Classical trajectories and quantum supersymmetry

TL;DR

This paper investigates a supersymmetric quantum system with flat directions, revealing unique spectral properties and comparing classical and quantum behaviors to explore classical signs of supersymmetry.

Contribution

It provides a detailed analysis of a supersymmetric system's spectral properties and compares classical and quantum results to identify classical signatures of supersymmetry.

Findings

Discrete and continuous spectra coexist in the same energy range.

Classical and quantum analyses reveal notable differences and similarities.

Comparison suggests possible classical manifestations of supersymmetry.

Abstract

We analyze a supersymmetric system with four flat directions. We observe several interesting properties, such as the coexistence of the discrete and continuous spectrum in the same range of energies. We also solve numerically the classical counterpart of this system. A similar analysis is then done for an alike, but non-supersymmetric system. The comparison of theses classical and quantum results may serve as a suggestion about classical manifestations of supersymmetry.