Superfluid nucleon matter in and out of equilibrium and weak interactions

TL;DR

This paper generalizes the Larkin-Migdal approach to non-equilibrium superfluid Fermi liquids using Schwinger-Keldysh techniques, enabling analysis of weak interactions and neutrino emission in nuclear matter.

Contribution

It introduces a formalism for non-equilibrium superfluid Fermi liquids applicable to arbitrary pairing states, incorporating diagram techniques and vertex renormalization.

Findings

Demonstrates the role of multi-piece diagrams in current conservation

Establishes correspondence between Schwinger-Kadanoff-Baym-Keldysh and Matsubara formalisms in equilibrium

Calculates neutrino emission from neutron pair breaking with correlation effects included

Abstract

The Larkin-Migdal approach to a cold superfluid Fermi liquid is generalized for a non-equilibrium system. The Schwinger-Keldysh diagram technique is applied. The developed formalism is applicable to the pairing in the states with arbitrary angular momenta. We consider the white body radiation problem by calculating probabilities of different direct reactions from a piece of a fermion superfluid. The closed diagram technique is formulated in terms of the full Green's functions for systems with the pairing correlation. The cutting rules are used to classify the diagrams representing one-nucleon, two-nucleon, etc. processes in the matter. The important role of multi-piece diagrams for the vector-current conservation is demonstrated. In the case of equilibrated systems, dealing with dressed Green's functions, we demonstrate correspondence between calculations in the Schwinger-Kadanoff-Baym-Keldysh formalism and the ordinary Matsubara technique. As an example we consider neutrino radiation from the neutron pair breaking and formation processes in case of a singlet pairing. Necessary correlation effects are included. The in-medium renormalization of normal and anomalous vertices is performed.