C. F. Huang, K. -N. Huang
By extending the mean-field Hamiltonian to include nonhermitian operators, the master equations for fermions and bosons can be derived. The derived equations reduce to the Markoff master equation in the low-density limit and to the quasiclassical master equation for homogeneuos systems.
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Relativistic model of spontaneous wave-function localization induced by nonHermitian colored noise
本文基于随机非厄米作用量发展相对论量子场论，通过带纯虚数项的狄拉克作用量耦合费米子密度算符与普适有色噪声，推导波包定域化长度并发现其随可观测宇宙增大而减小，为相对论自发波函数坍缩提供潜在框架。
A general master equation for eigenstates of Janus Faced commutation relations is constructed.
We show that integro-differential generalized Langevin and non-Markovian master equations can be transformed into larger sets of ordinary differential equations. .On the basis of this transformation we develop a numerical method for solving such integro-differential equations. Physically motivated example calculations are performed to demonstrate the accuracy and convergence of the method.
Exact non-Markovian master equations: a generalized derivation for Gaussian systems
本文提出了一种适用于玻色子和费米子体系的精确非马尔可夫主方程，通过高斯环境相关函数结构，实现了对开放量子系统动力学的精确计算。
The Monte Carlo wave function method or the quantum trajectory/jump approach is a powerful tool to study dissipative dynamics governed by the Markovian master equation, in particular for high-dimensional systems and when it is difficult to simulate directly. In this paper, we extend this method to the non-Markovian case described by the generalized Lindblad master equation. Two examples to illustrate the method are presented and discussed. The results show that the method can correctly reproduce the dissipative dynamics for the system. The difference between this method and the traditional Mar…
Recently a generalized master equation was derived that extends the Lindblad theory to highly non-Markovian quantum processes (H.-P. Breuer, Phys. Rev. A \textbf{75}, 022103 (2007)). We perform a stochastic unravelling of this master equation by considering $n$ random state vectors that satisfy the corresponding stochastic differential equation for a piecewise deterministic process. As an application we consider a two-state system randomly coupled to an environment consisting of two energy bands with finite number of levels. Our numerical results are compared to results obtained from the time-…
Dissipatons as generalized Brownian particles for open quantum systems: Dissipaton-embedded quantum master equation
本文重新审视耗散子理论，建立了等价的耗散子嵌入量子主方程（DQME），将耗散子视为广义布朗粒子，为研究开放量子系统中耗散子及混合浴模式的统计特性提供了直接方法。
The time-convolutionless (TCL) quantum master equation provides a powerful tool to simulate reduced dynamics of a quantum system coupled to a bath. The key quantity in the TCL master equation is the so-called kernel or generator, which describes effects of the bath degrees of freedom. Since the exact TCL generators are usually hard to calculate analytically, most applications of the TCL generalized master equation have relied on approximate generators using second and fourth order perturbative expansions. By using the hierarchical equation of motion (HEOM) and extended HEOM methods, we present…
In the preceding paper arXiv:0802.3252 [quant-ph] we treated a model given by a master equation with generalized Lindblad form, and examined the algebraic structure related to some Lie algebras and constructed an approximate solution. In this paper we apply a unitary transformation by the squeezing operator to the master equation. Then the generalized Lindblad form is tranformed to the usual Lindblad one, while the (original) Hamiltonian is tranformed to somewhat complicated one. As a result we have two different representations based on the Lie algebra su(1,1). We examine new algebraic struct…
The quantum damped harmonic oscillator is described by the master equation with usual Lindblad form. The equation has been solved completely by us in arXiv : 0710.2724 [quant-ph]. To construct the general solution a few facts of representation theory based on the Lie algebra $su(1,1)$ were used. In this paper we treat a general model described by a master equation with generalized Lindblad form. Then we examine the algebraic structure related to some Lie algebras and construct the interesting approximate solution.
