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.

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

The organization of the rating system for assessing the quality of university students training

In spite the universities use the rating system of assessing for a quite long time, this issue is still not fully considered. The article is based on the position of insufficient state of knowledge of the multifunctionality of the students rating. The rating helps to reveal the potential of students. It is mentioned that the rating system of assessment is a tool that will improve the quality of training and provide the required level of motivation. During the research, the following methods were used: analysis, synthesis, induction, deduction. As a result, the principles of the rating assessment system were revealed, a definition of the term "Rating" was given, its goals were indicated. As an example of the organization of the rating system of assessment, the Nyzhnii Novhorod State Pedagogical University and its "Regulations on the rating system for assessing the quality of student training" were used. It is noted that the rating includes: current check, midterm and final examinations. Further, all possible conditions under which the student receives points were identified and considered. On the example of the NSPU named after Kozma Minin transferring of the rating points into a five-point grading rating system is presented. Also, the types of violations for which points are discarded, are considered. As the study showed, comprehensive planned system yields productive results for students and the university.peer-reviewe

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

Civil society of modern Russia : problems of implementation of constitutional rights and freedoms

Purpose: The aim of this article is to identify problems of legal regulation of the development of civil society in modern Russia. Tasks: to analyze the position of legal regulation of legal relations, to compare formed legal relations in link "state - public authorities - society - person" Design/Methodology/Approach: The theoretical basis of the study is works of scientists in the field of administrative law and state administration concerning the guarantee of rights and freedoms of citizens by executive power rights. Authors revealed the features, essence, internal relations and the relationship of state policy and society, to identify the role of administrative law and make own view on their essence and content. Findings: Authors highlight the interconnections between the law and science and disclose the multi-dimensional concept of administration. Practical implications: Authors' development could be utilized in future developments of Russian legal frameworks at all levels of administration. Originality/Value: The contribution of the article is the comprehensive analysis of legal norm and clarification of basic concepts of administration.peer-reviewe

FORMATION OF MUNICIPAL SERVICE HUMAN RESOURCE POTENTIAL AS A STRATEGIC FACTOR FOR RUSSIAN TERRITORY SUSTAINABLE DEVELOPMENT

Purpose: The development of municipal service professional staff units is one of the most significant factors for Russian territory's sustainable development. Methodology: The information base of the research includes the results of sociological studies conducted by the All-Russia Council of Local Self-Government (ARCLSG) through the sending of questionnaires via the Internet: "Human Resources of Municipalities" (June-July 2013, N = 915); "Human Resources of Local Self-Government" (March-April 2016, N = 582). Result: The results of the expert survey showed that the leaders of local authorities are not fully satisfied with the level of municipal employee professional training. Evaluating the effectiveness of training programs implemented in recent years, most experts chose the following answer: "not all of the required issues have been covered, only a few things can be useful in practical activities". In modern conditions, it is necessary to specify the content of education, taking into account the specifics of the territory, its social and economic problems, the overcoming of a narrow theoretical orientation of the courses. Applications: This research can be used for the universities, teachers and education students. Novelty/Originality: In this research, the model of formation of municipal service human resource potential as a strategic factor for Russian territory sustainable development is presented in a comprehensive and complete manner