Strong vortex-antivortex fluctuations in the type II superconducting film

The small size vortex-antivortex pairs proliferation in type II superconducting film is considered for the wide interval of temperatures below Tc. The corresponding contribution to free energy is calculated. It is shown that these fluctuations give the main contribution to the heat capacity of the film both at low temperatures and in the vicinity of transition

Non-radially symmetric solutions to the Ginzburg-Landau equation

We study an atom with finitely many energy levels in contact with a heat bath consisting of photons (black body radiation) at a temperature $T >0$. The dynamics of this system is described by a Liouville operator, or thermal Hamiltonian, which is the sum of an atomic Liouville operator, of a Liouville operator describing the dynamics of a free, massless Bose field, and a local operator describing the interactions between the atom and the heat bath. We show that an arbitrary initial state which is normal with respect to the equilibrium state of the uncoupled system at temperature $T$ converges to an equilibrium state of the coupled system at the same temperature, as time tends to $+ \infty

On collapse of wave maps

We derive the universal collapse law of degree 1 equivariant wave maps (solutions of the sigma-model) from the 2+1 Minkowski space-time,to the 2-sphere. To this end we introduce a nonlinear transformation from original variables to blowup ones. Our formal derivations are confirmed by numerical simulations.Comment: 1 figur

Collapse of an Instanton

We construct a two parameter family of collapsing solutions to the 4+1 Yang-Mills equations and derive the dynamical law of the collapse. Our arguments indicate that this family of solutions is stable. The latter fact is also supported by numerical simulations.Comment: 17 pages, 1 figur

Macroscopic quantum tunneling in "small" Josephson junctions in magnetic field

We study the phenomenon of macroscopic quantum tunneling (MQT) in small Josephson junctions (JJ) with an externally applied magnetic field. The latter results in the appearance of the Fraunhofer type modulation of the current density along the barrier. The problem of MQT for a point-like JJ is reduced to the motion of the quantum particle in the washboard potential. In the case of a finite size JJ under consideration, this problem corresponds to a MQT in potential which itself, besides the phase, depends on space variables. Finally, the general expression for the crossover temperature T_0 between thermally activated and macroscopic quantum tunneling regimes and the escaping time tau_esc have been calculated

Risks in the Processes of Digitalization of Law and Supply Chain Strategy in Economic Relations

One of the main trends in the law development is its digitalization under the supply chain strategies, which is manifested both in the digitalization of legal regulation, legal technologies, legal processes and law enforcement. In the emergence of regulations affecting the issues of the digital economy, electronic state, information security. In this article, the authors assess some risks of digitalization of law through the prism of features of logical operations in legal thinking, analyze the interaction of a number of legal institutions and modern supply chain management systems that undergo radical changes in connection with digitalization

VIRTUAL CURRENCY AS AN OBJECT OF CIVIL RIGHTS IN RUSSIA

Purpose: The purpose of the article is to conduct a scientific analysis of the place of cryptocurrency in the system of objects of civil rights in Russia. Methodology: This research applies a system of general scientific, special scientific, and special methods of cognition of socio-legal and socio-economic phenomena, including historical-legal, comparative-legal, formal-logical methods, the method of dialectics, the method of system analysis. Result: Digital information technology has become a global trend in world economic development. This article deals with the study of the current state and prospects of legal regulation of virtual currencies (cryptocurrency) in Russia. Applications: This research can be used for universities, teachers, and students. Novelty/Originality: In this research, the model of Virtual currency as an object of civil rights in Russia is presented in a comprehensive and complete manner