High-frequency transport and zero-sound in an array of SYK quantum dots

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