Correlated behavior of conductance and phase rigidity in the transition from the weak-coupling to the strong-coupling regime

We study the transmission through different small systems as a function of the coupling strength $v$ to the two attached leads. The leads are identical with only one propagating mode $\xi^E_C$ in each of them. Besides the conductance $G$, we calculate the phase rigidity $\rho$ of the scattering wave function $\Psi^E_C$ in the interior of the system. Most interesting results are obtained in the regime of strongly overlapping resonance states where the crossover from staying to traveling modes takes place. The crossover is characterized by collective effects. Here, the conductance is plateau-like enhanced in some energy regions of finite length while corridors with zero transmission (total reflection) appear in other energy regions. This transmission picture depends only weakly on the spectrum of the closed system. It is caused by the alignment of some resonance states of the system with the propagating modes $\xi^E_C$ in the leads. The alignment of resonance states takes place stepwise by resonance trapping, i.e. it is accompanied by the decoupling of other resonance states from the continuum of propagating modes. This process is quantitatively described by the phase rigidity $\rho$ of the scattering wave function. Averaged over energy in the considered energy window, $$ is correlated with $1-$. In the regime of strong coupling, only two short-lived resonance states survive each aligned with one of the channel wave functions $\xi^E_C$. They may be identified with traveling modes through the system. The remaining $M-2$ trapped narrow resonance states are well separated from one another.Comment: Resonance trapping mechanism explained in the captions of Figs. 7 to 11. Recent papers added in the list of reference

Deformations of the Retaining Structures Upon Deep Excavations in Moscow

Foundation trenches for the buildings having underground floors and vehicular traffic tunnels are excavated in Moscow in congested urban housing environment. A retaining structure is a “slurry wall” made of cast-in-place reinforced concrete), and “soil-mixed-wall”. Retaining structures of trenches are fastened with the help of anchors, metal tie-beams, struts or floor structures. During the monitoring performed at major Moscow construction sites with deep trenches the (NIIOSP) named after Gersevanov created a database on retaining structures deformations

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

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

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

The brachistochrone problem in open quantum systems

Recently, the quantum brachistochrone problem is discussed in the literature by using non-Hermitian Hamilton operators of different type. Here, it is demonstrated that the passage time is tunable in realistic open quantum systems due to the biorthogonality of the eigenfunctions of the non-Hermitian Hamilton operator. As an example, the numerical results obtained by Bulgakov et al. for the transmission through microwave cavities of different shape are analyzed from the point of view of the brachistochrone problem. The passage time is shortened in the crossover from the weak-coupling to the strong-coupling regime where the resonance states overlap and many branch points (exceptional points) in the complex plane exist. The effect can {\it not} be described in the framework of standard quantum mechanics with Hermitian Hamilton operator and consideration of $S$ matrix poles.Comment: 18 page

Theory of motion of grain mixture particle in the process of aspiration separation

The paper describes the development of a mathematical model for the motion of a seed mixture particle in the aspiration channel of the separator after the particle passes the cone-shaped spreader and enters the workspace of the aspiration channel in the pneumatic dynamics and vibration unit devised by the authors. The unique feature of the proposed new design is the presence of the central pipe with sail members in the aspiration channel. The sail members in the air stream generate the self-oscillatory mode of motion of the central pipe, which results in the efficient separation of the grain seed mixture into the required fractions. On the basis of the prepared equivalent schematic model, the differential equations of the motion of a seed mixture particle in the process of aspiration separation have been generated. Basing on the results of the PC-assisted numerical modelling of the motion paths, on which the material particles (seeds) of the heavy and medium fractions travel, it has been established that they move on different courses, and the course of the heavy fraction seeds is such that, after they pass the cone-shaped spreader and advance further in the air stream through the space of the aspiration channel, they move closer to the pipe of the aspiration channel. Also, their velocities and accelerations are greater than the same kinematic parameters of the medium fraction seeds. The seeds of the light fraction move upwards under the action of the air stream and leave the aspiration separator at its top