We provide a general construction of quantum generalized master equations with memory kernel leading to well defined, that is completely positive and trace preserving, time evolutions. The approach builds on an operator generalization of memory kernels appearing in the description of non-Markovian classical processes, and puts into evidence the non uniqueness of the relationship arising due to the typical quantum issue of operator ordering. The approach provides a physical interpretation of the structure of the kernels, and its connection with the classical viewpoint allows for a trajectory de…
The non-Markovian master equation for open quantum systems is obtained by generalization of the ordinary Zwanzig-Nakajima (ZN) projection technique. To this end, a coupled chain of equations for the reduced density matrices of the bath $\varrho_{B}(t)$ and the system $\varrho_{S}(t)$ are written down. A formal solution of the equation for $\varrho_{B}(t)$, having been inserted in the equation for the reduced density matrix of the system, in the 2-nd approximation in interaction yields a very specific extra term in the generalized master equation. This term, being nonlinear in $\varrho_{S}(t)$,…
The measurement-induced phase transition (MIPT) occurs when the system is evolving under unitary evolution together with local measurements followed by post-selection. We propose a generalized version of the Lindblad master equation as a continuous equation, to describe the dynamics of second Rényi entropy in the MIPT. This generalized Lindblad equation explicitly takes into account the post-selection in the MIPT, which is realized as the Einstein-Podolsky-Rosen (EPR) state projection in the equation. Also, this generalized Lindblad equation preserves the Hermitian, unit trace, and positive de…
A generalization of the stochastic wave function method is presented which allows the unravelling of arbitrary linear quantum master equations which are not necessarily in Lindblad form and, moreover, the explicit treatment of memory effects by employing the time-convolutionless projection operator technique. The crucial point of this construction is the description of the open system in a doubled Hilbert space, which has already been successfully used for the computation of multitime correlation functions.
We propose a new form for the quantum master equation in the theory of open quantum systems. This new formalism allows one to describe the dynamics of two-level systems moving along different hyperbolic trajectories with distinct proper times. In the Born-Markov approximation, we consider a quantum massless scalar field coupled with two-level systems. Starting from a separable state we show the emergence of entanglement harvesting. For different proper accelerations we verify also the entanglement sudden death.
When deriving exact generalized master equations for the evolution of a reduced set of degrees of freedom, one is free to choose what quantities are relevant by specifying projection operators. However, obtaining a reduced description does not always need to be achieved through projections--one can also use conservation laws for this purpose. Such an operation should be considered as distinct from any kind of projection; that is, projection onto a single observable yields a different form of master equation compared to that resulting from a projection followed by the application of a constrain…
Generalized master equation for driven quantum oscillators: microscopic origin of nonlinear dissipation and asymmetric resonances
本文提出了一种广义Caldeira-Leggett主方程，用于描述驱动非线性量子振子的非线性耗散和非对称共振现象，通过保留完整非线性和时间依赖的系统动力学，建立了微观框架。
A generalized master equation (GME) governing quantum evolution of modular exciton density (MED) is derived for large scale light harvesting systems composed of weakly interacting modules of multiple chromophores. The GME-MED offers a practical framework to incorporate real time coherent quantum dynamics calculations at small length scales into dynamics over large length scales, without assumptions of time scale separation or specific forms of intra-module quantum dynamics. A test of the GME-MED for four sites of the Fenna-Matthews-Olson complex demonstrates how coherent dynamics of excitonic …
A quantum master equation is obtained for identical fermions by including a relaxation term in addition to the mean-field Hamiltonian. [Huang C F and Huang K N 2004 Chinese J. Phys. ${\bf 42}$ 221; Gebauer R and Car R 2004 Phys. Rev. B ${\bf 70}$ 125324] It is proven in this paper that both the positivity and Pauli's exclusion principle are preserved under this equation when there exists an upper bound for the transition rate. Such an equation can be generalized to model BCS-type quasiparticles, and is reduced to a Markoff master equation of Lindblad form in the low-density limit with respect …
