Using the fluctuation exchange approximation and a three-orbital model, we study the band renormalization, the Fermi surface reconstruction, and the superconducting pairing symmetry in iron-based superconductors. We find that the interorbital spin fluctuations lead to the strong anisotropic band renormalization and the renormalization is orbital dependent. As a result, the topology of Fermi surface displays distinct variation with doping from the electron type to the hole type, which is consistent with the recent experiments. This shows that the Coulomb interactions will have a strong effect on the band renormalization and the topology of the electron Fermi pocket. In addition, the pairing state mediated by the interorbital spin fluctuation is of an extended s-wave symmetry.

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We study the dynamical energy equipartition properties in the integrable Toda model with additional uniform or disordered on-site energies by extensive numerical simulations. The total energy is initially equidistributed among some of the lowest frequency linear modes. For the Toda model with uniform on-site potentials, the energy spectrum keeps its profile nearly unchanged in a relatively short time scale. On a much longer time scale, the energies of tail modes increase slowly with time. Energy equipartition is far away from being attached in our studied time scale. For the Toda model with disordered on-site potentials, the energy transfers continuously to the high frequency modes and eventually towards energy equipartition. We further perform a systematic study of the equipartition time t eq depending on the energy density ε and the nonlinear parameter α in the thermodynamic limit for the Toda model with disordered on-site potentials. We find t eq ∝ (1/ε) a (1/α) b , where b ≈ 2a. The values of a and b are increased when increasing the strengths of disordered on-site potentials or decreasing the number of initially excited modes.

We study the magnetic properties and the superconducting pairing mediated by spin fluctuations on the metallic kagome lattice by using the Hubbard model and the fluctuation exchange approximation. It is found that the spin susceptibility is caused by the nesting of the renormalized Fermi surface. We point out that superconductivity will be favored in the spin-singlet channel and may be more easily realized around 25% hole doping. We find an evolution of the pairing state from a d-wave-like symmetry, described by the E(2g) representation of the group D(6h) at low dopings, to that described by the A(2g) representation at heavy hole dopings.

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