Spin rotation for ballistic electron transmission induced by spin-orbit interaction

We study spin dependent electron transmission through one- and two-dimensional curved waveguides and quantum dots with account of spin-orbit interaction. We prove that for a transmission through arbitrary structure there is no spin polarization provided that electron transmits in isolated energy subband and only two leads are attached to the structure. In particular there is no spin polarization in the one-dimensional wire for which spin dependent solution is found analytically. The solution demonstrates spin evolution as dependent on a length of wire. Numerical solution for transmission of electrons through the two-dimensional curved waveguides coincides with the solution for the one-dimensional wire if the energy of electron is within the first energy subband. In the vicinity of edges of the energy subbands there are sharp anomalies of spin flipping.Comment: 9 oages, 7 figure

Research of the movement of agricultural aggregates using the methods of the movement stability theory

ArticleThe theory of the movement stability is of crucial practical importance for mobile agricultural machines and machine aggregates, since it determines how qualitative and stable their performance is in a particular technological process. It is especially urgent To ensure stable movement for operation at high speeds of contemporary agricultural aggregates. The aim of this investigation is detailed examination of criteria for the stability assessment of a mechanical system used in agriculture, enabling their wide application in order to study the performance of the system in the case when it is affected by random forces that were not taken into account in the original model. The considered calculation methods and examples of their application make it possible to evaluate the performance of complex dynamic systems without numerical solution of complicated differential equations of the movement in the presence of external disturbances. The considered example of the stability determination of the movement of a trailed cultivator showed that this research method can be successfully used for practical purposes. Besides, a differential equation of disturbed movement has been composed for an actually symmetrical trailed agricultural machine with a particular mass, which moves at a constant forward speed under the impact of summary resistance force running along the symmetry axis of the cultivator and is applied at its centre of gravity. Reduced to normal Cauchy form, this equation was solved on the PC, which made it possible to determine immediately the conditions for stable movement of the trailed cultivator

Lexical combinability of adjectives and nouns expressing elements of appraisal

The present article aims to examine and analyze the nature of lexical combinability in the English language, namely collocates expressing elements of appraisal found in authentic online news article

Research of the movement of agricultural aggregates using the methods of the movement stability theory

The theory of the movement stability is of crucial practical importance for mobile agricultural machines and machine aggregates, since it determines how qualitative and stable their performance is in a particular technological process. It is especially urgent To ensure stable movement for operation at high speeds of contemporary agricultural aggregates. The aim of this investigation is detailed examination of criteria for the stability assessment of a mechanical system used in agriculture, enabling their wide application in order to study the performance of the system in the case when it is affected by random forces that were not taken into account in the original model. The considered calculation methods and examples of their application make it possible to evaluate the performance of complex dynamic systems without numerical solution of complicated differential equations of the movement in the presence of external disturbances. The considered example of the stability determination of the movement of a trailed cultivator showed that this research method can be successfully used for practical purposes. Besides, a differential equation of disturbed movement has been composed for an actually symmetrical trailed agricultural machine with a particular mass, which moves at a constant forward speed under the impact of summary resistance force running along the symmetry axis of the cultivator and is applied at its centre of gravity. Reduced to normal Cauchy form, this equation was solved on the PC, which made it possible to determine immediately the conditions for stable movement of the trailed cultivator

Complex Energy Spectrum and Time Evolution of QBIC States in a Two-Channel Quantum wire with an Adatom Impurity

We provide detailed analysis of the complex energy eigenvalue spectrum for a two-channel quantum wire with an attached adatom impurity. The study is based on our previous work [Phys. Rev. Lett. 99, 210404 (2007)], in which we presented the quasi-bound states in continuum (or QBIC states). These are resonant states with very long lifetimes that form as a result of two overlapping continuous energy bands one of which, at least, has a divergent van Hove singularity at the band edge. We provide analysis of the full energy spectrum for all solutions, including the QBIC states, and obtain an expansion for the complex eigenvalue of the QBIC state. We show that it has a small decay rate of the order $g^6$, where $g$ is the coupling constant. As a result of this expansion, we find that this state is a non-analytic effect resulting from the van Hove singularity; it cannot be predicted from the ordinary perturbation analysis that relies on Fermi's golden rule. We will also numerically demonstrate the time evolution of the QBIC state using the effective potential method in order to show the stability of the QBIC wave function in comparison with that of the other eigenstates.Comment: Around 20 pages, 50 total figure

Hall-like effect induced by spin-orbit interaction

The effect of spin-orbit interaction on electron transport properties of a cross-junction structure is studied. It is shown that it results in spin polarization of left and right outgoing electron waves. Consequently, incoming electron wave of a proper polarization induces voltage drop perpendicularly to the direct current flow between source and drain of the considered four-terminal cross-structure. The resulting Hall-like resistance is estimated to be of the order of 10^-3 - 10^-2 h/e^2 for technologically available structures. The effect becomes more pronounced in the vicinity of resonances where Hall-like resistance changes its sign as function of the Fermi energy.Comment: 4 pages (RevTeX), 4 figures, will appear in Phys. Rev. Let

Effect of Quadratic Zeeman Energy on the Vortex of Spinor Bose-Einstein Condensates

The spinor Bose-Einstein condensate of atomic gases has been experimentally realized by a number of groups. Further, theoretical proposals of the possible vortex states have been sugessted. This paper studies the effects of the quadratic Zeeman energy on the vortex states. This energy was ignored in previous theoretical studies, although it exists in experimental systems. We present phase diagrams of various vortex states taking into account the quadratic Zeeman energy. The vortex states are calculated by the Gross-Pitaevskii equations. Several new kinds of vortex states are found. It is also found that the quadratic Zeeman energy affects the direction of total magnetization and causes a significant change in the phase diagrams.Comment: 6 pages, 5 figures. Published in J. Phys. Soc. Jp

Analysis technique for exceptional points in open quantum systems and QPT analogy for the appearance of irreversibility

We propose an analysis technique for the exceptional points (EPs) occurring in the discrete spectrum of open quantum systems (OQS), using a semi-infinite chain coupled to an endpoint impurity as a prototype. We outline our method to locate the EPs in OQS, further obtaining an eigenvalue expansion in the vicinity of the EPs that gives rise to characteristic exponents. We also report the precise number of EPs occurring in an OQS with a continuum described by a quadratic dispersion curve. In particular, the number of EPs occurring in a bare discrete Hamiltonian of dimension $n_\textrm{D}$ is given by $n_\textrm{D} (n_\textrm{D} - 1)$; if this discrete Hamiltonian is then coupled to continuum (or continua) to form an OQS, the interaction with the continuum generally produces an enlarged discrete solution space that includes a greater number of EPs, specifically $2^{n_\textrm{C}} (n_\textrm{C} + n_\textrm{D}) [2^{n_\textrm{C}} (n_\textrm{C} + n_\textrm{D}) - 1]$, in which $n_\textrm{C}$ is the number of (non-degenerate) continua to which the discrete sector is attached. Finally, we offer a heuristic quantum phase transition analogy for the emergence of the resonance (giving rise to irreversibility via exponential decay) in which the decay width plays the role of the order parameter; the associated critical exponent is then determined by the above eigenvalue expansion.Comment: 16 pages, 7 figure