  Noncentrosymmetric metals such as Li$_2$(Pd$_{1-x}$Pt$_x$)$_3$B have
different Fermi surface topology below and above the band touching point where
spin-degeneracy is not lifted by the spin-orbit coupling. We investigate
thermoelectric and optical response as probes for this Fermi surface topology
change. We show that the chemical potential displays a dimensional crossover
from a three-dimensional to one-dimensional characteristics as the descending
Fermi energy crosses the band touching point. This dimensional crossover is due
to the existence of different Fermi surface topology above and below the band
touching point. We obtain an exact expression of relaxation time due to
short-range scatterer by solving Boltzmann transport equations
self-consistently. The thermoelctric power and figure of merit are
significantly enhanced as the Fermi energy goes below the band touching point
owing to the underlying one-dimensional-like nature of noncentrosymmteric bulk
metals. The value of thermoelectric figure of merit goes beyond two as the
Fermi energy approaches to the van Hove singularity for lower spin-orbit
coupling. Similarly, the studies of the zero-frequency and finite-frequency
optical conductivities in the zero-momentum limit reflect the nature of
topological change of the Fermi surface. The Hall coefficient and optical
absorption width exhibit distinct signatures in response to the changes in
Fermi surface topology.
