G. W. Ford, R. F. O'Connell
The low temperature solution of the exact master equation for an oscillator coupled to a linear passive heat bath is known to give rise to serious divergences. We now show that, even in the high temperature regime, problems also exist, notably the fact that the density matrix is not necessarily positive.
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A simple algebraic procedure is described for deriving Maxwell-Bloch-type equations from single-atom cavity quantum electrodynamics (cavity QED) master equations via orthogonal projection onto a manifold of semiclassical states. In particular the usual Maxwell-Bloch Equations are obtained--up to a state-dependent correction factor of order unity--straightforwardly from the unconditional Jaynes-Cummings master equation. The technique of projecting onto a semiclassical manifold can also be applied with conditional master equations (quantum filters), leading to stochastic simulation models that i…
Making Non-Markovian master equations accessible with approximate environments
研究开放量子系统非马尔可夫动力学模拟难题，核心方法是将环境关联函数表示为阻尼正弦波之和，主要贡献是降低计算成本、简化兰姆移位修正计算，在弱耦合 regime 精度与数值精确方法相当，简化加速了模拟。
Nonequilibrium energy transport in driven-dissipative quantum systems
研究驱动耗散量子系统中非平衡能量输运问题，通过驱动量子主方程分析能量流动，验证其在 spin 和 boson 模型中的有效性，并探讨驱动相位对能量交换的影响。
A generalization of the stochastic wave function method to quantum master equations which are not in Lindblad form is developed. The proposed stochastic unravelling is based on a description of the reduced system in a doubled Hilbert space and it is shown, that this method is capable of simulating quantum master equations with negative transition rates. Non-Markovian effects in the reduced systems dynamics can be treated within this approach by employing the time-convolutionless projection operator technique. This ansatz yields a systematic perturbative expansion of the reduced systems dynamic…
A systematic first-order correction to the standard Markov master equation for open quantum systems interacting with a bosonic bath is presented. It extends the Markov Lindblad master equation to the more general case of non-Markovian evolution. The meaning and applications of our `post'-Markov master equation are illustrated with several examples, including a damped two-level atom, the spin-boson model and the quantum Brownian motion model. Limitations of the Markov approximation, the problem of positivity violation and initial slips are also discussed.
qdmag: A Python package for simulating nonequilibrium magnetization of molecules using quantum master equations
qdmag是一个Python包，通过求解广义Lindblad量子主方程模拟分子在时变磁场中的非平衡磁化，支持高阶自旋相互作用，并实现长时间演化，为自旋动力学研究提供计算工具。
The coarse-graining approach to deriving the quantum Markovian master equation is revisited, with close attention given to the underlying approximations. It is further argued that the time interval over which the coarse-graining is performed is a free parameter that can be given a physical measurement-based interpretation. In the case of the damping of composite systems to reservoirs of different temperatures, currently of much interest in the study of quantum thermal machines with regard to the validity of `local' and `global' forms of these equations, the coupling of the subsystems leads to …
Non-Markovian Second-Order Quantum Master Equation and Its Markovian Limit: Electronic Energy Transfer in Model Photosynthetic Systems
本研究提出求解二阶玻恩近似下非马尔可夫主方程的数值算法，分析了光合二聚体模型中马尔可夫与二阶近似的适用范围，给出解析判据并探究了初始相干性的影响。
Canonically consistent quantum master equation for proton-transfer reactions
本文基于CCQME方法研究TAA分子内质子转移，对比HEOM和Redfield理论，揭示Redfield在强耦合下偏离HEOM，而CCQME保持一致性。
We analyze and compare three different schemes that can be used to generate entanglement between spin qubits in optically-active single solid-state quantum systems. Each scheme is based on first generating entanglement between the spin degree of freedom and either the photon number, the time bin, or the polarization degree of freedom of photons emitted by the systems. We compute the time evolution of the entanglement generation process by decomposing the dynamics of a Markovian master equation into a set of propagation superoperators conditioned on the cumulative detector photon count. We then…
Quantum Markovian master equation in the high-temperature limit
该研究推导高温量子马尔可夫主方程（HTME），通过结合自旋哈密顿本征算子形式与统计系数线性展开得到推广ARH-IME的量子耗散项，纳入非热高阶初始态项，验证结果并揭示谱密度对称化条件，通过两个案例展示其有效性，挑战传统NMR理论边界。
Expansion of time-convolutionless non-Markovian quantum master equations: A case study using the Fano-Anderson model
本文通过Fano-Anderson模型探讨了时间无关投影算子技术的性能，分析了主方程展开在暂态和稳态行为中的表现，并讨论了TCL方法在开放量子系统中的优劣。
Capturing non-Markovian polaron dressing with the master equation formalism
本研究拓展了极化子主方程的适用范围，针对其难以刻画与极化子变换不对易可观测量的局限，引入Nakajima-Zwanzig投影算符修正项，在两个案例中验证了其在多时间尺度上的有效性。
Simulating Open Quantum System Dynamics on NISQ Computers with Generalized Quantum Master Equations
本文提出基于广义量子主方程的量子算法，通过Sz.-Nagy膨胀定理将非幺正传播子转化为高维幺正形式，在NISQ计算机上模拟开放量子系统动力学，并在自旋-玻色子模型上验证了其可靠性。
