Публикации

We consider the notion of number of degrees of freedom in number theory and thermodynamics. This notion is applied to notions of terminology such as terms, slogans, themes, rules, and regulations. Prohibitions are interpreted as restrictions on the number of degrees of freedom. We present a theorem on the small number of degrees of freedom as a consequence of the generalized partitio numerorum problem. We analyze the relationship between thermodynamically ideal liquids with the lexical background that a term acquires in the process of communication. Examples showing how this background may be enhanced are considered. We discuss the question of the coagulation of drops in connection with the forecast of analogs of the gas-ideal liquid phase transition in social-political processes. 

We consider a periodic sequence { ck }k=0 ∞ and investigate a numerical properties of an irrational number α =σk=0 ∞ ck/k!. As an application of our results we present a simple transformation of periodic sequence { ck }k=0 ∞ into aperiodic sequence. 

Вычислен однопетлевой сдвиг энергии основного состояния электрона в замагниченной плазме двумерной электродинамики с членом Черна-Саймонса. В предельном случае относительно слабого магнитного поля найдено точное выражение для вакуумного АММ электрона при нулевой температуре и плотности среды. Изучена зависимость АММ электрона от температуры и параметра Черна-Саймонса в зарядово-симметричной плазме. В высокотемпературной области получена новая асимптотика для АММ электрона. Исследован вклад эффектов конечной плотности в АММ электрона в вырожденном замагниченном электронном газе.

Dusty plasma structures in glow discharge in helium in the temperature range of 5–300 K are investigated experimentally. We have described the experimental setup that makes it possible to continuously vary the temperature regime. The method for experimental data processing has been described. We have measured interparticle distances in the temperature range of 9–295 K and compared them with the Debye radius. We indicate the ranges of variations in experimental parameters in which plasma–dust structures are formed and various types of their behavior are manifested (rotation, vibrations of structures, formation of vertical linear chains, etc.). The applicability of the Yukawa potential to the description of the structural properties of a dusty plasma in the experimental conditions is discussed.

We studied the quantum correlations between the nodes in a quantum neural network built of an array of quantum dots with dipole–dipole interaction. By means of the quasiadiabatic path integral simulation of the density matrix evolution in a presence of the common phonon bath we have shown the coherence in such system can survive up to the liquid nitrogen temperature of 77 K and above. The quantum correlations between quantum dots are studied by means of calculation of the entanglement of formation in a pair of quantum dots with the typical dot size of a few nanometers and interdot distance of the same order. We have shown that the proposed quantum neural network can keep the mixture of entangled states of QD pairs up to the above mentioned high temperatures.

Population annealing is a hybrid of sequential and Markov chain Monte Carlo methods geared towards the efficient parallel simulation of systems with complex free-energy landscapes. Systems with first-order phase transitions are among the problems in computational physics that are difficult to tackle with standard methods such as local-update simulations in the canonical ensemble, for example with the Metropolis algorithm. It is hence interesting to see whether such transitions can be more easily studied using population annealing. We report here our preliminary observations from population annealing runs for the two-dimensional Potts model with q>4, where it undergoes a first-order transition.