Physics at the meso-scale: toroidal moments and non-extensive entropies


Семинар «Адронная материя при экстремальных условиях»

Дата и время: вторник, 4 декабря 2018 г., в 15:00

Место: Конференц-зал им. Блохинцева (4-й этаж), Лаборатория теоретической физики им. Н.Н. Боголюбова

Тема семинара: «Physics at the meso-scale: toroidal moments and non-extensive entropies»

Докладчик: Драгос-Виктор Ангел (Национальный институт физики и ядерной инженерии «Хория Хулубей», Румыния)


1. Statistical processes of mesoscopic systems (e.g. nano-, nuclear, and astronomic systems) cannot be described, in general, by the Boltzmann-Gibbs entropy (mainly) because they are not extensive. In such cases, other types of entropies — the so called non-extensive entropies—seem to be better suited for the task. There are different techniques for calculating the equilibrium probability distributions of non-extensive systems, techniques which may not lead to the same results. The justification of these techniques come, eventually, a-posteriori, by comparing the calculated distributions with the ones measured or inferred from the experiment. In this presentation, we propose a general approach for calculating the equilibrium probability distributions, applicable to both, extensive and non-extensive systems, and to any expression of the entropy. We exemplify the procedure by applying it to Boltzmann-Gibbs, Renyi, Tsallis, and Landsberg-Vedral entropies and discuss the results (D. V. Anghel and A. S. Parvan, J. Phys. A: Math Theor. 51, 446002, 2018).
2. Although the multipole decomposition of charge and current densities is almost as old as classical electrodynamics, a whole class of terms has remained unknown for a long time. The history of toroidal moments began with Zeldovich’s pioneering work (Zh. Exp. Teor. Fiz. 33, 1531, 1957; Sov. Phys. JETP 6, 1184, 1958). He was the first to note that a closed toroidal current (which cannot be reduced to a usual charge or magnetic multipole moment) represents a certain new kind of dipole. The necessity for studying the toroidal momentum operator is justified by its large area of applicability in physics at any scale (subnuclear, nuclear, atomic, molecular and condensed matter physics). There is a whole class of particles-the Majorana fermions and self conjugate bosons-which are not allowed to possess any electromagnetic structure other than toroidal multipole moments and this comes from CPT invariance alone. Meanwhile, the most important facts we need to know about an operator are its spectrum and its eigenfunctions. Consequently, in this presentation, we shall solve this problem. In order to do this, we introduce the toroidal momentum operator and study some of its properties. We propose a new set of coordinates in which the operator becomes a simple derivative along one of the coordinates. This enables us to find the eigenvalues and the eigenfunctions (D. V. Anghel, J. Phys. A: Math. Gen. 30, 3515, 1997).