Self-Similar Random Processes and Infinite-Dimensional Configuration Spaces

We discuss various infinite-dimensional configuration spaces that carry measures quasiinvariant under compactly-supported diffeomorphisms of a manifold M corresponding to a physical space. Such measures allow the construction of unitary representations of the diffeomorphism group, which are important to nonrelativistic quantum statistical physics and to the quantum theory of extended objects in d-dimensional Euclidean space. Special attention is given to measurable structure and topology underlying measures on generalized configuration spaces obtained from self-similar random processes (both for d = 1 and d > 1), which describe infinite point configurations having accumulation points

Oscillatory instabilities in d.c. biased quantum dots

We consider a `quantum dot' in the Coulomb blockade regime, subject to an arbitrarily large source-drain voltage V. When V is small, quantum dots with odd electron occupation display the Kondo effect, giving rise to enhanced conductance. Here we investigate the regime where V is increased beyond the Kondo temperature and the Kondo resonance splits into two components. It is shown that interference between them results in spontaneous oscillations of the current through the dot. The theory predicts the appearance of ``Shapiro steps'' in the current-voltage characteristics of an irradiated quantum dot; these would constitute an experimental signature of the predicted effect.Comment: Four pages with embedded figure

On the virial coefficients of nonabelian anyons

We study a system of nonabelian anyons in the lowest Landau level of a strong magnetic field. Using diagrammatic techniques, we prove that the virial coefficients do not depend on the statistics parameter. This is true for all representations of all nonabelian groups for the statistics of the particles and relies solely on the fact that the effective statistical interaction is a traceless operator.Comment: 9 pages, 3 eps figure

Nonlinear Response of a Kondo system: Direct and Alternating Tunneling Currents

Non - equilibrium tunneling current of an Anderson impurity system subject to both constant and alternating electric fields is studied. A time - dependent Schrieffer - Wolff transformation maps the time - dependent Anderson Hamiltonian onto a Kondo one. Perturbation expansion in powers of the Kondo coupling strength is carried out up to third order, yielding a remarkably simple analytical expression for the tunneling current. It is found that the zero - bias anomaly is suppressed by an ac - field. Both dc and the first harmonic are equally enhanced by the Kondo effect, while the higher harmonics are relatively small. These results are shown to be valid also below the Kondo temperature.Comment: 7 pages, RevTeX, 3 PS figures attached, the article has been significantly developed: time - dependent Schrieffer - Wolff transformation is presented in the full form, the results are applied to the change in the direct current induced by an alternating field (2 figures are new

No familial aggregation in chronic myeloid leukemia.

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Resonance Kondo Tunneling through a Double Quantum Dot at Finite Bias

It is shown that the resonance Kondo tunneling through a double quantum dot (DQD) with even occupation and singlet ground state may arise at a strong bias, which compensates the energy of singlet/triplet excitation. Using the renormalization group technique we derive scaling equations and calculate the differential conductance as a function of an auxiliary dc-bias for parallel DQD described by SO(4) symmetry. We analyze the decoherence effects associated with the triplet/singlet relaxation in DQD and discuss the shape of differential conductance line as a function of dc-bias and temperature.Comment: 11 pages, 6 eps figures include

Assessing the adverse effects of a mixture of AMD and sewage effluent on a sub-tropical dam situated in a nature conservation area using a modified pollution index

Currently water resources in nature conservation areas are under severe pressure due to external drivers of anthropogenic pollution. There is a lack of monitoring tools to determine water quality status of dams situated in nature reserves receiving a mixture of pollutants over space and time. The present study was conducted over a 12-month period with the aim of applying a modified pollution index (PILD) to determine the water quality and phytoplankton status of the Loskop Dam situated in the Loskop nature reserve, South Africa. From the data generated in the current study, it was evident that the PILD effectively determined nutrient enrichment and heavy metal pollution in the dam. Furthermore, the study showed that the most pollution tolerant phytoplankton species was the diatom Melosira varians followed by the dinoflagellate Ceratuim hirundinella and the cyanobacteria Microcystis aeruginosa. Chemical variables during the sampling period that exceeded the limits of the South African, Canadian, Australia and New Zealand guideline levels were Zn, TP, Cl, Fe, Mn and NH4. The occurrence of concentrations of Cl above the target water quality range for aquatic ecosystems (5 µgl−1) over the entire sampling period, may have been related to point source sewage pollution in the upper catchment. The PILD showed poor water quality conditions during the months of September and October during the dam’s destratification (lake overturn)

Kondo effect in systems with dynamical symmetries

This paper is devoted to a systematic exposure of the Kondo physics in quantum dots for which the low energy spin excitations consist of a few different spin multiplets $|S_{i}M_{i}>$. Under certain conditions (to be explained below) some of the lowest energy levels $E_{S_{i}}$ are nearly degenerate. The dot in its ground state cannot then be regarded as a simple quantum top in the sense that beside its spin operator other dot (vector) operators ${\bf R}_{n}$ are needed (in order to fully determine its quantum states), which have non-zero matrix elements between states of different spin multiplets $\ne 0$. These "Runge-Lenz" operators do not appear in the isolated dot-Hamiltonian (so in some sense they are "hidden"). Yet, they are exposed when tunneling between dot and leads is switched on. The effective spin Hamiltonian which couples the metallic electron spin ${\bf s}$ with the operators of the dot then contains new exchange terms, $J_{n} {\bf s} \cdot {\bf R}_{n}$ beside the ubiquitous ones $J_{i} {\bf s}\cdot {\bf S}_{i}$. The operators ${\bf S}_{i}$ and ${\bf R}_{n}$ generate a dynamical group (usually SO(n)). Remarkably, the value of $n$ can be controlled by gate voltages, indicating that abstract concepts such as dynamical symmetry groups are experimentally realizable. Moreover, when an external magnetic field is applied then, under favorable circumstances, the exchange interaction involves solely the Runge-Lenz operators ${\bf R}_{n}$ and the corresponding dynamical symmetry group is SU(n). For example, the celebrated group SU(3) is realized in triple quantum dot with four electrons.Comment: 24 two-column page

Using penetration depth for phase matching in photonic crystal waveguides

A new method of design for the phase-matching in waveguides is suggested. The approach is based on utilizing the concept of the penetration depth of light into the waveguide walls. The lateral components of wavevectors are employed to adjust the phase-matching condition in the propagation direction. The method is demonstrated in two systems: one using single and the other using double photonic-crystal mirrors