We investigate single-particle excitations and strong-coupling effects in a two-dimensional Fermi gas. Including pairing fluctuations within a Gaussian fluctuation theory, we calculate the density of states $rho(omega)$ near the Berezinskii-Kosterlit
z-Thouless (BKT) transition temperature $T_{rm BKT}$. Near $T_{rm BKT}$, we show that superfluid fluctuations induce a pseudogap in $rho(omega)$. The pseudogap structure is very similar to the BCS superfluid density of states, although the superfluid order parameter is absent in the present two-dimensional case. Since a two-dimensional $^{40}$K Fermi gas has recently been realized, our results would contribute to the understanding of single-particle properties near the BKT instability.
We investigate tunneling properties of Bogoliubov phonons in a Bose-Einstein condensate. We find the anomalous enhancement of the quasiparticle current $J_{rm q}$ carried by Bogoliubov phonons near a potential barrier, due to the supply of the excess
current from the condensate. This effect leads to the increase of quasiparticle transmission probability in the low energy region found by Kovrizhin {it et al.}. We also show that the quasiparticle current twists the phase of the condensate wavefunction across the barrier, leading to a finite Josephson supercurrent $J_{rm s}$ through the barrier. This induced supercurrent flows in the opposite direction to the quasiparticle current so as to cancel out the enhancement of $J_{rm q}$ and conserve the total current $J=J_{rm q}+J_{rm s}$.
