  We propose that the non-equilibrium current measured in the $a-b$ plane of an
underdoped cuprate (in either the strange metal or pseudogap regime) in contact
with either an overdoped cuprate or a standard Fermi liquid can be used
diagnose how different the pseudogap and strange metals are from a Fermi
liquid. Naively one expects the strange metal to be more different from a Fermi
liquid than is the pseudogap. We compute the expected non-equilibrium transport
signal with the three Green functions that are available in the literature: 1)
marginal Fermi liquid theory, 2) the phenomenological ansatz for the pseudogap
regime and 3) the Wilsonian reduction of the Hubbard model which contains both
the strange metal and pseudogap. All three give linear IV curves at low bias
voltages. Significant deviations from linearity at higher voltages obtain only
in the marginal Fermi liquid approach. The key finding, however, is that IV
curves for the strange metal/Fermi liquid contact that exceed that of the
pseudogap/Fermi liquid system. If this is borne out experimentally, this
implies that the strange metal is less orthogonal to a Fermi liquid than is the
pseudogap. Within the Wilsonian reduction of the Hubbard model, this result is
explained in terms of a composite-particle picture. Namely, the pseudogap
corresponds to a confinement transition of the charge degrees of freedom
present in the strange metal. In the strange metal the composite excitations
break up and electron quasiparticles scatter off bosons. The bosons here,
however, do not arise from phonons but from the charge degrees of freedom
responsible for dynamical spectral weight transfer.