The generalized quantum master equation (GQME) approach provides a rigorous framework for deriving the exact equation of motion for any subset of electronic reduced density matrix elements (e.g., the diagonal elements). In the context of electronic dynamics, the memory kernel and inhomogeneous term of the GQME introduce the implicit coupling to nuclear motion or dynamics of electronic density matrix elements that are projected out (e.g., the off-diagonal elements), allowing for efficient quantum dynamics simulations. Here, we focus on benchmark quantum simulations of electronic dynamics in a s…
In the context of a charge qubit under continuous monitoring by a single electron transistor, we propose an unraveling of the generalized quantum Markovian master equation into an ensemble of individual quantum trajectories for stochastic point process. A suboptimal feedback algorism is implemented into individual quantum trajectories to protect a desired pure state. Coherent oscillations of the charge qubit could be maintained in principle for an arbitrarily long time in case of sufficient feedback strength. The effectiveness of the feedback control is also reflected in the detector's noise s…
Recursive perturbation approach to time-convolutionless master equations: Explicit construction of generalized Lindblad generators for arbitrary open systems
本文发展了一种递归微扰展开方法，将开放量子系统的时间卷积无（TCL）生成元表示为广义Lindblad形式，并在任意阶保持Lindblad-like结构，同时满足最小耗散条件，显式计算至四阶以验证其对非马尔可夫动力学和强耦合效应的有效性。
Generalized quantum master equation from memory kernel coupling theory
提出张量扩展的记忆核耦合理论（MKCT），通过将标量形式提升为张量框架，高效计算开放量子系统的非马尔可夫动力学，包括期望值、关联函数，并在自旋-玻色子模型、Fenna-Matthews-Olson复合物和晶格模型中验证了其准确性和效率。
The formalism of the generalized quantum master equation (GQME) is an effective tool to simultaneously increase the accuracy and the efficiency of quasiclassical trajectory methods in the simulation of nonadiabatic quantum dynamics. The GQME expresses correlation functions in terms of a non-Markovian equation of motion, involving memory kernels which are typically fast-decaying and can therefore be computed by short-time quasiclassical trajectories. In this paper we study the approximate solution of the GQME, obtained by calculating the kernels with two methods, namely Ehrenfest mean-field the…
Engineering classical capacity of generalized Pauli channels with admissible memory kernels
该研究分析记忆核主方程生成的广义Pauli信道经典容量，发现调控核参数可使非局域噪声演化的动力学映射容量高于纯马尔可夫演化，并给出量子比特和qutrit示例，且该现象未在时间局域主方程中出现。
A general approach for transitionless quantum driving in open quantum systems is introduced. Under the assumption of adiabatic evolution for time-local master equations, we derive the generalized transitionless Lindbladian required to implement a shortcut to adiabaticity in an open system scenario. The general counter-diabatic Lindbladian obtained accounts for a phase freedom, which translates into a set of free parameters throughout the dynamics. We then discuss how our generalized approach allows us to recover the transitionless Lindbladian introduced by G. Vacanti et al. [New J. Phys. 16, 0…
How to improve the accuracy of semiclassical and quasiclassical dynamics with and without generalized quantum master equations
通过短时分析揭示半经典动力学精度提升机制，发现左手时间导数可延迟误差但导致长时不稳定性，提出记忆核截断协议以兼顾短时精度与长时稳定。
The "correlated-projection technique" has been successfully applied to derive a large class of highly non Markovian dynamics, the so called non Markovian generalized Lindblad type equations or Lindblad rate equations. In this article, general unravellings are presented for these equations, described in terms of jump-diffusion stochastic differential equations for wave functions. We show also that the proposed unravelling can be interpreted in terms of measurements continuous in time, but with some conceptual restrictions. The main point in the measurement interpretation is that the structure i…
We show that the exact master equation incorporating initial correlations for open quantum systems, within the Nakajima-Zwanzig operator-projection method, is a homegenous master equation for the reduced density matrix. We also derive explicitly the exact master equation for a large class of bosonic and fermionic open quantum systems incorporating initial correlations, the resulting master equation is homogenous. We find that the effects of the initial correlations can be fully embedded into the fluctuation dynamics through the exact homogenous master equation. Also a generalized nonequilibriu…
