Spectral properties of the Goldstino in supersymmetric Bose-Fermi mixtures

TL;DR

This paper investigates the spectral characteristics of the Goldstino in supersymmetric Bose-Fermi mixtures, deriving model-independent results and explicit calculations to understand its dispersion and effects of supersymmetry breaking.

Contribution

It provides the first detailed analysis of Goldstino spectral properties in cold atom mixtures using sum rules and the Random Phase Approximation.

Findings

Analytic expressions for Goldstino dispersion at small momentum.

Identification of supersymmetry-specific features of the Goldstino.

Highlighting the large effects of the Fermi sea at moderate and large momenta.

Abstract

We evaluate the spectral properties of the Goldstino in a Bose-Fermi mixture of cold atoms and molecules whose dynamics is governed by a supersymmetric hamiltonian. Model independent results are obtained from sum rules obeyed by the spectral function. We carry out specific calculations, at zero and finite temperature, using the Random Phase Approximation, and obtain in particular analytic expressions for the dispersion relation at small momentum. These explicit calculations allow us to pin down more precisely the features of the Goldstino that can be attributed to the supersymmetry alone, together with its spontaneous breaking. The anomalous large effect of the Fermi sea at moderate and large momenta is emphasized.