Spectroscopic properties of large open quantum-chaotic cavities with and without separated time scales

The spectroscopic properties of an open large Bunimovich cavity are studied numerically in the framework of the effective Hamiltonian formalism. The cavity is opened by attaching leads to it in four different ways. In some cases, short-lived and long-lived resonance states coexist. The short-lived states cause traveling waves in the transmission while the long-lived ones generate superposed fluctuations. The traveling waves oscillate as a function of energy. They are not localized in the interior of the large chaotic cavity. In other cases, the transmission takes place via standing waves with an intensity that closely follows the profile of the resonances. In all considered cases, the phase rigidity fluctuates with energy. It is mostly near to its maximum value and agrees well with the theoretical value for the two-channel case. As shown in the foregoing paper \cite{1}, all cases are described well by the Poisson kernel when the calculation is restricted to an energy region in which the average $S$ matrix is (nearly) constant.Comment: 13 pages, 4 figure

Phase rigidity and avoided level crossings in the complex energy plane

We consider the effective Hamiltonian of an open quantum system, its biorthogonal eigenfunctions $\phi_\lambda$ and define the value $r_\lambda = (\phi_\lambda|\phi_\lambda)/$ that characterizes the phase rigidity of the eigenfunctions $\phi_\lambda$. In the scenario with avoided level crossings, $r_\lambda$ varies between 1 and 0 due to the mutual influence of neighboring resonances. The variation of $r_\lambda$ may be considered as an internal property of an {\it open} quantum system. In the literature, the phase rigidity $\rho$ of the scattering wave function $\Psi^E_C$ is considered. Since $\Psi^E_C$ can be represented in the interior of the system by the $\phi_\lambda$, the phase rigidity $\rho$ of the $\Psi^E_C$ is related to the $r_\lambda$ and therefore also to the mutual influence of neighboring resonances. As a consequence, the reduction of the phase rigidity $\rho$ to values smaller than 1 should be considered, at least partly, as an internal property of an open quantum system in the overlapping regime. The relation to measurable values such as the transmission through a quantum dot, follows from the fact that the transmission is, in any case, resonant with respect to the effective Hamiltonian. We illustrate the relation between phase rigidity $\rho$ and transmission numerically for small open cavities.Comment: 6 pages, 3 figure

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

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

Remote sensing observations of the coherent and non-coherent ring structures in the vicinity of Lesser Antilles

The North Brazil Current Rings (NBCR) penetration into the Caribbean Sea is being investigated by employing a merged altimeter-derived sea height anomaly (TOPEX/Poseidon, Jason-1 and ERS-1, 2), the ocean surface color data (SeaWiFS) and Global Drifter Program information. Four strategies are being applied to process the data: (1) calculations of the Okubo-Weiss parameter for NBCR identification, (2) longitude-time plots (also known as Hovmöller diagrams), (3) two-dimensional Radon transforms and (4) two-dimensional Fourier transforms. <br><br> A twofold NBCR structure has been detected in the region under investigation. The results have shown that NBC rings mainly propagate into the Caribbean Sea along two principal pathways (near 12° N and 17° N) in the ring translation corridor. Thus, rings following the southern pathway in the fall-winter period can enter through very shallow southern straits as non-coherent structures. A different behavior is observed near the northern pathway (~17° N), where NBC rings are thought to have a coherent structure during their squeezing into the eastern Caribbean, i.e. conserving the principal characteristics of the incident rings. We attribute this difference in the rings' behavior to the vertical scales of the rings and to the bottom topography features in the vicinity of the Lesser Antilles

Statistical study of the conductance and shot noise in open quantum-chaotic cavities: Contribution from whispering gallery modes

In the past, a maximum-entropy model was introduced and applied to the study of statistical scattering by chaotic cavities, when short paths may play an important role in the scattering process. In particular, the validity of the model was investigated in relation with the statistical properties of the conductance in open chaotic cavities. In this article we investigate further the validity of the maximum-entropy model, by comparing the theoretical predictions with the results of computer simulations, in which the Schroedinger equation is solved numerically inside the cavity for one and two open channels in the leads; we analyze, in addition to the conductance, the zero-frequency limit of the shot-noise power spectrum. We also obtain theoretical results for the ensemble average of this last quantity, for the orthogonal and unitary cases of the circular ensemble and an arbitrary number of channels. Generally speaking, the agreement between theory and numerics is good. In some of the cavities that we study, short paths consist of whispering gallery modes, which were excluded in previous studies. These cavities turn out to be all the more interesting, as it is in relation with them that we found certain systematic discrepancies in the comparison with theory. We give evidence that it is the lack of stationarity inside the energy interval that is analyzed, and hence the lack of ergodicity that gives rise to the discrepancies. Indeed, the agreement between theory and numerical simulations is improved when the energy interval is reduced to a point and the statistics is then collected over an ensemble. It thus appears that the maximum-entropy model is valid beyond the domain where it was originally derived. An understanding of this situation is still lacking at the present moment.Comment: Revised version, minor modifications, 28 pages, 7 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

Two-component model of a spin-polarized transport

Effect of the spin-involved interaction of electrons with impurity atoms or defects to the transport properties of a two-dimensional electron gas is described by using a simplifying two-component model. Components representing spin-up and spin-down states are supposed to be coupled at a discrete set of points within a conduction channel. The used limit of the short-range interaction allows to solve the relevant scattering problem exactly. By varying the model parameters different transport regimes of two-terminal devices with ferromagnetic contacts can be described. In a quasi-ballistic regime the resulting difference between conductances for the parallel and antiparallel orientation of the contact magnetization changes its sign as a function of the length of the conduction channel if appropriate model parameters are chosen. The effect is in agreement with recent experimental observations.Comment: 4 RevTeX pages with 4 figure