Investigation of Zero-Sound Dispersion Equation in the Complex Plane of Frequency

TL;DR

This paper explores the solutions of the zero-sound dispersion equation in the complex frequency plane, distinguishing between physical and unphysical sheets to better understand their properties.

Contribution

It provides a detailed analysis of the placement of zero-sound solutions on different sheets in the complex plane, enhancing theoretical understanding.

Findings

Solutions are located on physical and unphysical sheets in the complex plane.

The dispersion equation's solutions exhibit specific behaviors depending on their sheet placement.

Insights into the nature of zero-sound modes in complex frequency space.

Abstract

The known solutions to the zero-sound dispersion equation are considered as placed on the physical and unphysical sheets in the complex plane of frequency.