We examine energy relaxation of non-equilibrium quasiparticles in different vortex configurations in ``dirty'' $s$-wave superconductors. The heat flow from the electronic subsystem to phonons in a mesoscopic superconducting disk with a radius of the order of several coherence lengths is calculated both in the Meissner and giant vortex states using the Usadel approach. The recombination process is shown to be strongly affected by interplay of the subgap states, located in the vortex core and in the region at the sample edge where the spectral gap $E_{\rm g}$ is reduced by the Meissner currents. In order to uncover physical origin of the results, we develop a semiquantitative analytical approximation based on the combination of homogeneous solutions of Usadel equations in Meissner and vortex states of a mesoscopic superconducting disc and analytically calculate the corresponding spatially resolved electron-phonon heat rates. Our approach provides an important information about non-equilibrium quasiparticles cooling by the magnetic-field induced traps in various mesoscopic superconducting devices.

The dynamics of large, significantly exceeding the wavelength open systems such as free-standing multi-wire lines with a large number of built-in Josephson junctions is analyzed using direct numerical simulation. Such systems represent the simplest version of the Josephson active antennas proposed in our earlier studies and show promise as generators of terahertz and subterahertz radiation. Detailed simulation results reveal a multitude of phase transitions between the dynamical states, which differ in the number of Josephson junctions synchronized by the excited current waves and, hence, in the intensity of radiation emitted into open space and radiation patterns.

The electronic structure of the giant vortex states in a mesoscopic superconducting disk is studied in a dirty limit using the Usadel approach. The local density of states profiles are shown to be strongly affected by the effect of quasiparticle (QP) tunneling between the states localized in the vortex core and the ones bound to the sample edge. Decreasing temperature leads to a crossover between the edge-dominated and core-dominated regimes in the magnetic field dependence of the tunneling conductance. This crossover is discussed in the context of the efficiency of quasiparticle cooling by the magnetic field induced QP traps in various mesoscopic superconducting devices.

A terahertz superconducting oscillators based on large amount of Josephson junction embedded in open system guiding traveling electromagnetic wave is theoretically considered and computer simulated. It is shown that such active Josephson antennae represent oscillator effectively radiated into open space with power scaled with the system size and number of junctions. Dynamics and directivity patterns of such Josephson antennae depending on bias current is investigated and it is shown that such oscillator with sufficiently large junction amount can be competitive with quantum cascade lasers.

We propose a new approach to the problem of obtaining coherent radiation from systems with a great number of Josephson junctions, which is based on the concept of traveling-wave antennas. The traveling wave in a line ensures identity of the electrodynamic conditions, under which the junctions operate, whereas the energy leakage to radiation in the lateral direction prevents saturation of the nonlinearity of the individual junctions having a small dynamic range. Simple analytical models, which demonstrate feasibility of the traveling-wave regime, are considered. A code for direct numerical simulation of Josephson microchips including microantennas, lumped elements, and power supply circuits have been developed. Using the direct numerical simulation, a version of the Josephson antenna, which is similar to the simplest single-wire antenna, is studied and the possibility to realize the traveling-wave regime is demonstrated.

We present the mathematical model and algorithm for simulation of active Josephson antenna, which consists of a few lumped Josephson junctions and sources of bias voltage, connected by perfectly conducting wires placed on dielectric substrate. For simple model of such antenna, we present some results of simulation, in particular, current-voltage characteristics of junctions and examples of antenna patterns.

Starting from the self-consistent Bogolubov - de Gennes theory for one-dimensional p-wave superconductors, we study numerically the inhomogeneous solutions for the gap function. We find a set of metastable solutions with a kink-like behavior of the gap function and several quasiparticle eigenstates localized both at the kink position and the sample edges. These results can be of interest for possible application of such superconducting systems in topological quantum computations etc.

It has been shown that the magnetostatic interaction in an inhomogeneous medium leads to the removal of the chiral degeneracy of magnetic distributions. Noncollinear states of two magnetic dipoles and a helical cycloid placed over a superconducting half-space have been considered as examples. The influence of a finite penetration depth of the magnetic field on the efficiency of removal of the chiral degeneracy has been studied in the framework of the London approximation.

