Dissipaton Equation of Motion Theory versus Fokker-Planck Quantum Master Equation

The quest of exact and nonperturbative methods on quantum dissipation with nonlinear coupling environments remains in general a great challenge.In this review we present a comprehensive account on two approaches to the entangled system-and-environment dynamics,in the presence of linear-plus-quadratic coupling bath.One is the dissipaton-equation-ofmotion(DEOM)theory that has been extended recently to treat the nonlinear coupling environment.Another is the extended Fokker-Planck quantum master equation(FP-QME)approach that will be constructed in this work,based on its DEOM correspondence.We closely compare these two approaches,with the focus on the underlying quasi-particle picture,physical implications,and implementations.

Shot noise in electron transport through a double quantum dot:a master equation approach

We study shot noise in tunneling current through a double quantum dot connected to two electric leads. We derive two master equations in the occupation-state basis and the eigenstate basis to describe the electron dynamics. The approach based on the occupation-state basis, despite being widely used in many previous studies, is valid only when the interdot coupling strength is much smaller than the energy difference between the two dots. In contrast, the calculations using the eigenstate basis are valid for an arbitrary interdot coupling. Using realistic model parameters, we demonstrate that the predicted currents and shot-noise properties from the two approaches are significantly different when the interdot coupling is not small. Furthermore, properties of the shot noise predicted using the eigenstate basis successfully reproduce qualitative features found in a recent experiment.

Generalized Quantum Master Equation:A Tutorial Review and Recent Advances

The generalized quantum master equation(GQME)provides a general and exact approach for simulating the reduced dynamics in open quantum systems where a quantum system is embedded in a quantum environment.Dynamics of open quantum systems is important in excitation energy,charge,and quantum coherence transfer as well as reactive photochemistry.The system is usually chosen to be the interested degrees of freedom such as the electronicstates in light-harvesting molecules or tagged vibrational modes in a condensed-phase system.The environment is also called the bath,whose influence on the system has to be considered,and for instance can be described by the GQME formalisms using the projection operator technique.In this review,we provide a heuristic description of the development of two canonical forms of GQME,namely the time-convoluted Nakajima-Zwanzig form(NZ-GQME)and the time-convolutionless form(TCL-GQME).In the more popular NZ-GQME form,the memory kernel serves as the essential part that reflects the non-Markovian and non-perturbative effects,which gives formally exact dynamics of the reduced density matrix.We summarize several schemes to express the projection-based memory kernel of NZ-GQME in terms of projection-free time correlation function inputs that contain molecular information.In particular,the recently proposed modified GQME approach based on NZ-GQME partitions the Hamiltonian into a more general diagonal and off-diagonal parts.The projection-free inputs in the above-mentioned schemes expressed in terms of different system-dependent time correlation functions can be calculated via numerically exact or approximate dynamical methods.We hope this contribution would help lower the barrier of understanding the theoretical pillars for GQME-based quantum dynamics methods and also envisage that their combination with the quantum computing techniques will pave the way for solving complex problems related to quantum dynamics and quantum information that are currently intractable even with today’s state-of-the-art classical supercomputers.

GLOBAL CLASSICAL SOLUTIONS FOR QUANTUM KINETIC FOKKER-PLANCK EQUATIONS

We consider a class of nonlinear kinetic Fokker-Planck equations modeling quantum particles which obey the Bose-Einstein and Fermi-Dirac statistics, respectively. We establish the existence and convergence rate to the steady state of global classical solution to such kind of equations around the steady state.

Nonlinear Liouville Equation and Information Soliton

In this work, some types of nonlinear Liouville equation (NLE) and nonlinear Master equations (NME) are studied. We found that the nonlinear terms in the equation can resist state of system damping so that an information solitonic structure appears. Furthermore, the power in the non-linear term is independent of limitation of the solution. This characteristic offers a possibility to construct complicated information solitons from some simple solutions, which allow one to solve complicated NLE or NME. The results obtained in this work may provide an innovated channel for the quantum information transmission over far distance against dissipation and decoherence, and also open a constructive way to resist age decaying of system by designing adjusted field interaction with the system nonlinearly.

Number-resolved master equation approach to quantum transport under the self-consistent Born approximation

We construct a particle-number （n）-resolved master equation （ME） approach under the self-consistent Born approximation （SCBA） for quantum transport through mesoscopic systems. The formulation is essentially non-Markovian and incorporates the interplay of the multi-tunneling processes and many-body correlations. The proposed n-SCBA-ME goes beyond the scope of the Born- Markov master equation, being applicable to transport under small bias voltage, in non-Markovian regime and with strong Coulomb correlations. For steady state, it can recover not only the exact result of noninteracting transport under arbitrary voltages, but also the challenging nonequilibrium Kondo effect. Moreover, the n-SCBA-ME approach is efficient for the study of shot noise. We demonstrate the application by a couple of representative examples, including particularly the nonequilibrium Kondo system.

