Hartree-Fock-Bogoliubov Theory of Polarized Fermi Systems

TL;DR

This paper explores a method for describing polarized Fermi systems with an odd number of particles using a two-chemical-potential approach within Hartree-Fock-Bogoliubov theory, connecting it to cranking and blocking techniques.

Contribution

It introduces a novel two-chemical-potential method for modeling polarized Fermi systems and relates it to existing cranking and blocking approaches.

Findings

The two-chemical-potential method effectively models particle-number parity changes.

Relations between the two-chemical-potential approach and cranking approximation are established.

Applications demonstrated for Fermi gases and atomic nuclei.

Abstract

Condensed Fermi systems with an odd number of particles can be described by means of polarizing external fields having a time-odd character. We illustrate how this works for Fermi gases and atomic nuclei treated by density functional theory or Hartree-Fock-Bogoliubov (HFB) theory. We discuss the method based on introducing two chemical potentials for different superfluid components, whereby one may change the particle-number parity of the underlying quasiparticle vacuum. Formally, this method is a variant of non-collective cranking, and the procedure is equivalent to the so-called blocking. We present and exemplify relations between the two-chemical-potential method and the cranking approximation for Fermi gases and nuclei.