Many-body correlations in nuclear superfluidity

Nuclear superfluidity at finite temperature

“…Following our previous developments reported in Ref. [31] for the zero-temperature case, in Section II we generate the EOM for the fermionic pair, or particleparticle, propagator, but now evolving in the domain of imaginary time introduced by Matsubara [32]. We show that the four-fermion correlation function in the dynamical kernel of the resulting EOM, which is responsible for the induced pairing, can be approximated with various degrees of accuracy, in analogy with the zero-temperature case.…”

“…In analogy with Ref. [31], we stay within the formalism of correlation functions, such as the Green functions, or propagators. As the propagators are directly related to observed excitation spectra and ground state properties of the manybody systems, this formalism is one of the most convenient and powerful ones in the description of phenomena that occur in strongly-coupled media.…”

“…so that T (0) is the instantaneous, or static, part of the Tmatrix and T (r) is its dynamical part. In analogy with the case of the particle-hole response [35] and the zerotemperature particle-particle response [31], Eq. ( 11) can be transformed to an equation of the Dyson type…”

“…As we showed in detail in Refs. [31,35], the in-medium dynamical kernel in the form of the phononexchange interaction is completely analogous to the mesonexchange interaction between the nucleons in the vacuum. In turn, the latter interaction should be, in principle, derivable from the Hamiltonian of quarks and gluons.…”

Many-body theory for quasiparticle states in superfluid fermionic systems

“…The EOM's for these functions were discussed, in particular, in Refs. [34,46]. However, similarly to the one-fermion EOM, in the superfluid regime the EOM's for the particle-hole response and for the pair propagator are coupled as these propagators form the components of one object, the two-quasiparticle propagator.…”