Number-resolved master equation approach to quantum measurement and quantum transport

In addition to the well-known Landauer-Bfittiker scattering theory and the nonequilibrium Green＇s function technique for mesoscopic transports, an alternative （and very useful） scheme is quantum master equation approach. In this article, we review the particle-number （n）-resolved master equation （n-ME） approach and its systematic applications in quantum measurement and quantum transport problems. The n-ME contains rich dynamical information, allowing efficient study of topics such as shot noise and flfll counting statistics analysis. Moreover, we also review a newly developed master equation approach （and its n-resolved version） under self-consistent Born approximation. The application potential of this new approach is critically examined via its ability to recover the exact results for noninteracting systems under arbitrary voltage and in presence of strong quantum interference, and the challenging non-equilibrium Kondo effect.

Master equation approach to transient quantum transport in nanostructures

In this review article, we present a non-equilibrium quantum transport theory for transient electron dynamics in nanodevices based on exact Master equation derived with the path integral method in the fermion coherent-state representation. Applying the exact Master equation to nanodevices, we also establish the connection of the reduced density matrix and the transient quantum transport current with the Keldysh nonequilibrium Green functions. The theory enables us to study transient quantum transport in nanostructures with back-reaction effects from the contacts, with non-Markovian dissipa- tion and decoherence being fully taken into account. In applications, we utilize the theory to specific quantum transport systems, a variety of quantum decoherence and quantum transport phenomena involving the non-Markovian memory effect are investigated in both transient and stationary scenarios at arbitrary initial temperatures of the contacts.

Wave-function approach to Master equations for quantum transport and measurement

This paper presents a comprehensive review of the wave-flmction approach for derivation of the number- resolved Master equations, used for description of transport and measurement in mesoseopie systems. The review contains important amendments, clarifying subtle points in derivation of the Master equa- tions and their validity. This completes the earlier works on the subject. It is demonstrated that the derivation does not assume weak coupling with the environment and reservoirs, but needs only high bias condition. This condition is very essential for validity of the Markovian Master equations, widely used for a phenomenological description of different physical processes.

On a tilted Liouville-master equation of open quantum systems

A tilted Liouville-master equation in Hilbert space is presented for Markovian open quantum systems.We demonstrate that it is the unraveling of the tilted quantum master equation.The latter is widely used in the analysis and calculations of stochastic thermodynamic quantities in quantum stochastic thermodynamics.

Quantum speed limit of a single atom in a squeezed optical cavity mode

We theoretically study the quantum speed limit of a single atom trapped in a Fabry-Perot microresonator.The cavity mode will be squeezed when a driving laser is applied to the second-order nonlinear medium,and the effective Hamiltonian can be obtained under the Bogoliubov squeezing transformation.The analytical expression of the evolved atom state can be obtained by using the non-Hermitian Schr¨odinger equation for the initial excited state,and the quantum speed limit time coincides very well for both the analytical expression and the master equation method.From the perspective of quantum speed limit,it is more conducive to accelerate the evolution of the quantum state for the large detuning,strong driving,and coupling strength.For the case of the initial superposition state,the form of the initial state has more influence on the evolution speed.The quantum speed limit time is not only dependent on the system parameters but also determined by the initial state.

Quantum exceptional points of non-Hermitian Hamiltonian and Liouvillian in dissipative quantum Rabi model

The open quantum system can be described by either a Lindblad master equation or a non-Hermitian Hamiltonian(NHH).However,these two descriptions usually have different exceptional points(EPs),associated with the degeneracies in the open quantum system.Here,considering a dissipative quantum Rabi model,we study the spectral features of EPs in these two descriptions and explore their connections.We find that,although the EPs in these two descriptions are usually different,the EPs of NHH will be consistent with the EPs of master equation in the weak coupling regime.Further,we find that the quantum Fisher information(QFI),which measures the statistical distance between quantum states,can be used as a signature for the appearance of EPs.Our study may give a theoretical guidance for exploring the properties of EPs in open quantum systems.

A fluctuation theorem for Floquet quantum master equations

We present a fluctuation theorem for Floquet quantum master equations. This is a detailed version of the famous Gallavotti–Cohen theorem. In contrast to the latter theorem, which involves the probability distribution of the total heat current, the former involves the joint probability distribution of positive and negative heat currents and can be used to derive the latter. A quantum two-level system driven by a periodic external field is used to verify this result.

