Dynamic properties of superconductors: from BCS to BEC regime

We analyze the evolution of the dynamics of neutral superconductors between BCS and BEC regimes. We consider 2D case, when BCS-BEC crossover occurs already at weak coupling and is governed by the ratio of the two scales -- the Fermi energy E_F and the bound state energy for two fermions in a vacuum, E_0. BCS and BEC regimes correspond to E_F >> E_0 and E_F << E_0, respectively. We compute the spectrum of low-energy bosonic excitations and show that the velocity of phase fluctuations remains v_F/\sqrt{2} through BCS-BEC crossover. We also derive the prefactor of the topological $A {\dot \phi}$ term in the effective action and argue that A = N_0 E_0 for E_F > E_0, and A = N_0 E_F for E_0 > E_F (N_0 is the density of states per spin). We apply our approach to a propagating vortex in a superconductor and compute the Magnus force acting on a vortex and the effective mass of a vortex. Our results partly agree and partly disagree with earlier studies.