Homogeneous spaces with symmetries

We give a brief survey of main recent results about invariant pseudo-Riemannian metrics and classical affinor structures on homogeneous spaces with symmetries obtained by the participants of the joint BRFFI-RFFI project “Homogeneous spaces with symmetries”

Charge relaxation resistance in the Coulomb blockade problem

We study the dissipation in a system consisting of a small metallic island coupled to a gate electrode and to a massive reservoir via single tunneling junction. The dissipation of energy is caused by a slowly oscillating gate voltage. We compute it in the regimes of weak and strong Coulomb blockade. We focus on the regime of not very low temperatures when electron coherence can be neglected but quantum fluctuations of charge are strong due to Coulomb interaction. The answers assume a particularly transparent form while expressed in terms of specially chosen physical observables. We discovered that the dissipation rate is given by a universal expression in both limiting cases.Comment: 21 pages, 12 figure

2,4,6-trinitrotoluene as a trigger of oxidative stress in Fagopyrum tataricum callus cells

Effect of 2,4,6-trinitrotoluene (TNT) on callus cells of Tartar buckwheat (Fagopyrum tataricum (L.) Gaertn.) was accompanied by six-electron reduction of ortho- or para-nitro groups of the xenobiotic with the production of 2-amino-4,6-dinitrotoluene (2-ADNT) and 4-amino-2,6-dinitrotoluene (4-ADNT). It was discovered that the xenobiotic TNT impairs integrity of cell membrane, which apparently results from its one-electron reduction coupled with production of nitro radical-anion and superoxide anion. © 2013 Pleiades Publishing, Ltd

Improving Josephson junction reproducibility for superconducting quantum circuits: junction area fluctuation

Josephson superconducting qubits and parametric amplifiers are prominent examples of superconducting quantum circuits that have shown rapid progress in recent years. With the growing complexity of such devices, the requirements for reproducibility of their electrical properties across a chip have become stricter. Thus, the critical current $I_c$ variation of the Josephson junction, as the most important electrical parameter, needs to be minimized. Critical current, in turn, is related to normal-state resistance the Ambegaokar-Baratoff formula, which can be measured at room temperature. Here, we focus on the dominant source of Josephson junction critical current non-uniformity junction area variation. We optimized Josephson junctions fabrication process and demonstrate resistance variation of $9.8-4.4\%$ and $4.8-2.3\%$ across $22{\times}22$ $mm^2$ and $5{\times}10$ $mm^2$ chip areas, respectively. For a wide range of junction areas from $0.008$ ${\mu}m^2$ to $0.12$ ${\mu}m^2$ we ensure a small linewidth standard deviation of $4$ $nm$ measured over 4500 junctions with linear dimensions from $80$ to $680$ $nm$. The developed process was tested on superconducting highly coherent transmon qubits $(T_1 > 100\:{\mu}s)$ and a nonlinear asymmetric inductive element parametric amplifier

High-Q trenched aluminum coplanar resonators with an ultrasonic edge microcutting for superconducting quantum devices

Dielectric losses are one of the key factors limiting the coherence of superconducting qubits. The impact of materials and fabrication steps on dielectric losses can be evaluated using coplanar waveguide (CPW) microwave resonators. Here, we report on superconducting CPW microwave resonators with internal quality factors systematically exceeding 5x106 at high powers and 2x106 (with the best value of 4.4x106) at low power. Such performance is demonstrated for 100-nm-thick aluminum resonators with 7-10.5 um center trace on high-resistivity silicon substrates commonly used in quantum Josephson junction circuits. We investigate internal quality factors of the resonators with both dry and wet aluminum etching, as well as deep and isotropic reactive ion etching of silicon substrate. Josephson junction compatible CPW resonators fabrication process with both airbridges and silicon substrate etching is proposed. Finally, we demonstrate the effect of airbridges positions and extra process steps on the overall dielectric losses. The best quality fa ctors are obtained for the wet etched aluminum resonators and isotropically removed substrate with the proposed ultrasonic metal edge microcutting.Comment: 6 pages, 2 figure

The Energy Level Shifts, Wave Functions and the Probability Current Distributions for the Bound Scalar and Spinor Particles Moving in a Uniform Magnetic Field

We discuss the equations for the bound one-active electron states based on the analytic solutions of the Schrodinger and Pauli equations for a uniform magnetic field and a single attractive $\delta({\bf r})$-potential. It is vary important that ground electron states in the magnetic field differ essentially from the analogous state of spin-0 particles, whose binding energy was intensively studied more than forty years ago. We show that binding energy equations for spin-1/2 particles can be obtained without using the language of boundary conditions in the $\delta$-potential model developed in pioneering works. We use the obtained equations to calculate the energy level displacements analytically and demonstrate nonlinear dependencies on field intensity. We show that the magnetic field indeed plays a stabilizing role in considered systems in a case of the weak intensity, but the opposite occurs in the case of strong intensity. These properties may be important for real quantum mechanical fermionic systems in two and three dimensions. We also analyze the exact solution of the Pauli equation for an electron moving in the potential field determined by the three-dimensional $\delta$-well in the presence of a strong magnetic field. We obtain asymptotic expressions for this solution for different values of the problem parameters. In addition, we consider electron probability currents and their dependence on the magnetic field. We show that including the spin in the framework of the nonrelativistic approach allows correctly taking the effect of the magnetic field on the electric current into account. The obtained dependencies of the current distribution, which is an experimentally observable quantity, can be manifested directly in scattering processes, for example.Comment: 31 pages, 10 figure