Inhomogeneous superconductivity arises when the species participating in the pairing phenomenon have different Fermi surfaces with a large enough separation. In these conditions it could be more favorable for each of the pairing fermions to stay close to its Fermi surface and, unlike the usual BCS state, for the Cooper pair to have a nonzero total momentum. For this reason, in this state the gap varies in space, the ground state is inhomogeneous, and a crystalline structure might be formed. This situation was considered for the first time by Fulde and Ferrell (1964) and Larkin and Ovchinnikov (1964), after whom the corresponding state is called the LOFF state. The spontaneous breaking of the space symmetries in the vacuum state is a characteristic feature of this phase and is associated with the presence of long-wavelength excitations of zero mass. The situation described here is of interest both in solid-state and in elementary-particle physics, in particular in quantum chromodynamics at high density and low temperature. This review presents the theoretical approach to the LOFF state and its phenomenological applications using the language of the effective field theories.

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Inhomogeneous superconductivity in condensed matter and QCD

Self-consistent Green's function method for nuclei and nuclear matter

http://cds.cern.ch/record/389573/files/9906016.pdf

The properties of K̄ in the nuclear medium

Nucleon Effective Masses in Neutron-Rich Matter

The research on the superfluidity of neutron matter can be traced back to Migdal’s observation that neutron stars are good candidates for being macroscopic superfluid systems [1] And, in fact, during more than two decades of neutron-star physics the presence of neutron and proton superfluid phases has been invoked to explain the dynamical and thermal evolution of a neutron star The most striking evidence is given by post-glitch timing observations [2],[3], but also the cooling history is strongly influenced by the possible presence of super- fluid phases [4],[5] On the theoretical side, the onset of superfluidity in neutron matter or in the more general context of nuclear matter was investigated soon after the formulation of the Bardeen, Cooper, and Schrieffer (BCS) theory of superconductivity [6] and the pairing theory in atomic nuclei [7],[8]

Superfluidity in Neutron Star Matter

A separable representation of the Paris interaction is used as input for the investigation of various nuclear matter properties. The faithfulness of the separable representation is checked by comparison with results previously obtained from the original Paris interaction. Calculations are performed for four different values of the Fermi momentum, namely ${\mathit{k}}_{\mathit{F}}$=1.10, 1.36, 1.55, and 1.75 ${\mathrm{fm}}^{\mathrm{\ensuremath{-}}1}$. One evaluates the contributions to the quasiparticle potential energy that are of first, second, and third order in the reaction matrix. The momentum distribution n(k) in the correlated ground state is calculated up to second order in the reaction matrix. For 0k2 ${\mathrm{fm}}^{\mathrm{\ensuremath{-}}1}$, it mainly depends upon the ratio k/${\mathit{k}}_{\mathit{F}}$; in the domain 2k4.5 ${\mathrm{fm}}^{\mathrm{\ensuremath{-}}1}$, it is accurately reproduced by the expression 1/7${\mathit{k}}_{\mathit{F}}^{5}$${\mathit{e}}^{\mathrm{\ensuremath{-}}1.6\mathit{k}}$, with k and ${\mathit{k}}_{\mathit{F}}$ in units of ${\mathrm{fm}}^{\mathrm{\ensuremath{-}}1}$. The quasiparticle strength at the Fermi surface is calculated, as well as the mean-square deviation of the one-body density matrix from that of the unperturbed Fermi sea: This quantity gives an estimate of the minimum value of the norm of the difference between the one-body density matrix of a correlated nucleus and that associated with any Slater determinant. The average kinetic energy per nucleon is evaluated. Various contributions to the average binding energy per nucleon are investigated in the framework of Brueckner's expansion; particular attention is paid to the dependence of the calculated binding energy upon the choice of the ``auxiliary'' potential which is added to and subtracted from the Hamiltonian before performing the expansion. One also evaluates diagrams that are characteristic of the difference between the Green's function and the Brueckner hole-line expansions. The fulfillment of the Hugenholtz--Van Hove theorem is studied.

U. Lombardo

Papers

Nuclear matter properties from a separable representation of the Paris interaction.

Off-the-energy-shell properties of the mass operator and spectral functions in nuclear matter

Nuclear matter superfluidity in the SD channel

Giant dipole and quadrupole modes in highly rotating nuclei

A complete Lagrangian formulation of superconductivity