  We study an array of strongly correlated quantum dots of complex SYK type and
account for the effects of quadratic terms added to the SYK Hamiltonian; both
local terms and inter-dot tunneling are considered in the non-Fermi-liquid
temperature range $T \gg T_{FL}$. We take into account soft-mode fluctuations
and demonstrate their relevance for physical observables. Electric
$\sigma(\omega,p)$ and thermal $\kappa(\omega,p)$ conductivities are calculated
as functions of frequency and momentum for arbitrary values of the
particle-hole asymmetry parameter $\mathcal{E}$. At low-frequencies $\omega \ll
T$ we find the Lorenz ratio $L = \kappa(0,0)/T\sigma(0,0)$ to be non-universal
and temperature-dependent. At $\omega \gg T$ the conductivity
$\sigma(\omega,p)$ contains a pole with nearly linear dispersion $\omega
\approx sp\sqrt{\ln\frac{\omega}{T}}$ reminiscent of the "zero-sound", known
for Fermi-liquids. We demonstrate also that the developed approach makes it
possible to understand the origin of heavy Fermi liquids with anomalously large
Kadowaki-Woods ratio.
