Multiple bound states in scissor-shaped waveguides

We study bound states of the two-dimensional Helmholtz equations with Dirichlet boundary conditions in an open geometry given by two straight leads of the same width which cross at an angle $\theta$. Such a four-terminal junction with a tunable $\theta$ can realized experimentally if a right-angle structure is filled by a ferrite. It is known that for $\theta=90^o$ there is one proper bound state and one eigenvalue embedded in the continuum. We show that the number of eigenvalues becomes larger with increasing asymmetry and the bound-state energies are increasing as functions of $\theta$ in the interval $(0,90^o)$. Moreover, states which are sufficiently strongly bent exist in pairs with a small energy difference and opposite parities. Finally, we discuss how with increasing $\theta$ the bound states transform into the quasi-bound states with a complex wave vector.Comment: 6 pages, 6 figure

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

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

Localization corrections to the anomalous Hall effect in a ferromagnet

We calculate the localization corrections to the anomalous Hall conductivity related to the contribution of spin-orbit scattering into the current vertex (side-jump mechanism). We show that in contrast to the ordinary Hall effect, there exists a nonvanishing localization correction to the anomalous Hall resistivity. The correction to the anomalous Hall conductivity vanishes in the case of side-jump mechanism, but is nonzero for the skew scattering. The total correction to the nondiagonal conductivity related to both mechanisms, does not compensate the correction to the diagonal conductivity.Comment: 7 pages with 7 figure

Statistics of wave functions and currents induced by spin-orbit interaction in chaotic billiards

The statistics of wave functions and currents induced by spin-orbit interaction (SOI) in chaotic billiards were investigated. It was observed that for small constant the current statistics was described by universal current distributions derived for slightly opened chaotic billiards. It was also observed that for SOI both components of the spinor eigenstate were complex random Gaussian fields. It was found that for intermediate values of the statistics of the eigenstates and currents, both were deeply nonuniversal.</p

Generation of upwelling near the Pacific Coast of Mexico

In a series of numerical experiments, we simulate the process of generation of coastal upwelling induced by the winds of various directions in the central part of the Pacific Coast of Mexico (18°N, 103-107°W). The numerical nonlinear multilevel model [see É.N. Mikhailova, I. M. Semenyuk, and N. B. Shapiro, "Modeling of the variability of hydrophysical fields in the Tropical Atlantic," Izv. Akad. Nauk SSSR, Fiz. Atmosf. Okean., 27, No. 10, 1139-1148 (1991)] is adapted to the region of investigations with 9-km space resolution by specifying the conditions of flow through the open lateral boundaries. The results of numerical experiments demonstrate that the NW, N, NE, and E winds are especially favorable for the generation of intense upwelling. © 2005 Springer Science+Business Media, Inc