A discussion of an anisotropic (
p state) Fermi superfluid with a spatially varying order parameter is presented. We restrict ourself to the Landau-Ginzburg region and consider spatial variations governed by the linear gap equation. The kernel of the linearized gap equation is shown to be related to a current-current correlation function of quasiparticles in the normal state. This relation permits the calculation of the two coherence lengths ${\ensuremath{\xi}}_{L}$ and ${\ensuremath{\xi}}_{T}$ defined earlier in the framework of a phenomenological Landau-Ginzburg theory, and a discussion of boundary conditions for the order parameter at interfaces. A significant anisotropy in the coherence lengths is found (${\ensuremath{\xi}}_{L}=\sqrt{3}{\ensuremath{\xi}}_{T}$), which reflects itself in the nature of the supercurrents. The boundary conditions at specularly and diffusely reflecting surfaces lead us to expect that the vector $\stackrel{^}{l}$, which describes the orbital angular momentum of a Cooper pair in an "axial" state, is anchored normal to the walls. Some consequences of these results on various experimental problems (fourth sound, monodomain production, Josephson couplings, behavior in thin capillaries) are briefly discussed.
The Ginzburg–Landau (GL) equation is derived for the spatially inhomogeneous order parameter (OP) of the He3 type superfluid Fermi liquid (SFL) (composed of electrically neutral fermions with triplet p-wave pairing) for a uniform flow of the normal component of the SFL with a velocity vn≪2Tc/pF (Tc is the temperature of phase transition from the normal to the superfluid state, and pF is the Fermi momentum). The derivation is based on the integrodifferential equation for OP, which is valid at temperatures near Tc in the absence of strong-coupling effects. The main results are the corrections for the coefficients of the OP gradients in the GL equation (caused by the fact that vn≠0), which are calculated in the perturbation theory. These corrections, which indicate the deformation of the OP due to the SFL flow with the velocity vn, can be not only comparable for vn≪2Tc/pF, but also greater than the so-called nontrivial strong-coupling corrections to these coefficients, depending on the value of vn, and hence can be of practical importance for describing He–B3 at low pressures, when the strong-coupling effects are weak.
The Fermi-liquid approach generalized to superfluid systems is used to derive general formulas for the normal and abnormal distribution functions (DF) for quasiparticles of a superfluid Fermi liquid (SFL) consisting of electrically neutral fermions with spin-triplet pairing (the spin of a pair s=1, the orbital angular momentum l of the pair being an arbitrary odd number) in a static uniform magnetic field, taking into account the Landau spin-exchange Fermi-liquid interaction at temperatures 0<T<Tc (Tc is the temperature of phase transition from the normal to the superfluid state). In deriving the DF, the explicit form of the energy functional (EF) for SFL is not used. A system of coupled equations is obtained for the order parameter, energy of quasiparticles, and effective magnetic field for the SFL under investigation in the case of an EF quadratic in DF. The obtained DF and the system of equations are applicable for describing both unitary and nonunitary phases of superfluid He3 in a magnetic field, e.g., for determining the magnetization and magnetic susceptibility of these phases.
After reminding of properties of the condensate of the complex scalar field in the external uniform magnetic field
H, focus is made on the study of phases of the complex neutral vector-boson fields coupled with magnetic field by the Zeeman coupling and phases of the charged vector-boson fields. The systems may behave as nonmagnetic and ferromagnetic superfluids and ordinary and ferromagnetic superconductors. Response of these superfluid and superconducting systems occupying half of space on the external uniform static magnetic field
H is thoroughly studied. Then the spin-triplet pairing of neutral fermions at conserved spin is considered. Novel phases are found. In external magnetic field, the phase with zero mean spin proves to be unstable to the formation of a phase with a nonzero spin. For a certain parameter choice ferromagnetic superfluid phases are formed already for
H=0, characterized by an own magnetic field
h. For
H>Hcr2, the spin-triplet pairing and ferromagnetic superfluidity continue to exist above the ``old'' phase transition critical temperature
Tcr. Formation of domains is discussed. Next, spin-triplet pairing of charged fermions is studied. Novel phases are found. Then, the
3P2 nn pairing in neutron star matter is studied. Also, a
3P2 pp pairing is considered. Numerical estimates are performed in the BCS weak-coupling limit and beyond it for the
3P2 nn and
pp pairings, as well as for the
3S1 np pairing.
A possibility of the condensation of excitations with non-zero momentum in moving superfluid media is considered in terms of the Ginzburg-Landau model. The results might be applicable to the superfluid
4He, ultracold atomic Bose gases, various superconducting and neutral systems with pairing, like ultracold atomic Fermi gases and the neutron component in compact stars. The order parameters, the energy gain, and critical velocities are found.
General expressions are obtained in explicit form for the anomalous and normal distribution functions of quasiparticles in nonunitary phases of a superfluid paramagnetic Fermi liquid consisting of electrically neutral fermions with triplet pairing (the pairs have spin s=1 and an arbitrary odd value of the orbital angular momentum l) in a uniform static magnetic field. A generalized Fermi-liquid approach is used which takes into account the exchange Fermi-liquid interaction but does not specify the form of the energy functional of the superfluid Fermi liquid. The results are valid at any temperature in the interval 0⩽T⩽Tc, where Tc is the temperature of the phase transition from the normal to the superfluid state. When an explicit form of the energy functional is specified, the general formulas for the distribution function can be used to describe the various nonunitary phases of a superfluid Fermi liquid of the He3 type in a high magnetic field. In particular, for He3-A1, He3-A2, and the nonunitary two-dimensional phase of He3 in a high magnetic field at 0⩽T⩽Tc, an energy functional quadratic in the distribution function is used to find a system of coupled equations for the order parameter and the effective magnetic field and to obtain an expression is obtained for the nonlinear magnetic susceptibility.