In this paper, we generalize the quantum Brownian motion to include momentum-dependent system-environment couplings. The conventional QBM model corresponds to the spacial case $W_k = V_k$. The generalized QBM is more complicated but the generalization is necessary. This is because the particle transition and the pair production between the system and the environment represent two very different physical processes, and usually cannot have the same coupling strengths. Thus, the conventional QBM model, which is well-defined at classical level, is hardly realized in real quantum physical world. We…
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。
Generalized Dicke model and gauge-invariant master equations for two atoms in ultrastrongly-coupled cavity quantum electrodynamics
本文提出超强耦合腔量子电动力学中两不同原子的广义Dicke模型，采用规范不变主方程确保多极与Coulomb规范结果一致，揭示了复杂耦合效应、额外共振及反交叉光谱特征。
Generalized quantum master equations can improve the accuracy of semiclassical predictions of multitime correlation functions
针对多时间量子关联函数精确模拟成本高、半经典方法准确性差的问题，研究结合半经典记忆核精度提升公式与多时间GQME，首次提出多时间半经典GQME，可提升Ehrenfest动力学精度并实现数量级效率提升。
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。
We develop a scattering theory to investigate the multi-photon transmission in a one-dimensional waveguide in the presence of quantum emitters. It is based on a path integral formalism, uses displacement transformations, and does not require the Markov approximation. We obtain the full time-evolution of the global system, including the emitters and the photonic field. Our theory allows us to compute the transition amplitude between arbitrary initial and final states, as well as the S-matrix of the asymptotic in- and out- states. For the case of few incident photons in the waveguide, we also re…
Generalized master equations valid for the third order response of an optically driven multi-level electronic system are derived within Zwanzig projection formalism. Each of three time intervals of the response function is found to require specific master equation and projection operator. Exact cumulant response functions for the harmonic profiles of the potential energy surfaces leading to Gaussian spectral diffusion are reproduced. The proposed method accounts for the nonequilibrium state of bath at the border of intervals, and can be used to improve calculations of ultrafast non-linear spec…
Double-Bracket Master Equations: Phase-Space Representation and Classical Limit
本文通过Wigner-Weyl变换和Moyal括号形式，系统推导了双括号耗散主方程的经典极限，并建立了量子与半经典框架下的梯度流表示，研究了谐振子与驱动非谐振子的半经典演化。
Invariant-based master equation applied to driven qutrit coupled to a bath and a leaky cavity
研究驱动开放N能级量子系统主方程，用基于Lewis-Riesenfeld不变量的广义方法，避免传统方法驱动强度限制，能统一多种主方程框架，还应用于量子点，为有耗散时的量子控制应用铺路。
Complete Positivity and Thermal Relaxation in Quadratic Quantum Master Equations
本文提出一种系统方法，通过广义布朗运动的正则量子化推导满足完全正定且保迹（CPTP）映射的量子主方程，并针对多体二次哈密顿量建立 CPTP 判据，以描述热弛豫过程并应用于网络模型等相互作用体系。
Space-local memory in generalized master equations: Reaching the thermodynamic limit for the cost of a small lattice simulation
提出利用时间和空间上的有限记忆来高效预测耗散晶格多体动力学的新方法，通过小晶格短时数据模拟任意大系统的长时演化，消除了有限尺寸效应并显著降低计算开销。
On the Discretization Error of the Discrete Generalized Quantum Master Equation
本文分析TTM的离散化结构，解释初始时刻虚假修正项的来源，建立其离散记忆核与连续NZ-QME核的一致关系，并经spin-boson模型验证收敛性。
In this paper we investigate the non-Markovian dynamics of a qubit by comparing two generalized master equations with memory. In the case of a thermal bath, we derive the solution of the post-Markovian master equation recently proposed in Ref. [A. Shabani and D.A. Lidar, Phys. Rev. A {\bf 71}, 020101(R) (2005)] and we study the dynamics for an exponentially decaying memory kernel. We compare the solution of the post-Markovian master equation with the solution of the typical memory kernel master equation. Our results lead to a new physical interpretation of the reservoir correlation function an…
We address the microscopic derivation of a quantum master equation in Lindblad form for the dynamics of a massive test particle with internal degrees of freedom interacting through collisions with a background ideal gas. When either internal or centre of mass degrees of freedom can be treated classically, previously established equations are obtained as special cases. If in an interferometric setup the internal degrees of freedom are not detected at the output, the equation can be recast in the form of a generalized Lindblad structure, which describes non-Markovian effects. The effect of inter…
