The Sachdev-Ye-Kitaev (SYK) model describes interacting fermionic zero modes in zero spatial dimensions, e.g. quantum dot, with interactions strong enough to completely washout quasiparticle excitations in the infrared. In this note, we consider the
complex-valued SYK model at temperature $T$ coupled to a zero temperature reservoir by a quench. We find out that the tunneling current dynamics reveals a way to distinguish the SYK non-Fermi liquid (nFL) initial state of the subsystem from the disordered Fermi liquid. Temperature dependent contribution to the currents half-life scales linearly in $T$ at low temperatures for the SYK nFl state, while for the Fermi liquid it scales as $T^2$. This provides a characteristic signature of the SYK non-Fermi liquid in a non-equilibrium measurement.
The Planckian relaxation rate $hbar/t_mathrm{P} = 2pi k_mathrm{B} T$ sets a characteristic time scale for both equilibration of quantum critical systems and maximal quantum chaos. In this note, we show that at the critical coupling between a supercon
ducting dot and the complex Sachdev-Ye-Kitaev model, known to be maximally chaotic, the pairing gap $Delta$ behaves as $eta ,, hbar/t_mathrm{P}$ at low temperatures, where $eta$ is an order one constant. The lower critical temperature emerges with a further increase of the coupling strength so that the finite $Delta$ domain is settled between the two critical temperatures.
