We relate the memory kernel in the Nakajima-Zwanzig-Mori time-convolution approach to the system propagator which is often used to obtain the kernel in the Tokuyama-Mori time-convolutionless approach. The connection provides a robust and simple formalism to compute the memory kernel for a generalized system-bath model circumventing the need to compute high order system-bath observables, thus streamlining the use of numerically exact solvers for calculating the memory kernel. We illustrate this for a model system with electron-electron and electron-phonon couplings, driven away from equilibrium.

The generalized quantum master equation provides a powerful tool to describe the dynamics in quantum impurity models driven away from equilibrium. Two complementary approaches, one based on Nakajima-Zwanzig-Mori time-convolution (TC) and the other on the Tokuyama-Mori time-convolutionless (TCL) formulations provide a starting point to describe the time-evolution of the reduced density matrix. A key in both approaches is to obtain the so called "memory kernel" or "generator," going beyond second or fourth order perturbation techniques. While numerically converged techniques are available for the TC memory kernel, the canonical approach to obtain the TCL generator is based on inverting a super-operator in the full Hilbert space, which is difficult to perform and thus, nearly all applications of the TCL approach rely on a perturbative scheme of some sort. Here, the TCL generator is expressed using a reduced system propagator which can be obtained from system observables alone and requires the calculation of super-operators and their inverse in the reduced Hilbert space rather than the full one. This makes the formulation amenable to quantum impurity solvers or to diagrammatic techniques, such as the nonequilibrium Green's function. We implement the TCL approach for the resonant level model driven away from equilibrium and compare the time scales for the decay of the generator with that of the memory kernel in the TC approach. Furthermore, the effects of temperature, source-drain bias, and gate potential on the TCL/TC generators are discussed.

In this report, we show that a new mechanism for carrier transport in solutionprocessed colloidal semiconductor nanocrystal arrays exists at high excitation intensity on ultra-fast timescales, and allows for facile intrinsic transport between as-prepared nanocrystals over long distances. By combining a high speed photoconductive switch with an ultra-fast laser excitation in a sub-40 ps photoconductor, we observed transient photocurrents with peak densities of 3 •10 4 −10 6 mA/cm 2 in self-assembled PbSe nanocrystals capped with long native oleic acid ligands. The ratio between the transient photocurrent peak and the steady-state dark current is ten orders of magnitude. The transient mobility at the peak current is estimated to range between 0.5−17.5 cm 2 /Vs for the various nanocrystal sizes studied, which is 6 to 9 orders of magnitude higher than the dark current steady-state mobility in PbSe, CdSe, and CdTe nanocrystals capped with native ligands. The results are analyzed using a kinetic model which 1 attributes the ultra-high transient photocurrent to multiple photo-generated excitons undergoing on-particle Auger recombination, followed by rapid tunneling at high energies. This mechanism is demonstrated for a wide range of PbSe nanocrystals sizes (diameters from 2.7 nmto 7.1nm) and experimental parameters. Our observations indicate that native ligand-capped nanocrystal arrays are promising for optoelectronics applications wherein multiple carriers are photo-injected to inter-band states.