Response functions of cold neutron matter: density, spin and current fluctuations

TL;DR

This paper analyzes the response functions of cold neutron matter to various perturbations, deriving spectral functions and dispersion relations, and assessing their impact on specific heat, using both analytical and numerical methods.

Contribution

It provides a comprehensive derivation of response functions for neutron matter, including collective excitations and their spectral properties, validated through combined analytical and numerical approaches.

Findings

Density fluctuations form exciton-like bound states.

Spin excitations are diffusive modes above pair-breaking threshold.

Collective pair-breaking modes significantly contribute to neutron matter's specific heat.

Abstract

We study the response of a single-component pair-correlated baryonic Fermi-liquid to density, spin, and their current perturbations. A complete set of response functions is derived in the low-temperature regime both within an effective theory based on a small momentum transfer expansion and within a numerical scheme valid for arbitrary momentum transfers. A comparison of these two approaches validates the perturbative approximation within the domain of its convergence. We derive the spectral functions of collective excitations associated with the density, density-current, spin, and spin-current perturbations. The dispersion relations of density and spin fluctuations are derived and it is shown that the density fluctuations lead to exciton-like undamped bound states, whereas the spin excitations correspond to diffusive modes above the pair-breaking threshold. The contribution of the collective pair-breaking modes to the specific heat of neutron matter at subnuclear densities is computed and is shown to be comparable to that of the degenerate electron gas at not too low temperatures.