  High-Tc cuprate, A3C60 and other unconventional superconductors (SCs) have
very high Tc with respect to the energy scale of superconducting (SC) charges
inferred from the superfluid density (SFD). The observed linear dependence of
Tc on the SFD can hardly be expected in BCS SCs while being reminiscent of Bose
Einstein Condensation of pre-formed pairs. As additional non-BCS like
behaviors, responses similar to those in the bulk SC states have been observed
at temperatures (T) well above Tc in the vortex-like Nernst effect, diamagnetic
susceptibility, and transient optical conductivity in photo-excitation (PEX)
measurements. Here we propose a picture based on equilibrium and transient SFD
to understand these unconventional behaviors. This picture assumes: (1) Dynamic
SC responses in the Nernst and PEX measurements emerge at the formation of the
local phase coherence (LPC) among wave functions of pre-formed pairs. (2) Its
onset T (TLPC) is distinct from and lower than the pair-formation pseudo-gap T
(Tstr). (3) The bulk SC Tc is reduced from TLPC, due to the competition between
the SC and antiferromagnetic (AF) order. (4) The magnetic resonance mode (MRM)
controls Tc in the SC-AF competition. (5) The transient optical responses can
be attributed to a change of the balance between the competing SC and AF orders
caused by PEX. The assumptions (1) and (2) explain the relationship between Tc
and the transient SFD in PEX studies and equilibrium SFD in Nernst effect. (3)
and (4) are inferred from the linear dependence of Tc on the MRM energy. (4)
and (5) are consistent with the behaviors of the 400 cm-1 optical mode in
equilibrium and PEX studies, whose intensity represents the MRM intensity.
Unlike previous phase-fluctuation pictures which expect dynamic responses
between Tstr and Tc, the present picture involving competing order indicates
that dynamic SC responses are seen between TLPC and Tc.
