Exact dynamics of open electronic systems: Quantum transport and dissipation

Jinshuang Jin, Xiao Hong Zheng, YiJing Yan

A generalized quantum master equation theory that governs the exact, nonperturbative quantum dissipation and quantum transport is formulated in terms of hierarchically coupled equations of motion for an arbitrary electronic system in contact with electrodes under either a stationary or a nonstationary electrochemical potential bias. The theoretical construction starts with the influence functional in path integral, in which the electron creation and annihilation operators are Grassmann variables. Time derivatives on the influence functionals are then performed in a hierarchical manner. Both the multiple-frequency dispersion and the non-Markovian reservoir parametrization schemes are considered for the desired hierarchy construction. The resulting hierarchical equations of motion formalism is in principle exact and applicable to arbitrary electronic systems, including Coulomb interactions, under the influence of arbitrary time-dependent applied bias voltage and external fields. Both the conventional quantum master equation and the real-time diagrammatic formalism of Schon and co-workers can be readily obtained at well defined limits of the present theory. We also show that for a noninteracting electron system, the present hierarchical equations of motion formalism terminates at the second tier exactly, and the Landuer-Buttiker transport current expression is recovered. The present theory renders an exact and numerically tractable tool to evaluate various transient and stationary quantum transport properties of many-electron systems, together with the involving nonperturbative dissipative dynamics.

I. Knežević, David K. Ferry

Keith H. Hughes

Jinshuang Jin, Xiao Hong Zheng, YiJing Yan +2 more

We present an exact quantum dissipation theory in terms of the hierarchical equations‐of‐motion formalism for an arbitrary open electronic system. This formalism provides a theoretical tool to study various transient and stationary properties of many‐body systems far away from equilibrium. In contact with transport current, we explicitly show that how the hierarchial scheme relates to various tunneling processes, such as sequential tunneling, cotunneling, and high‐order events. The present hierarchical scheme numerically converges in general. It accounts for the combined effects of the many‐particle interaction within the system and the nature of the system‐bath coupling. In particular, for noninteracting systems, it terminates at the second tier exactly.

Dvira Segal, Andrew J. Millis, David R. Reichman

We develop an iterative, numerically exact approach for the treatment of nonequilibrium quantum transport and dissipation problems that avoids the real-time sign problem associated with standard Monte Carlo techniques. The method requires a well-defined decorrelation time of the nonlocal influence functional for proper convergence to the exact limit. Since finite decorrelation times may arise either from temperature or from a voltage drop at zero temperature, the approach is well suited for the description of the real-time dynamics of single-molecule devices and quantum dots driven to a steady state via interaction with two or more electron leads. We numerically investigate two nontrivial models: the evolution of the nonequilibrium population of a two-level system coupled to two electronic reservoirs, and quantum transport in the nonequilibrium Anderson model. For the latter case, two distinct formulations are described. Results are compared to those obtained by other techniques.

Jacek Okołowicz, Marek Płoszajczak, I. Rotter