Criterion of stability of the superconducting state

TL;DR

This paper introduces a stability criterion for the superconducting current state using rough systems mathematics, linking it to dielectric permittivity and phonon trajectories to explain superconductivity behavior.

Contribution

It presents a novel mathematical model connecting superconductor stability with phonon dynamics and dielectric properties, offering new insights into superconductivity mechanisms.

Findings

Established a stability criterion based on dielectric permittivity.

Linked phonon trajectories to the stability of superconducting states.

Proposed a mathematical framework for analyzing superconductor stability.

Abstract

In this paper, we propose to draw attention to the stability criterion of the superconductor current state. We use for this purpose the rough systems mathematical apparatus allowing us to relate the desired criterion with the dielectric permittivity of the matter and to identify the type of all possible phonons trajectories in its superconducting state. The state of superconductivity in the matter can be explained only by the phonons behavior peculiarity. And on the basis of the above-mentioned assumption, the corresponding mathematical model is constructed.