Aftermath of the Chernobyl Catastrophe from the Point of View of the Security Concept

• Published in: Mathematical Notes Vol. 106; no. 5-6; pp. 757 - 770
• Main Author: Maslov, V. P.
• Format: Journal Article
• Language: English
• Published: Moscow Pleiades Publishing 01.11.2019; Springer Nature B.V
• Subjects: Chemical elements; Mathematical analysis; Mathematics; Mathematics and Statistics; Nuclear engineering; Nuclear matter; Nuclear physics; Nuclear safety; Operators (mathematics); Organic chemistry; Radioisotopes; Thermodynamics; Uncertainty; Variation; radioactive elements; law of corresponding states; time fluctuations; Gentile statistics; uncertainty relations; energy representation
• ISSN: 0001-4346; 1067-9073; 1573-8876
• DOI: 10.1134/S0001434619110099

The paper deals with uncertainty relations for time and energy operators, and the aftermath of the Chernobyl catastrophe is considered as an example. The mathematical approach developed by Holevo is analyzed, which allows us to assign the corresponding observables to non-self-adjoint operators and to establish uncertainty relations for nonstandard canonical conjugate pairs. Relations for calculating the minimal time interval in which the energy jump can be discovered are given. Based on the intensity parameter introduced by the author, which is related to a special statistics called Gentile statistics and to the polylogarithm function, properties of stable chemical elements, such as time fluctuations and the jump of specific energy in the transition from the Bose—Einstein distribution to the Fermi—Dirac distribution, are mathematically described with regard to experimental data. The obtained data are arranged in a table for 255 stable chemical elements. The mathematical approach developed by the author of the present paper allows one to describe the “antipode” (in a certain sense) of the standard thermodynamics, i.e., the thermodynamics of nuclear matter. This field of nuclear physics is very important for the study of properties of radioactive elements and, accordingly, from the standpoint of ensuring nuclear safety.