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.

Several recent advancements for the hierarchical equations of motion (HEOM) approach are reported. First, we propose an a priori estimate for the optimal number of basis functions for the reservoir memory decomposition. Second, we make use of the sparsity of auxiliary density operators (ADOs) and propose two ansatzs to screen out all the intrinsic zero ADO elements. Third, we propose a new truncation scheme by utilizing the time derivatives of higher-tier ADOs. These novel techniques greatly reduce the memory cost of the HEOM approach, and thus enhance its efficiency and applicability. The improved HEOM approach is applied to simulate the coherent dynamics of Aharonov-Bohm double quantum dot interferometers. Quantitatively accurate dynamics is obtained for both noninteracting and interacting quantum dots. The crucial role of the quantum phase for the magnitude of quantum coherence and quantum entanglement is revealed.

We propose a hierarchical dynamics approach for evaluation of nonequilibrium dynamic response properties of quantum impurity systems. It is based on a hierarchical equations of motion formalism, in conjunction with a linear response theory established in the hierarchical Liouville space. This provides an accurate and universal tool for characterization of a variety of response and correlation functions of local impurities, as well as transport related response properties. The practicality of our proposed approach is demonstrated via the evaluation of various dynamical properties of a single-impurity Anderson model. These include the impurity spectral density, local charge fluctuation, local magnetic susceptibility, and current-voltage admittance, in both equilibrium and nonequilibrium situations. The numerical results are considered to be quantitatively accurate, as long as they converge quantitatively with respect to the truncation of the hierarchy.

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