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## AC anomalous Hall effect in topological insulator Josephson junctions

A nonstationary anomalous Hall current is calculated for a voltage biased Josephson junction, which is composed of two s-wave superconducting contacts deposited on the top of a three-dimensional topological insulator (TI). A homogeneous Zeeman field was assumed at the surface of the TI. The problem has been considered within the ballistic approximation and on the assumption that tunneling of electrons between contacts and the surface of the TI is weak. In this regime the Josephson current has no features of the 4π-periodic topological effect which is associated with Andreev bound states. It is shown that the Hall current oscillates in time. The phase of these oscillations is shifted by π/2 with respect to the Josephson current and their amplitude linearly decreases with the electric potential difference between contacts. It is also shown that the Hall current cannot be induced by a stationary phase difference of the contact's order parameters.A nonstationary anomalous Hall current is calculated for a voltage biased Josephson junction, which is composed of two s-wave superconducting contacts deposited on the top of a three-dimensional topological insulator (TI). A homogeneous Zeeman field was assumed at the surface of the TI. The problem has been considered within the ballistic approximation and on the assumption that tunneling of electrons between contacts and the surface of the TI is weak. In this regime the Josephson current has no features of the 4π-periodic topological effect which is associated with Andreev bound states. It is shown that the Hall current oscillates in time. The phase of these oscillations is shifted by π/2 with respect to the Josephson current and their amplitude linearly decreases with the electric potential difference between contacts. It is also shown that the Hall current cannot be induced by a stationary phase difference of the contact's order parameters.

Collective plasmon excitations in a helical electron liquid on the surface of strong three-dimensional topological insulator are considered. The properties and internal structure of these excitations are studied. Due to spin-momentum locking in helical liquid on a surface of topological insulator, the collective excitations should manifest themselves as coupled charge- and spin-density waves.

We analyze the entanglement spectrum of superfluid phases of $^3$He, the 3D B-phase and the planar phase in two dimensions. We find explicitly the wave functions of the low-lying eigenstates, including Majorana zero modes, as well as the corresponding part of the spectrum of the entanglement Hamiltonian.

The dynamics of a two-component Davydov-Scott (DS) soliton with a small mismatch of the initial location or velocity of the high-frequency (HF) component was investigated within the framework of the Zakharov-type system of two coupled equations for the HF and low-frequency (LF) fields. In this system, the HF field is described by the linear Schrödinger equation with the potential generated by the LF component varying in time and space. The LF component in this system is described by the Korteweg-de Vries equation with a term of quadratic influence of the HF field on the LF field. The frequency of the DS soliton`s component oscillation was found analytically using the balance equation. The perturbed DS soliton was shown to be stable. The analytical results were confirmed by numerical simulations.

Radiation conditions are described for various space regions, radiation-induced effects in spacecraft materials and equipment components are considered and information on theoretical, computational, and experimental methods for studying radiation effects are presented. The peculiarities of radiation effects on nanostructures and some problems related to modeling and radiation testing of such structures are considered.

This volume presents new results in the study and optimization of information transmission models in telecommunication networks using different approaches, mainly based on theiries of queueing systems and queueing networks .

The paper provides a number of proposed draft operational guidelines for technology measurement and includes a number of tentative technology definitions to be used for statistical purposes, principles for identification and classification of potentially growing technology areas, suggestions on the survey strategies and indicators. These are the key components of an internationally harmonized framework for collecting and interpreting technology data that would need to be further developed through a broader consultation process. A summary of definitions of technology already available in OECD manuals and the stocktaking results are provided in the Annex section.