Efficient formulation of multitime generalized quantum master equations: Taming the cost of simulating 2D spectra
针对四波混频光谱模拟成本高、多相互作用下GQME存在时间三次方标度的问题，提出基于离散卷积的高效多时间GQME表述，可粗化分辨率减少数据点，还能分解关联判断马尔可夫区制，实现短时间数据生成长时间光谱。
Heat transport in driven quantum systems: Comparison between the Floquet-Redfield equation and the master equation in the instantaneous eigenbasis
该研究结合主方程与Floquet方法，针对受驱动自旋玻色子模型，对比无近似的Floquet-Redfield方程与含近似的主方程在热输运研究中的结果，还讨论了相关绝热区，为热输运研究提供参考。
Simple master equations for describing driven systems subject to classical non-Markovian noise
提出基于广义累积展开的方法推导受经典非马尔可夫噪声驱动的量子系统的时间局域主方程，发现负退相干率和哈密顿重整化等特征，并在 Rabi 量子比特案例中验证了其比唯象主方程更准确。
We derive simple formulas connecting the generalized Wigner functions for $s$-ordering with the density matrix, and vice-versa. These formulas proved very useful for quantum mechanical applications, as, for example, for connecting master equations with Fokker-Planck equations, or for evaluating the quantum state from Monte Carlo simulations of Fokker-Planck equations, and finally for studying positivity of the generalized Wigner functions in the complex plane.
The quantum Zeno effect, in its original form, uses frequent projective measurements to freeze the evolution of a quantum system that is initially governed by a fixed Hamiltonian. We generalize this effect simultaneously in three directions by allowing open system dynamics, time-dependent evolution equations and general quantum operations in place of projective measurements. More precisely, we study Markovian master equations with bounded generators whose time dependence is Lipschitz continuous. Under a spectral gap condition on the quantum operation, we show how frequent measurements again fr…
We outline a non-perturbative approach for simulating the behavior of open quantum systems interacting with a bosonic environment defined by a generalized spectral density function. The method is based on replacing the environment by a set of damped harmonic oscillators - the pseudomodes - thereby forming an enlarged open system whose dynamics is governed by a Markovian master equation. Each pseudomode is connected to one of the poles of the spectral density when analytically continued to the lower-half complex frequency plane. Here, we extend previous results to a completely generic class of …
We prove a generalization of the quantum Markovian equation for observables. In this generalized equation, we use superoperators that are fractional powers of completely dissipative superoperators. We prove that the suggested superoperators are infinitesimal generators of completely positive semigroups and describe the properties of this semigroup. We solve the proposed fractional quantum Markovian equation for the harmonic oscillator with linear friction. A fractional power of the Markovian superoperator can be considered a parameter describing a measure of "screening" of the environment of t…
We introduce an alternative way to derive the generalized form of the master equation recently presented by J. P. Pekola et al. [Phys. Rev. Lett. 105, 030401 (2010)] for an adiabatically steered two-level quantum system interacting with a Markovian environment. The original derivation employed the effective Hamiltonian in the adiabatic basis with the standard interaction picture approach but without the usual secular approximation. Our approach is based on utilizing a master equation for a non-steered system in the first super-adiabatic basis. It is potentially efficient in obtaining higher-or…
We have studied the dynamics of a generalized toric code based on qudits at finite temperature by finding the master equation coupling the code's degrees of freedom to a thermal bath. As a consequence, we find that for qutrits new types of anyons and thermal processes appear that are forbidden for qubits. These include creation, annihilation and diffusion throughout the system code. It is possible to solve the master equation in a short-time regime and find expressions for the decay rates as a function of the dimension $d$ of the qudits. Although we provide an explicit proof that the system re…
We investigate generalized non-Markovian stochastic Schroeodinger equations (SSEs), driven by a multidimensional counting process and multidimensional Brownian motion introduced by A. Barchielli and C. Pellegrini [J. Math. Phys. 51, 112104 (2010)]. We show, that these SSEs can be translated in a non-linear form, which can be efficiently simulated. The simulation is illustrated by the model of a two-level system in a structured bath and the results of the simulations are compared with the exact solution of the generalized master equation.
