Numerical approach to time-dependent quantum transport and dynamical Kondo transition

Abstract

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.

Time-dependent density functional theory for quantum transport

“…However, care must be taken when treating the "deviation" contribution, as some of the K x αq may assume large values, due to the nontrivial value of complex Gaussian function at certain z = ǫ q + iy. 32 have confirmed that as the temperature lowers, the total number of exponential functions needed to accurately resolve the selfenergies in the hybrid scheme grows much slower than that in the Matsubara expansion scheme.…”

“…10 The exact QDT is formulated in terms of hierarchical equations of motion (HEOM), and applied to solve time-dependent quantum transport problems. [29][30][31][32] The HEOM-QDT is intrinsically a nonperturbative method, and is constructed to resolve the combined effects of the many-particle interaction, dissipative coupling strength, and memory time. The HEOM-QDT is by far the most tractable exact approach to time-dependent transient current through interacting electronic systems under arbitrary time-dependent voltage.…”

Correlation effects in bistability at the nanoscale: Steady state and beyond

“…To overcome the problem we implement a time-dependent strategy. [20][21][22][23][24][25][26][27][28][29][31][32][33][34] We first solve the steady-state equations of DFT and mean-field theory to determine the parameter range for bistability. Then we go beyond the current state-of-the-art and provide a TD description of the bistability phenomenon in adiabatic TDDFT [23][24][25][26][27][28][29] and TD mean-field theory.…”

Hierarchical quantum master equation with semiclassical Drude dissipation

“…5,6,7,8,9,10,11,12,13 This formalism is in principle exact and nonperturbative. However, its specified form depends on the way of treating the bath correlation function, under the constraint of the exact fluctuation-dissipation theorem [Eq.…”

“…For Gaussian bath, exact QDT can be formulated with path integral 1,2,3 or its differential version in terms of hierarchical equations of motion (HEOM). 4,5,6,7,8,9,10,11,12,13,14,15,16,17 However, exact approaches are numerically expensive in general. In this paper, we propose an approximate HEOM theory, which will be termed hereafter as hierarchical quantum master equation (HQME).…”