shuang Jin

Exact dynamics of dissipative electronic systems and quantum transport: Hierarchical equations of motion approach

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.

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

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.

Dynamic electronic response of a quantum dot driven by time-dependent voltage

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.

Non-equilibrium quantum theory for nanodevices based on the Feynman?Vernon influence functional

In this paper, we present a non-equilibrium quantum theory for transient electron dynamics in nanodevices based on the Feynman?Vernon influence functional. Applying the exact master equation for nanodevices we recently developed to the more general case in which all the constituents of a device vary in time in response to time-dependent external voltages, we obtained non-perturbatively the transient quantum transport theory in terms of the reduced density matrix. The theory enables us to study transient quantum transport in nanostructures with back-reaction effects from the contacts, with non-Markovian dissipation and decoherence being fully taken into account. For a simple illustration, we apply the theory to a single-electron transistor subjected to ac bias voltages. The non-Markovian memory structure and the nonlinear response functions describing transient electron transport are obtained.Jinshuang Jin, 2 Matisse Wei-Yuan Tu, 3 Wei-Min Zhang, ∗ and YiJing Yan Department of Physics and Center for Quantum Information Science, National Cheng Kung University, Tainan 70101, Taiwan 2 Department of Physics, Hangzhou Normal University, Hangzhou 310036, China Institute for Materials Science and Max Bergmann Center of Biomaterials, Dresden University of Technology, D-01069 Dresden, Germany. Department of Chemistry, Hong Kong University of Science and Technology, Kowloon, Hong Kong

Phase diagram and thermodynamics of the Polyakov linear sigma model with three quark flavors

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 (T-E, mu(E)) = (188 MeV, 139.5 MeV). In the transition region, the thermodynamic properties and the bulk viscosity over entropy density ratio zeta/s are also discussed in the PLSM.

Dynamics of quantum dissipation systems interacting with fermion and boson grand canonical bath ensembles: Hierarchical equations of motion approach

A hierarchical equations of motion formalism for a quantum dissipation system in a grand canonical bath ensemble surrounding is constructed on the basis of the calculus-on-path-integral algorithm, together with the parametrization of arbitrary non-Markovian bath that satisfies fluctuation-dissipation theorem. The influence functionals for both the fermion or boson bath interaction are found to be of the same path integral expression as the canonical bath, assuming they all satisfy the Gaussian statistics. However, the equation of motion formalism is different due to the fluctuation-dissipation theories that are distinct and used explicitly. The implications of the present work to quantum transport through molecular wires and electron transfer in complex molecular systems are discussed.

Complex non-Markovian effect on time-dependent quantum transport

Transient electronic dynamics of a single-lead double-quantum-dot system is significantly affected by intrasystem or lead-mediated interdot coupling. Unique occupancy-state transition features are distinguished in the response current spectrum, due to the presence of irreducible frequency-dependent correlation functions. The complex non-Markovian effects are demonstrated numerically by implementing the exact theory, based on the hierarchical equations of motion for the reduced dynamics of quantum transport systems. They are expected to play a prevalent and nontrivial role in the quantum dynamics of realistic nanoelectronic devices.

Current noise spectra and mechanisms with dissipaton equation of motion theory.

Based on the Yans 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.

Non-Markovian shot noise spectrum of quantum transport through quantum dots

The generalized quantum master equation with transport particle number resolution, similar to its conventional unconditioned counterpart, also has time-local and time-nonlocal configurations. The latter is found to be more suitable for the effect of an electrode’s bandwidth on quantum transport and noise spectrum for weak system-reservoir coupling, as calibrated with the exact results in the absence of a Coulomb interaction. We further analyze the effect of the Coulomb interaction on the noise spectrum of the transport current through quantum dot systems, and show that the realistic finite Coulomb interaction and finite bandwidth are manifested only with the non-Markovian treatment. We demonstrate a number of non-Markovian characteristics of the shot noise spectrum, including that which is due to finite bandwidth and that which is sensitive to and enhanced by the magnitude of the Coulomb interaction.

Continuous weak measurement and feedback control of a solid-state charge qubit: A physical unravelling of non-Lindblad master equation

Conventional quantum trajectory theory developed in quantum optics is largely based on the physical unravelling of a Lindblad-type master equation, which constitutes the theoretical basis of continuous quantum measurement and feedback control. In this work, in the context of continuous quantum measurement and feedback control of a solid-state charge qubit, we present a physical unravelling scheme of a non-Lindblad-type master equation. Self-consistency and numerical efficiency are well demonstrated. In particular, the control effect is manifested in the detector noise spectrum, and the effect of measurement voltage is discussed.