We investigate the dynamics of open quantum systems which are initially correlated with their environment. The strategy of our approach is to analyze how given, fixed initial correlations modify the evolution of the open system with respect to the corresponding uncorrelated dynamical behavior with the same fixed initial environmental state, described by a completely positive dynamical map. We show that, for any predetermined initial correlations, one can introduce a linear dynamical map on the space of operators of the open system which acts like the proper dynamical map on the set of physical…
A field-biased quantum master equation and its Markovian limit
本文提出一个非平衡量子主方程，用于描述在持续电磁场作用下驱动的开放量子系统，探讨了场偏置噪声相关性和非马尔可夫动力学的机制。
A microscopic derivation of an open quantum walk on a two node graph is presented. It is shown that for the considered microscopic model of the system-bath interaction the resulting quantum master equation takes the form of a generalized master equation. The explicit form of the "quantum coin" operators is derived. The formalism is demonstrated for the example of a two-level system walking on a two-node graph.
The heating of trapped ions due to the interaction with a {\it quantized environment} is studied {\it without performing the Born-Markov approximation}. A generalized master equation local in time is derived and a novel theoretical approach to solve it analytically is proposed. Our master equation is in the Lindblad form with time dependent coefficients, thus allowing the simulation of the dynamics by means of the Monte Carlo Wave Function (MCWF) method.
Starting from a microscopic system-baths description, we derive the general conditions for a time-local quantum master equation (QME) to satisfy the first and second law of thermodynamics at the fluctuating level. Using counting statistics, we show that the fluctuating second law can be rephrased as a Generalized Quantum Detailed Balance condition (GQDB), i.e., a symmetry of the time-local generators which ensures the validity of the fluctuation theorem. When requiring in addition a strict system-bath energy conservation, the GQDB reduces to the usual notion of detailed balance which ensures Q…
Master equations are commonly used to describe time evolution of open systems. We introduce a general method for calculating a Markovian solution of the Nakajima-Zwanzig generalized master equation. We do so for a time dependent transport of interacting electrons through a complex nano scale system in a photon cavity. The central system, described by 120 many-body states in a Fock space, is weakly coupled to the external leads. The very diverse relaxation times of the open system, reflecting radiative or non-radiative transitions, require information about the time evolution through many order…
We investigate the spectral properties of an open interacting system by solving the Generalized Kadanoff-Baym Ansatz (GKBA) master equation for the single-particle density matrix, namely the time-diagonal lesser Green's function. To benchmark its validity, we compare the solution obtained within the GKBA with the solution of the Dyson equation (equivalently the full Kadanoff-Baym equations). In both approaches, we treat the interaction within the self-consistent second-order Born approximation, whereas the GKBA still retains the retarded propagator calculated at the Hartree-Fock level. We cons…
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