of the parameter $a=k_0d$ ($d$ is the initial width of wave packet). As a result, the direction of the packet motion is determined not only by the orientation of the average momentum, but mainly by the phase difference between the up- and low- components of the wave functions. Similar peculiarities of the dynamics of 2D electron wave packet connected with initial spin polarization should take place in the semiconductor quantum well under the influence of the Rashba spin-orbit coupling.Comment: 7 pages, 8 figures, to be published in Phys. Rev.

Функції держави у регулюванні відносин власності

ДВНЗ «Київ. нац. екон. ун-т ім. Вадима Гетьмана»Окреслено основні функції держави в регулюванні трансформаційними процесами в системі і відносинах власності на нинішньому етапі розвитку ринкової економіки в Україні. Обґрунтовано, що вдосконалення відносин власності має здійснюватися шляхом формування раціональної структури власності та бюджетних видатків, якісного правового поля, ефективної системи контролю, якісної нормативно-правової бази, підвищення конкурентоспроможності національного виробництва.Определены основные функции государства в регулировании трансформационными процессами в системе и отношениях собственности на нынешнем этапе развития рыночной экономики в Украине. Обосновано, что совершенствование отношений собственности должно осуществляться путем формирования рациональной структуры собственности и бюджетных расходов, качественного правового поля, эффективной системы контроля, качественной нормативно-правовой базы, повышения конкурентоспособности национального производства.The basic functions of the state in regulating the transformation processes in the system and property relations at the present stage of development of the market economy in Ukraine are determined in the article. It is proved that the improvement of relations of ownership must be achieved by the formation of a rational structure of ownership and low cost, high quality legal framework, an effective control system, high-quality regulatory framework, improve the competitiveness of domestic production

Wave packet dynamics in hole Luttinger systems

For hole systems with an effective spin 3/2 we analyzed analytically and numerically the evolution of wave packets with the different initial polarizations. The dynamics of such systems is determined by the $4\times 4$ Luttinger Hamiltonian. We work in the space of arbitrary superposition of light- and heavy-hole states of the "one-particle system". For 2D packets we obtained the analytical solution for the components of wave function and analyzed the space-time dependence of probability densities as well as angular momentum densities. Depending on the value of the parameter $a=k_0d$ ($k_0$ is the average momentum vector and $d$ is the packet width) two scenarios of evolution are realized. For $a>>1$ the initial wave packet splits into two parts and the coordinates of packet center experience the transient oscillations or {\it Zitterbewegung} (ZB) as for other two-band systems. In the case when $a0$ remains almost cylindrically symmetric and the ripples arise at the circumference of wave packet. The ZB in this case is absent. We evaluated and visualized for different values of parameter $a$ the space-time dependence of angular momentum densities, which have the multipole structure. It was shown that the average momentum components can precess in the absence of external or effective magnetic fields due to the interference of the light- and heavy hole states. For localized initial states this precession has a transient character.Comment: 9 pages, 8 gigur

Опыт применения нетрадиционных удобрений при выращивании сеянцев сосны обыкновенной (Рinus sylvestris l.) на Урале)

Представлена информация о возможности использования нетрадиционных удобрений, которые приготовлены на основе отходов производств. В настоящее время они являются доступными, недорогими и высокоэффективными средствами повышения плодородия лесных почв. Проанализированы изменения параметров посадочного материала при внесении данных смесе

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

Adenine and guanine recognition of stop codon is mediated by different N domain conformations of translation termination factor eRF1

Positioning of release factor eRF1 toward adenines and the ribose-phosphate backbone of the UAAA stop signal in the ribosomal decoding site was studied using messenger RNA (mRNA) analogs containing stop signal UAA/UAAA and a photoactivatable cross-linker at definite locations. The human eRF1 peptides cross-linked to these analogs were identified. Cross-linkers on the adenines at the 2nd, 3rd or 4th position modified eRF1 near the conserved YxCxxxF loop (positions 125–131 in the N domain), but cross-linker at the 4th position mainly modified the tripeptide 26-AAR-28. This tripeptide cross-linked also with derivatized 3′-phosphate of UAA, while the same cross-linker at the 3′-phosphate of UAAA modified both the 26–28 and 67–73 fragments. A comparison of the results with those obtained earlier with mRNA analogs bearing a similar cross-linker at the guanines indicates that positioning of eRF1 toward adenines and guanines of stop signals in the 80S termination complex is different. Molecular modeling of eRF1 in the 80S termination complex showed that eRF1 fragments neighboring guanines and adenines of stop signals are compatible with different N domain conformations of eRF1. These conformations vary by positioning of stop signal purines toward the universally conserved dipeptide 31-GT-32, which neighbors guanines but is oriented more distantly from adenines