Quantized transport in two-dimensional spin-ordered structures

We study in detail the transport properties of a model of conducting electrons in the presence of double exchange between localized spins arranged on a 2D Kagome lattice, as introduced by Ohgushi, Murakami and Nagaosa. The relationship between the canting angle of the spin texture θ and the Berry phase field flux per triangular plaquette φ is derived explicitly and we emphasize the similarities between this model and Haldane's honeycomb lattice version of the quantum Hall effect. The quantization of the transverse (Hall) conductivity σ _xy is derived explicitly from the Kubo formula and a direct calculation of the longitudinal conductivity σ _xx shows the existence of a metal–insulator transition as a function of the canting angle θ (or flux density φ). This transition might be linked to that observable in the manganite compounds or in the pyrochlore ones, as the spin ordering changes from ferromagnetic to canted.     

Quantized charge transport,chiral anomalies,and fractional charge

The phenomenon of quantized charge transport is studied using relativistic field theory. Perhaps surprisingly, the charge outflow per period is sometimes quantized in units of two. The interplay between quantized transport, chiral anomalies, and charge fractionization is clarified. In particular, yet another derivation of the relation between π → 2γ and γ → 3π is given.     

Nonlinear resonant transport of Bose-Einstein condensates

The coherent flow of a Bose-Einstein condensate through a quantum dot in a magnetic waveguide is studied. By the numerical integration of the time-dependent Gross-Pitaevskii equation in the presence of a source term, we simulate the propagation process of the condensate through a double barrier potential in the waveguide. We find that resonant transport is suppressed in interaction-induced regimes of bistability, where multiple scattering states exist at the same chemical potential and the same incident current. We demonstrate, however, that a temporal control of the external potential can be used to circumvent this limitation and to obtain enhanced transmission near the resonance on experimentally realistic time scales.     

Neoclassical radial electric field and transport with finite orbits

Neoclassical transport in a toroidal plasma with finite ion orbits is studied, including for the first time the self-consistent radial electric field. Using a low-noise deltaf particle simulation, we demonstrate that a deep electric-field well develops in a region with a steep density gradient, because of the self-collision-driven ion flux. We find that the electric field agrees with the standard neoclassical expression, when the toroidal rotation is zero, even for a steep density gradient. Ion thermal transport is modified by the electric-field well in a way which is consistent with the orbit squeezing effect, but smoothed by the finite orbits.     

Photon-assisted resonant transport through a multi-terminal mesoscopic system

The coherent transport through a multi-terminal mesoscopic system is investigated by using the nonequilibrium Green function technique. The sample is composed of two coupled Anderson impurities which are referred as the quantum dots. One dot is connected to N complete onedimensional wires, while the other one is linked to M wires. Each terminal is supplied an external oscillating field with potential V _α cos ω₀ t. The Landauer-Büttiker-like formulae are derived, and the resonant behaviors are discussed. We find these currents contributed by the channel-invariant and channel-variant tunneling processes. This effect signifies the tunneling electron perturbed by many photons. The resonant peaks are displayed analytically to be associated with the frequency, from which we observe that the main resonant peaks are modified by the frequency disturbings of photons. The locations of the peaks are determined by the spectrum levels of these dots, and at some points these peaks overlap to reduce the number of the peaks.     

Clock transport synchronization and the dragging of inertial frames for elliptical orbits

It is shown that is is possible to test for the dragging of inertial frames in Einstein's theory of general relativity by using the discrepancy between clocks synchronized by clock transport in elliptical orbits. Possible experiments are discussed.     

Quantum interference effect of resonant transport in nano-scale systems

We propose a new method of analyzing the quantum interference effect of the resonant transport in ballistic open systems. The new method is to obtain the resonant eigenvalues by computing the norm of the retarded and advanced Green's functions. Using the method, we illustrate for a fullerene and an AB-ring the relation between each resonant state and each asymmetric conductance peak, namely the Fano peak. We show that the combination of resonant states determines the symmetry of a conductance peak and that the Fano peak is caused by the asymmetry of the numerator of the conductance around a resonance. The Fano peak appears not only due to the quantum interference effect as often claimed, but more generally due to the resonant transport.     

Quantized superfields

We construct quantized free superfields and represent them as operator‐valued distributions in Fock space starting with the Majorana field. We then analyse the algebras generated by free component quantum fields together with the Susy generators Q, . This enables us to obtain the quantized chiral superfield by finite Susy transformation from its scalar component. To get hermitian superfields we study by the same method a second scalar field algebra from which various scalar superfields can be obtained by exponentiation. Next we investigate the vector algebra and use it to construct the massive vector superfield. Surprisingly enough, the result is totally different from the vector multiplet in the literature. It contains two hermitian four‐vector components instead of one and a spin‐3/2 field similar to the gravitino in supergravity.     

Quantized turbulence physics

We elaborate the physics of systems of unconstrained, reconnecting vortex filaments with dynamic finite cores of uniform ("quantized") circulation interacting via Biot-Savart and viscous forces. The phenomenology of this purely structured turbulent system includes an inertial range with Kolmogorov's k(-5/3) scaling for the energy spectrum, as well as Kolmogorov's linear in r scaling for the third order longitudinal structure function.     

Quantized fracture mechanics

A new energy-based theory, quantized fracture mechanics (QFM), is presented that modifies continuum-based fracture mechanics; stress- and strain-based QFM analogs are also proposed. The differentials in Griffith's criterion are substituted with finite differences; the implications are remarkable. Fracture of tiny systems with a given geometry and type of loading occurs at ‘quantized’ stresses that are well predicted by QFM: strengths predicted by QFM are compared with experimental results on carbon nanotubes, β-SiC nanorods, α-Si₃N₄ whiskers, and polysilicon thin films; and also with molecular mechanics/dynamics simulation of fracture of carbon nanotubes and graphene with cracks and holes, and statistical mechanics-based simulations on fracture of two-dimensional spring networks. QFM is self-consistent, agreeing to first-order with linear elastic fracture mechanics (LEFM), and to second-order with non-linear fracture mechanics (NLFM). For vanishing crack length QFM predicts a finite ideal strength in agreement with Orowan's prediction. In contrast to LEFM, QFM has no restrictions on treating defect size and shape. The different fracture Modes (opening I, sliding II and tearing III), and the stability of the fracture propagations, are treated in a simple way.     

Quantized Dirac operators

We determine what should correspond to the Dirac operator on certain quantized hermitian symmetric spaces and what its properties are. A new insight into the quantized wave operator is obtained. Presented at the 9th Colloquium “Quantum Groups and Integrable Systems”, Prague, 22–24 June 2000.     

Quantized string models

We discuss and compare the Lorentz covariant path integral quantization of the three bose string models, namely, the Nambu, Eguchi and Brink-Di Vecchia-Howe-Polyakov (BDHP) ones. Along with a critical review of the subject with some uncertainties and ambiguities clearly stated, various new results are presented. We work out the form of the BDHP string ansatz for the Wilson average and prove a formal inequivalence of the exact Nambu and BDHP models for any space-time dimension d. The above three models, known to be equivalent on the classical level, are shown to be equivalent in a semiclassical approximation near a minimal surface and also in the leading $\text{1}\text{d}\text{-}\text{approximation}$ for the static $\text{q}$q-potential. We analyse scattering amplitudes predicted by the BDHP string and find that when exactly calculated for d < 26 they are different from the old dual ones, and possess a non-linear spectrum which may be considered as free from tachyons in the ground state.