The study of the energy spectrum of a system of quantum micro-vortices in a bounded spatial domain

Abstract: This study focuses on microscopic-sized quantum vortex filaments that are shaped like a circle. The model we considered examines loops with different radii and a small but non-zero core diameter. These loops are located in a bounded domain $D$. The quantization scheme of the classical vortices is based on the new approach proposed by the author \cite{Tal22_1,Tal24_2}. For these loops, we calculate both the quantized circulation and the energy spectrum, which are perfectly non-trivial. To understand how the results we have obtained can be used to describe the initial stage of turbulence in a quantum fluid, we study a system of $K$ random, non-interacting vortices. We explain how specific energy and circulation spectra lead to the occurrence of turbulence in the context of the developed approach.