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## Persistent current noise in normal and superconducting nanorings

We investigate fluctuations of persistent current (PC) in nanorings both with and without dissipation and decoherence. We demonstrate that such PC fluctuations may persist down to zero temperature provided there exists either interaction with an external environment or an external (periodic) potential produced, e.g., by quantum phase slips in superconducting nanorings. Provided quantum coherence is maintained in the system PC noise remains coherent and can be tuned by an external magnetic flux piercing the ring. If quantum coherence gets suppressed by interactions with a dissipative bath PC noise becomes incoherent and independent.

We investigate the effect of interacting quantum phase slips on persistent current and its fluctuations in ultrathin superconducting nanowires and nanorings pierced by the external magnetic flux. We derive the effective action for these systems and map the original problem onto an effective sine-Gordon theory on torus. We evaluate both the flux dependent persistent current and the critical radius of the ring beyond which this current gets exponentially suppressed by quantum fluctuations. We also analyze fluctuations of persistent current caused by quantum phase slips. At low temperatures the supercurrent noise spectrum has the form of coherent peaks which can be tuned by the magnetic flux. Experimental observation of these peaks can directly demonstrate the existence of plasma modes in superconducting nanorings.

We investigate how the interplay of quantum confinement and level broadening caused by disorder affects superconducting correlations in ultra-small metallic grains. We use the electron-phonon interaction-induced electron mass renormalization and the reduced static-path approximation of the BCS formalism to calculate the critical temperature as a function of the grain size. We show how the strong electron-impurity scattering additionally smears the peak structure in the electronic density of states of a metallic grain and imposes additional limits on the critical temperature under strong quantum confinement.

International Conference \Advanced Element Base of Micro- and Nano-Electronics with Using To-date Achievements of Theoretical Physics" is an annual conference of Faculty for Physics and Mathematics of Moscow Region State University (MRSU). MRSU is a leading Russian regional university. This conference is traditionally organized by Department of Theoretical Physics. The conference attracted around 120 participants from many countries and Russian regions. They have applied 83 papers to a special JPCS issue. Special session was devoted to RD of graduate and post-graduate students. The Conference program included sessions as follows:

To-Date Theoretical Physics Problems Electronics Technologies and Materials Condensed Matter Physics Aerohydrodynamics Plasma Physics Electronic devices for biological applications Space Physics and Technologies Education of Physics, Electronics and Information TechnologiesBesides of oral talks at typical scienti c sessions many papers are to be presented on-line with using to-date communication facilities. Therefore, many participants from oversea countries and Russian regions have a good opportunity to tell about their recent RD results and discuss to-date scienti c problems. Many famous scienti c organizations applied their participation in the Conference: Institute of Solid State Physics of Russian Academy of Sciences (RAS), Steklov Mathematics Institute of RAS, Moscow Institute of Physics and Technology (Technical University), Lomonosov Moscow State University, Federal RD Center of RAS \Crystallography and Photonics", Saint-Petersburg State University, Kurchatov Institute, Alikhanov Institute of Theoretical and Applied Physics, Keldysh Institute of Applied Mathematics of RAS, Computational Center of RAS, RUDN University, Bauman Moscow State Technology University, Donghua University (Shanghai, China), Higher School of Economics - National Research University, Moscow Aviation Institute (Technology University), JSC Cyclon, JSC Pulsar, BOE (China, Russian Oce), Northern Federal University (Arkhangelsk), Demidov Yaroslavl State University, Saratov National Research State University named after N. G. Chernyshevsky, Moscow Regional Research and Clinical Institute "MONIKI", K.G. Razumovsky Moscow State University of Technologies and Management (the First Cossack University), Moscow State University of Design and Technology and many others.

A big group of master, bachelor and post-graduate students from Institute of Solid State Physics of RAS, MRSU, MIPT, RUDN University presented their research results. The International Conference \Advanced Element Base of Micro- and Nano-Electronics with Using To-date Achievements of Theoretical Physics" becomes very important scienti c event with signi cant results of big importance for basic science and practical application.

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.