Abstract:
We prove the existence of a set of two-scale magnetic Wannier orbitals w_{m,n}(r) on the infinite plane. The quantum numbers of these states are the positions {m,n} of their centers which form a von Neumann lattice. Function w_{00}localized at the origin has a nearly Gaussian shape of exp(-r^2/4l^2)/sqrt(2Pi) for r < sqrt(2Pi)l,where l is the magnetic length. This region makes a dominating contribution to the normalization integral. Outside this region function, w_{00}(r) is small, oscillates, and falls off with the Thouless critical exponent for magnetic orbitals, r^(-2). These functions form a convenient basis for many electron problems.

Abstract:
The mathematical model of a rotating electrohydrodynamic flow in a thin suspended liquid film is proposed and studied. The motion is driven by the given difference of potentials in one direction and constant external electrical field $\vE_\text{out}$ in another direction in the plane of a film. To derive the model we employ the spatial averaging over the normal coordinate to a film that leads to the average Reynolds stress that is proportional to $|\vE_\text{out}|^3$. This stress generates tangential velocity in the vicinity of the edges of a film that, in turn, causes the rotational motion of a liquid. The proposed model is aimed to explain the experimental observations of the \emph{liquid film motor} (see arXiv:0805.0490v2).

Abstract:
The zonal electrophoresis in the channels of complex forms is considered mathematically with the use of computations. We show that for plane S-type rectangular channels stagnation regions can appear that cause the strong variations of the spatial distribution of an admixture. Besides, the shape of an admixture zone is strongly influenced by the effects of electromigration and by a convective mixing. Taking into account the zone spreading caused by electromigration, the influence of vertex points of cannel walls, and convection would explain the results of electrophoretic experiments, which are difficult to understand otherwise.

Abstract:
We study the interactions of the vortex lattice with a periodic square array of holes in a superconducting Nb film using magnetic and resistive measurements. Three different temperature regions have been observed. They are governed by interplay between vortex-vortex interactions and pinning by holes. At low temperatures flux jumps suppress the commensurability anomalies. In all measurements a peak has been observed close to commensurate states 5-7. The Cole-Cole plot reveals significant changes in the flux penetration mechanism at this point.

Abstract:
Magnetotransport of superconducting Nd_{2-x}Ce_xCuO_{4+y} (NdCeCuO) films is studied in the temperature interval 0.3-30 K. The microscopic theory of the quantum corrections to conductivity, both in the Cooper and in the diffusion channels, qualitatively describes the main features of the experiment including the negative magnetoresistance in the high field limit. Comparison with the model of the field-induced superconductor-insulator transition (SIT) is included and a crossover between these two theoretical approaches is discussed.

Abstract:
A natural atom placed into a cavity with time-dependent parameters can be parametrically excited due to the interaction with the quantized photon mode. One of the channels of such a process is the dynamical Lamb effect, induced by a nonadiabatic modulation of atomic level Lamb shift. However, in experiments with natural atoms it is quite difficult to isolate this effect from other mechanisms of atom excitation. We point out that a transmission line cavity coupled with a superconducting qubit (artificial macroscopic atom) provides a unique platform for the observation of the dynamical Lamb effect. A key idea is to exploit a dynamically tunable qubit-resonator coupling, which was implemented quite recently. By varying nonadiabatically the coupling, it is possible to parametrically excite a qubit through a nonadiabatic modulation of the Lamb shift, even if the cavity was initially empty. A dynamics of such a coupled system is studied within the Rabi model with time-dependent coupling constant and beyond the rotating wave approximation. An efficient method to increase the effect through the periodic and nonadiabatic switching of a qubit-resonator coupling energy is proposed.

Abstract:
We study optically induced nuclear spin dynamics in a fluorine-doped ZnSe epilayer. The nuclear spin relaxation time $T_{1}$ of the $^{77}\text{Se}$ isotope under illumination is measured using an all-optical method in a magnetic field range from 10 to 130 mT and a lower limit for the spin relaxation time $T_{1}^{\text{dark}}$ without illumination is estimated. We combine optical methods with radio frequency techniques to measure Rabi oscillations, Ramsey fringes and the nuclear spin echo. The inhomogeneous nuclear spin dephasing time $T_{2}^{*}$ and the nuclear spin coherence time $T_{2}$ are measured using these techniques. While the $T_{1}$ time is on the order of several milliseconds, the $T_{2}$ time is on the order of several hundred microseconds. We find $T_{1}\gg T_{2}$ and conclude that the optically induced nuclear spin polarization can be described using the classical model of nuclear spin cooling.

Abstract:
We present results of electrochemical deposition of superconducting Pb in the pores of templates prepared by self-assembly from colloidal suspensions of polystyrene latex spheres. This technique enables us to create highly ordered superconducting nano-structures with 3D architectures on length scales ranging from 50 - 1000 nm. The prepared samples show pronounced Little-Parks oscillations in Tc and matching effects in magnetization and magnetic susceptibility. Real and imaginary parts of susceptibility follow a universal Cole-Cole curve. Self-field effects play an important role in commensurability behaviour of magnetic moment at low temperatures.

Abstract:
The spin dynamics of the strongly localized, donor-bound electrons in fluorine-doped ZnSe epilayers is studied by pump-probe Kerr rotation techniques. A method exploiting the spin inertia is developed and used to measure the longitudinal spin relaxation time, $T_1$, in a wide range of magnetic fields, temperatures, and pump densities. The $T_1$ time of the donor-bound electron spin of about 1.6 $\mu$s remains nearly constant for external magnetic fields varied from zero up to 2.5 T (Faraday geometry) and in a temperature range $1.8-45$ K. The inhomogeneous spin dephasing time, $T_2^*=8-33$ ns, is measured using the resonant spin amplification and Hanle effects under pulsed and steady-state pumping, respectively. These findings impose severe restrictions on possible spin relaxation mechanisms.

Abstract:
The mechanisms for generation of long-lived spin coherence in a two-dimensional electron gas (2DEG) have been studied experimentally by means of a picosecond pump-probe Kerr rotation technique. CdTe/(Cd,Mg)Te quantum wells with a diluted 2DEG were investigated. The strong Coulomb interaction between electrons and holes, which results in large binding energies of neutral excitons and negatively charged excitons (trions), allows one to address selectively the exciton or trion states by resonant optical excitation. Different scenarios of spin coherence generation were analyzed theoretically, among them the direct trion photocreation, the formation of trions from photogenerated excitons and the electron-exciton exchange scattering. Good agreement between experiment and theory is found.