偏二甲肼分解及NO_(2)脱氢反应速率常数计算

针对偏二甲肼与N_(2)O_(4)化学反应动力学模型的不准确问题,开展了关键反应的高精度量子化学计算。首先,基于从头算方法,开展了偏二甲肼单分子分解及NO_(2)脱氢反应速率常数计算,利用CCSD(T)/cc-pVTZ//B2PLYPD3/6-311++G(d,p)计算级别得到反应体系的势能面;接着,采用多参考态方法和CASPT2/CBS//CASPT2/cc-pVTZ计算级别,修正了无势垒反应的势能面;最后,通过气相单分子反应理论/主方程理论求解温度和压力相关的速率常数,采用变分过渡态理论求解无势垒反应的速率常数。数值结果表明:计算得到的速率常数与实验结果吻合良好,得到的生成焓与活性热化学表及NIST数据库的结果相差不超过4.18 kJ·mol^(-1),熵相差不超过2.09 J·K^(-1)·mol^(-1);偏二甲肼分解的主要反应通道为CH_(3)+CH_(3)NNH_(2)及NH_(2)+CH_(3)NCH_(3),NO_(2)脱氢的关键反应通道为CH_(3)(CH_(2))NNH_(2)+HONO;对于低势垒和无势垒反应,相较于传统过渡态理论,变分过渡态理论能够更准确地计算出所有速率常数,并同时给出其在不同压力和温度下的不确定度。研究结果可为火箭发动机燃烧室的数值模拟提供理论支撑。

Tunneling Electrons Triggered Energy Transfer between Coherently Coupled Donor-Acceptor Molecules

Energy transfer is ubiquitous in natural and artificial lightharvesting systems,and coherent energy transfer,a highly efficient energy transfer process,has been accepted to play a vital role in such systems.However,the energy oscillation of coherent energy transfer is exceedingly difficult to capture because of its evanescence due to the interaction with a thermal environment.Here a microscopic quantum model is used to study the time evolution of electrons triggered energy transfer between coherently coupled donoracceptor molecules in scanning tunneling microscope(STM).A series of topics in the plasmonic nanocavity(PNC)coupled donor-acceptor molecules system are discussed,including resonant and nonresonant coherent energy transfer,dephasing assisted energy transfer,PNC coupling strength dependent energy transfer,Fano resonance of coherently coupled donor-acceptor molecules,and polariton-mediated energy transfer.

三端自旋交换耦合双量子点体系的热流特性

运用量子主方程方法,研究了三端自旋交换耦合双量子点体系的热流和电流随偏压的变化行为.在电子交换作用为铁磁情况下,偏压较低时两电极量子点的电流和热流出现阻塞现象,这是由于电极的电子费米能低于跃迁量子点多体态之间的能量差.高偏压时,所有输运通道完全打开,电流到达一个平台,但是热流随偏压增加呈线性增长行为.与此不同的是,反铁磁情况下没有出现阻塞现象,因为此时主导输运的跃迁通道能级差较小,更容易产生电流并且到达平台所需的偏压较低.这些结果可以为设计基于量子点的热流器件提供理论依据.

Perturbative Treatment for Stationary State of Local Master Equation

The local approach to construct master equation for a composite open system with a weak internal coupling is simple and seems reasonable. However, it is thermodynamic consistent only when the subsystems are resonantly coupled. Efforts are being made to understand the inconsistency and test the validity of the local master equation. We present a perturbative method to solve the steady-state solutions of linear local master equations, which are demonstrated by two simple models. The solving process shows the stationary state as the result of competition between incoherent operations and the unitary creating quantum coherence, and consequently relate quantum coherence with thermodynamic consistency.

Non-Markovian Master Equation for Distant Resonators Embedded in a One-Dimensional Waveguide

We develop a master equation approach to describe the dynamics of distant resonators coupled through a one-dimensional waveguide. Our method takes into account the back-actions of the reservoirs, and enables us to calculate the exact dynamics of the complete system at all times. We show that such system can cause nonexponential and long-lived photon decay due to the existence of a relaxation effect. The physical origin of non-Markovianity in our model system is the finite propagation speed resulting in time delays in communication between the nodes, and strong decay rate of the emitters into the waveguide. When the distance satisfies the standing wave condition, we find that when the time delay is increased, the dark modes formation is no longer perfect, and the average photon number of dark mode decreases in steady time limit.

在任意温度的热库中量子位的消相干

本文在Ｍａｒｋｏｖ 近似下推导了在任意温度的热库中，一个量子位（ｑｕｂｉｔ）的主方程，并由此讨论了由于振幅阻尼而引起的量子位消相干（ｄｅｃｏｈｅｒｅｎｃｅ）． 结论表明量子位的跃迁频率与热库的特征频率及截止频率的关系对消相干有明显的影响．

与库相互作用的非耦合两比特系统量子失协动力学

推导出一个关于X结构密度矩阵的量子失协表达式。在单一激发下,给出两个非耦合的量子比特分别与库相互作用构成系统的动力学的精确解,用非马尔科夫主方程方法精确求解了这个系统的耗散动力学。在失谐光谱密度下,讨论和比较不同耦合区域内系统的量子失协动力学特征。结果表明:量子失协表达式适用于任意有X型密度矩阵的物理系统,在失谐光谱密度下,证实两类主方程分别适用于不同的耦合区域。这将为以后更加简便地计算量子失协,以及在不同的耦合区域运用哪一类主方程提供一定的参考依据。