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## Thermodynamical Properties of a Superconducting Quantum Cylinder

The thermodynamical potential of a superconducting quantum cylinder is calculated. The dependence of the critical temperature and the heat capacity of a superconducting system of the surface concentration of electrons and on the radius of the nanotube is studied.

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The contribution of electron–phonon scattering to conductivity of a quantum cylinder in a lon-gitudinal magnetic field has been studied. It has been shown that the conductivity of the nanotube undergoes Aharonov–Bohm oscillations with variations in the magnetic flux through the nanotube cross section. The formulas describing the temperature dependence of the resistance of the nanostructure both in the case of an isotropic phonon spectrum and with allowance for the effects of phonon confinement have been obtained in the analytical form.

These notes have appeared as a result of a one-term course in superfluidity and superconductivity given by the author to fourth-year undergraduate students and first-year graduate students of the Department of Physics, Moscow State University of Education. The goal was not to give a detailed picture of these two macroscopic quantum phenomena with an extensive coverage of the experimental background and all the modern developments, but rather to show how the knowledge of undergraduate quantum mechanics and statistical physics could be used to discuss the basic concepts and simple problems, and draw parallels between superconductivity and superfluidity.

Superconductivity and superfluidity are two phenomena where quantum mechanics, typically constrained to the microscopic realm, shows itself on the macroscopic level. Conceptually and mathematically, these phenomena are related very closely, and some results obtained for one can, with a few modifications, be immediately carried over to the other. However, the student of these notes should be aware of important differences between superconductivity and superfluidity that stem mainly from two facts: (1) electrons in a superconductor carry a charge, therefore one has to take into account interaction with electromagnetic radiation; (2) electrons move in a lattice, therefore phonons play a role not only a mediators of attractive interaction between pairs of electrons, but also as scatterers of charge carriers.

Although these are notes on superfluidity *and *superconductivity, and there are a few cross-references, the two subjects can be studied independently with, perhaps, a little extra work by the student to fill in the gaps resulting from such study. The material of Chapter 1 introduces the method of second quantisation that is commonly used to discuss systems with many interacting particles. It is then applied in Chaper 2 to treat the uniform weakly interacting Bose gas within the approach by N. Bogoliubov, and in Chapter 4 to formulate the theory of the uniform superconducting state put forth by J. Bardeen, L. Cooper and R. Schrieffer. Chapter 3 presents the theory proposed independently by E. Gross and L. Pitaevskii of a non-uniform weakly interacting Bose gas, with a discussion of vortices, rotation of the condensate, and the Bogoliubov equations. In Chapter 5 we discuss the Ginzburd-Landau theory of a non-uniform superconductor near the critical temperature and apply it to a few simple problems such as the surface energy of the boundary between a normal metal and a superconductor, critical current and critical magnetic field, and vortices.

A contribution of the electron-phonon scattering to the conductivity of a quantum cylinder in a magnetic field is calculated. It is demonstrated that the nanotube conductivity undergoes the Aharonov–Bohm oscillations with changes of the magnetic flux through the nanotube cross section.

In this paper, we construct a new distribution corresponding to a real noble gas as well as the equation of state for it.

Overview This book concisely presents the latest trends in the physics of superconductivity and superfluidity and magnetismin novel systems, as well as the problem of BCS-BEC crossover in ultracold quantum gases and high-Tc superconductors. It further illuminates the intensive exchange of ideas between these closely related fields of condensed matter physics over the last 30 years of their dynamic development. The content is based on the author’s original findings obtained at the Kapitza Institute, as well as advanced lecture courses he held at the Moscow Engineering Physical Institute, Amsterdam University, Loughborough University and LPTMS Orsay between 1994 and 2011. In addition to the findings of his group, the author discusses the most recent concepts in these fields, obtained both in Russia and in the West. The book consists of 16 chapters which are divided into four parts. The first part describes recent developments in superfluid hydrodynamics of quantum fluids and solids, including the fashionable subject of possible supersolidity in quantum crystals of 4He, while the second describes BCS-BEC crossover in quantum Fermi-Bose gases and mixtures, as well as in the underdoped states of cuprates. The third part is devoted to non-phonon mechanisms of superconductivity in unconventional (anomalous) superconductors, including some important aspects of the theory of high-Tc superconductivity. |The last part considers the anomalous normal state of novel superconductive materials and materials with colossal magnetoresistance (CMR). The book offers a valuable guide for senior-level undergraduate students and graduate students, postdoctoral and other researchers specializing in solid-state and low-temperature physics.

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.