The magnetocaloric effect in ferromagnet/paramagnet multilayer structures is studied in the framework of the Landau phenomenological theory of phase transitions. The performed estimations demonstrate the possibility of achieving record cooling efficiency with such structures.

The dependence of the magnetization reversal field of an elliptic submicrometer magnetic particle on the parameters of the material and sample configuration has been numerically studied. A method for calculating the magnetostatic field using the Fourier transform has been described in detail. The simulation results have demonstrated, in particular, that the normalized magnetization reversal field of a particle is independent of the exchange length at its rather large values.

We present the mathematical model and algorithm of simulation of active Josephson antenna, which consists of a few lumped Josephson junctions, in two-dimensional electrodynamic system. First we discuss some problems, connected with the formulation of mathematical models of the considered system. We suggest a system of equations which contains the discrete model of Maxwell equations, known as Yee scheme [1, 2], the equations for the dynamics of lumped Josephson junctions biased by d.c. voltage, and conditions which connect the current and voltage on the junctions with electromagnetic field in the waveguide. We use so-called Perfectly Matched Layer boundary conditions [1, 3] to avoid the reflection of electromagnetic waves at the artificial boundary of calculating domain. To simulate the dynamic of electromagnetic field we use the known FDTD explicit method [1] and semi-implicit scheme for the Josephson equations. We also discuss the implementation of suggested algorithm. By using near-to-far field transformation [1], the antenna diagram at the Josephson frequency is calculated.

The magnetic configurations of the system of magnetic dipoles that have different values and are arranged in a staggered order on a square lattice are studied. A numerical simulation is used to study the phase transitions in the system when the mismatch between the dipoles changes. The restructuring of the magnetic configuration of the system induced by a change in the mismatch is shown to proceed via sequential second-order phase transitions between collinear and noncollinear phases. The numerical simulation results are supported by analytical calculations performed with trial functions.

We investigate numerically the formation of vortex–antivortex pairs in thin-film superconducting strip in the presence of a straight current-carrying wire, oriented perpendicular to this strip. We demonstrate that the change in the number of the trapped vortices/antivortices inside the strip near the current-carrying wire results in a oscillatory dependence of the critical current Ic on the magnitude of the control current Iw in the wire. We consider the effect of the width of the superconducting strip and the width of the control wire on the period and the amplitude of the dc-Josephson-like oscillations of the critical current.

Within the Ginzburg-Landau model we study the critical field and temperature enhancement for crossing superconducting channels formed either along the sample edges or domain walls in thin-film magnetically coupled superconducting - ferromagnetic bilayers. The corresponding Cooper pair wave function can be viewed as a hybridization of two order parameter (OP) modes propagating along the boundaries and/or domain walls. Different momenta of hybridized OP modes result in the formation of vortex chains outgoing from the crossing point of these channels. Near this crossing point the wave functions of the modes merge giving rise to the increase in the critical temperature for a localized superconducting state. The origin of this critical temperature enhancement caused by the wave function squeezing is illustrated for a limiting case of approaching parallel boundaries and/or domain walls. Using both the variational method and numerical simulations we have studied the critical temperature dependence and OP structure vs the applied magnetic field and the angle between the crossing channels.

We present the numerical method for retrieving of the profile of layered media permittivity from the near field microscopy data. The method is based on the minimization of the discrepancy function describing the difference between the experimental measured of the near field antenna impedance and the calculated one for given permittivity profile. Such calculation is based on the numerical algorithm which developed on the base of rigorous solution of corresponding direct problem. We suppose that the profile to be retrieved is described by the function with finite number of unknown parameters and the discrepancy is minimized with respect of these parameters. We present some results of numerical experiments with method suggested.

The distribution of the magnetization over multilayer particles, including three ferromagnetic layers separated by insulating spacers, is studied experimentally and theoretically. Experimental data on the magnetic state of these particles are obtained by measuring their magnetoresistance. For the case of zero applied field, it is shown that a multilayer particle with easy-plane magnetic anisotropy is a noncollinear helical state.