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.

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An accurate and efficient numerical approach is developed for the transient electronic dynamics of open quantum systems at low temperatures. The calculations are based on a formally exact hierarchical equations of motion quantum dissipation theory [J. S. Jin et al., J. Chem. Phys. 128, 234703 (2008)]. We propose a hybrid scheme that combines the Matsubara expansion technique and a frequency dispersion treatment to account for reservoir correlation functions. The new scheme not just admits various forms of reservoir spectral functions but also greatly reduces the computational cost of the resulting hierarchical equations, especially in the low temperature regime. Dynamical Kondo effects are obtained and the cotunneling induced Kondo transitions are resolved in the transient current in response to time-dependent external voltages.

The phase diagram at finite temperature and density is investigated in the framework of the Polyakov linear sigma model (PLSM) with three light quark flavors in the mean field approximation. It is found that in the PLSM, the three phase transitions, i.e. the chiral restoration of u, d quarks, the chiral restoration of s quark and the deconfinement phase transition, are independent. There exists a two-flavor quarkyonic phase at low-density and a three-flavor quarkyonic phase at high density. The critical end point (CEP) which separates the crossover from the first-order line in the PLSM model is located at (TE, μE) = (188 MeV, 139.5 MeV). In the transition region, the thermodynamic properties and the bulk viscosity over entropy density ratio ζ/s are also discussed in the PLSM.

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We investigate transient dynamic response of an Anderson impurity quantum dot to a family of ramp-up driving voltage applied to the single coupling lead. Transient current is calculated based on a hierarchical equations of motion formalism for open dissipative systems [J. Chem. Phys. 128, 234703 (2008)]. In the nonlinear response and nonadiabatic charging regime, characteristic resonance features of transient response current reveal distinctly and faithfully the energetic configuration of the quantum dot. We also discuss and comment on both the physical and numerical aspects of the theoretical formalism used in this work.

We present a comprehensive theoretical investigation on the dynamic electronic response of a noninteracting quantum dot system to various forms of time-dependent voltage applied to the single contact lead. Numerical simulations are carried out by implementing a recently developed hierarchical equations of motion formalism [J. S. Jin et al., J. Chem. Phys. 128, 234703 (2008)], which is formally exact for a fermionic system interacting with grand canonical fermionic reservoirs, in the presence of arbitrary time-dependent applied chemical potentials. The dynamical characteristics of the transient transport current evaluated in both linear and nonlinear-response regimes are analyzed, and the equivalent classic circuit corresponding to the coupled dot-lead system is also discussed.

Based on the Yan's dissipaton equation of motion (DEOM) theory [J. Chem. Phys. 140, 054105 (2014)], we investigate the characteristic features of current noise spectrum in several typical transport regimes of a single-impurity Anderson model. Many well-known features such as Kondo features are correctly recovered by our DEOM calculations. More importantly, it is revealed that the intrinsic electron cotunneling process is responsible for the characteristic signature of current noise at anti-Stokes frequency. We also identify completely destructive interference in the noise spectra of noninteracting systems with two degenerate transport channels.