We first review the usefulness of the Wigner distribution functions (WDF), associated with Lindblad and pre-master equations, for analyzing a host of problems in Quantum Optics where dissipation plays a major role, an arena where weak coupling and long-time approximations are valid. However, we also show their limitations for the discussion of decoherence, which is generally a short-time phenomenon with decay rates typically much smaller than typical dissipative decay rates. We discuss two approaches to the problem both of which use a quantum Langevin equation (QLE) as a starting-point: (a) us…
Suppressed Energy Relaxation in the Quantum Rabi Model at the Critical Point
该研究推导了量子拉比模型在临界区域的修正主方程，发现临界点处因谱坍缩而几乎无能量弛豫，相位相干性消失，并揭示了退相干对相移估计精度的强烈限制。
We present the Born-Markov approximated Redfield quantum master equation (RQME) description for an open system of non-interacting particles (bosons or fermions) on an arbitrary lattice of $N$ sites in any dimension and weakly connected to multiple reservoirs at different temperatures and chemical potentials. The RQME can be reduced to the Lindblad equation, of various forms, by making further approximations. By studying the $N=2$ case, we show that RQME gives results which agree with exact analytical results for steady state properties and with exact numerics for time-dependent properties, ove…
The quantum collision models are a useful method to describe the dynamics of an open quantum system by means of repeated interactions between the system and some particles of the environment, which are usually termed "ancillas". In this paper, we review the main collision models for the dynamics of multipartite open quantum systems, which are composed of several subsystems. In particular, we are interested in models that are based on elementary collisions between the subsystems and the ancillas, and that simulate global and/or local Markovian master equations in the limit of infinitesimal time…
In a recent Letter, Guarnieri et al. [1] reported on the possibility of generating steady-state coherence (SSC) in the energy basis of a two-level system by the sole action of a single thermal bath also for weak system-bath coupling and due to a composite form of this interaction. The results are based on a time-local Bloch-Redfield master equation without secular approximation and the associated set of Bloch equations, all derived in the Supplemental Material (SM) of Ref. [1]. We comment that the results reported by the authors present both technical flaws and conceptual limitations that subs…
Partially polaron-transformed quantum master equation for exciton and charge transport dynamics
本文提出了一种部分极化子变换方法，用于解决极化子变换在描述电荷和激子传输动力学时出现的过度弛豫问题。
Path integral Lindblad master equation through transfer tensor method & the generalized quantum master equation
本文结合 Nakajima-Zwanzig 主方程与路径积分，提出可免费纳入经验 Lindblad 耗散时间尺度的数值精确非微扰方法，并用于 FMO 4 位点模型。
It is very common in the literature to write down a Markovian quantum master equation in Lindblad form to describe a system with multiple degrees of freedom and weakly connected to multiple thermal baths which can, in general, be at different temperatures and chemical potentials. However, the microscopically derived quantum master equation up to leading order in system-bath coupling is of the so-called Redfield form which is known to not preserve complete positivity in most cases. Additional approximations to the Redfield equation are required to obtain a Lindblad form. We lay down some fundam…
The study of open system quantum dynamics has been transformed by the hierarchical equations of motion (HEOM) method, which gives the exact dynamics for a system coupled to a harmonic bath at arbitrary temperature and system-bath coupling strength. However in its standard form the method is only consistent with the weak-coupling quantum master equation at all temperatures when many auxiliary density operators are included in the hierarchy, even when low temperature corrections are included. Here we propose a new low temperature correction scheme for the termination of the hierarchy based on Zw…
An efficient variational polaron master equation for non-Markovian spin-boson dynamics: Transformed initial states and general observables
本研究提出一种高效变分极化子主方程方法，通过变换初始态并引入非齐次项，准确描述非马尔可夫自旋-玻色子动力学，实现一般可观测量的统一处理，并揭示中等耦合下的延迟现象与相干叠加态的更强非平衡效应。
The continuous-time differential Lyapunov equation is widely used in linear optimal control theory, a branch of mathematics and engineering. In quantum physics, it is known to appear in Markovian descriptions of linear (quadratic Hamiltonian, linear equations of motion) open quantum systems, typically from quantum master equations. Despite this, the Lyapunov equation is seldom considered a fundamental formalism for linear open quantum systems. In this work we aim to change that. We establish the Lyapunov equation as a fundamental and efficient formalism for linear open quantum systems that can…
Local Non-Hermitian Hamiltonian Formalism for Dissipative Fermionic Systems and Loss-Induced Population Increase in Fermi Superfluids
本文提出局域非厄米哈密顿量形式论，以克服常规方案在耗散费米子系统中的不足，并揭示费米超流中损耗诱导的粒子数增加现象。
Limitations of the Markovian approximation in the harmonic oscillator
本文研究了两种典型单个阻尼谐振子模型中马尔可夫近似的局限性，揭示了其在经典极限、厄恩费斯特定理违反、正性破裂及热化行为异常等方面的问题，强调了非马尔可夫框架在开放量子动力学描述中的重要性。
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