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The solutions of the Wigner-transformed time-dependent Hartree--Fock--Bogoliubov equations are studied in the constant-$Delta$ approximation. This approximation is known to violate particle-number conservation. As a consequence, the density fluctuation and the longitudinal response function given by this approximation contain spurious contributions. A simple prescription for restoring both local and global particle-number conservation is proposed. Explicit expressions for the eigenfrequencies of the correlated systems and for the density response function are derived and it is shown that the semiclassical analogous of the quantum single--particle spectrum has an excitation gap of $2Delta$, in agreement with the quantum result. The collective response is studied for a simplified form of the residual interaction.
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An algebraic Quantum Field Theory formulation of separable pairing interaction for spherical finite systems is presented. The Lipkin formulation of the model Hamiltonian and model wave function is used. The Green function technique is applied to obtain the model energy through the spectral function. Closed equation for the many-body energy of the system is given and comparison with exact models are performed.
Fluid of spin-1/2 fermions is represented by a complex scalar field and a four-vector field coupled both to the scalar and the Dirac fields. We present the underlying action and show that the resulting equations of motion are identical to the (hydrodynamic) Euler equations in the presence of Coriolis force. As a consequence of the gauge invariances of this action we established the quantum kinetic equation which takes account of noninertial properties of the fluid in the presence of electromagnetic fields. The equations of the field components of Wigner function in Clifford algebra basis are employed to construct new semiclassical covariant kinetic equations of the vector and axial-vector field components for massless as well as massive fermions. Nonrelativistic limit of the chiral kinetic equation is studied and shown that it generates a novel three-dimensional transport theory which does not depend on spatial variables explicitly and possesses a Coriolis force term. We demonstrated that the three-dimensional chiral transport equations are consistent with the chiral anomaly. For massive fermions the three-dimensional kinetic transport theory generated by the new covariant kinetic equations is established in small mass limit. It possesses the Coriolis force and the massless limit can be obtained directly.
We formulate the kinetic master equation describing the production of charged particles which are created or destroyed only in pairs due to the conservation of their Abelian charge.Our equation applies to arbitrary particle multiplicities and reproduces the equilibrium results for both canonical (rare particles) and grand canonical (abundant particles) systems. For canonical systems, the equilibrium multiplicity is much lower and the relaxation time is much shorter than the naive extrapolation from the grand canonical ensemble results. Implications for particle chemical equilibration in heavy-ion collisions are discussed.
A simplified version of the Wigner--transformed time--dependent Hartree--Fock--Bogoliubov equations, leading to a solvable model for finite systems of fermions with pairing correlations, is introduced. In this model, pairing correlations result in a coupling of the Vlasov--type equation for the normal phase--space density with that for the imaginary part of the anomalous density. The effect of pairing correlations on the linear response of the system is studied for a finite one--dimensional system and an explicit expression for the correlated propagator is given.
Majorana fermions, quantum particles that are their own anti-particles, are not only of fundamental importance in elementary particle physics and dark matter, but also building blocks for fault-tolerant quantum computation. Recently Majorana fermions have been intensively studied in solid state and cold atomic systems. These studies are generally based on superconducting pairing between two Fermions with opposite momenta (textit{% i.e.}, zero total momentum). On the other hand, finite total momentum Cooper pairings, known as Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) states, were predicted 50 years ago and then widely studied in many branches of physics. However, whether FFLO superconductors can also support Majorana fermions has not been explored. Here we show that Majorana fermions can exist in certain types of gapped FFLO states, yielding a new topological quantum matter: topological FFLO superfluids/superconductors. We demonstrate the existence of such topological FFLO superfluids and the associated Majorana fermions using spin-orbit coupled degenerate Fermi gases and derive their physical parameter regions. The potential implementation of topological FFLO superconductors in semiconductor/superconductor heterostructures are also discussed.
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