本文将三次量子化方法推广到用4 n × 4 n矩阵对角化的方法统一精确地处理n个费米子二次系统的Redfield和Lindblad主方程。从Redfield方程出发，详细分析了非平衡热驱动。我们解释如何计算所有物理相关的量，如非平衡期望值的本地观测，各种熵或信息措施，或时间演化和性质的放松。我们还讨论了如何确切地处理显式时间相关的问题。然后，一般的形式主义，研究热驱动的开放XY自旋1/2链。我们发现，最近提出的非平衡量子相变在开放的XY链生存的Redfield模型内的热驱动。特别是，长程磁相关的相位可以通过非平衡稳态对外部（浴或体）参数的超敏性来表征。研究的热传输，我们发现足够强的热驱动的负热导，以及非单调依赖的热流浴耦合的强度。
英文摘要：
We generalize the method of third quantization to a unified exact treatment of Redfield and Lindblad master equations for open quadratic systems of n fermions in terms of diagonalization of 4n x 4n matrix. Non-equilibrium thermal driving in terms of the Redfield equation is analyzed in detail. We explain how to compute all physically relevant quantities, such as non-equilibrium expectation values of local observables, various entropies or information measures, or time evolution and properties of relaxation. We also discuss how to exactly treat explicitly time dependent problems. The general formalism is then applied to study a thermally driven open XY spin 1/2 chain. We find that recently proposed non-equilibrium quantum phase transition in the open XY chain survives the thermal driving within the Redfield model. In particular, the phase of long-range magnetic correlations can be characterized by hypersensitivity of the non-equilibrium-steady state to external (bath or bulk) parameters. Studying the heat transport we find negative thermal conductance for sufficiently strong thermal driving, as well as non-monotonic dependence of the heat current on the strength of the bath coupling.
A rapid restoration of the bath state is usually required to induce Markovian dynamics for an open quantum system, which typically can be realized only in limits such as weak system-bath coupling and infinitely large bath. In this work, we investigate the Markovianity of a qubit system coupled to a single-qubit bath with the qubit bath being continuously refreshed by quantum cooling. A surprising result is that there exists a finite threshold for the cooling rate at which the system transitions from non-Markovian dynamics to Markovian dynamics, which is in sharp contrast to the usual understan…
The concept of non-Markovianity in open quantum systems is traditionally associated with the existence of information backflows from the environment to the system. Meanwhile, the mechanisms through which such backflows emerge are still a subject of debate. In this work, we use collision models to study memory effects in the dynamics of a qubit system in contact with a thermal bath made up of few ancillas, in which system-ancilla and ancilla-ancilla interactions are considered. In the single-ancilla limit case, we show that the system-bath information flow exhibits an interesting mixture of cha…
An open quantum system in contact with an infinite bath approaches equilibrium, while the state of the bath remains unchanged. If the bath is finite, the open system still relaxes to equilibrium, but it induces a dynamical evolution of the bath state. In this work, we study the dynamics of open quantum systems in contact with finite baths. We obtain a hierarchy of master equations that improve their accuracy by including more dynamical information of the bath. For instance, as the least accurate but simplest description in the hierarchy we obtain the conventional Born-Markov-secular master equ…
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We investigate quantum synchronization and correlations of two qutrits in one non-Markovian environment using the hierarchy equation method. There is no direct interaction between two qutrits and each qutrit interacts with the same non-Markovian environment. The influence of the temperature of the bath, correlation time, and coupling strength between qutrits and bath on the quantum synchronzation and correlations of two qutrits are studied without the Markovian, Born, and rotating wave approximations. We also discuss the influence of dissipation and dephasing on the synchronization of two qutr…
An easily solvable quantum master equation has long been sought that takes into account memory effects induced on the system by the bath, i.e., non-Markovian effects. We briefly review the Post-Markovian master equation (PMME), which is relatively easy to solve, and analyze a simple example where solutions obtained exhibit non-Markovianity. We apply the distinguishability measure introduced by Breuer et al., and we also explicitly analyze the divisibility of the associated quantum dynamical maps. We give a mathematical condition on the memory kernel used in the PMME that guarantees non-CP-divi…
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 $\varrho_{S}(t)$,…
A quantum collision model (CM), also known as repeated interactions model, can be built from the standard microscopic framework where a system S is coupled to a white-noise bosonic bath under the rotating wave approximation, which typically results in Markovian dynamics. Here, we discuss how to generalize the CM construction to the case of frequency-dependent system-bath coupling, which defines a class of colored-noise baths. This leads to an intrinsically non-Markovian CM, where each ancilla (bath subunit) collides repeatedly with S at different steps. We discuss the illustrative example of a…
We study the non-Markovian quantum interference phenomenon of a multi-state atomic system coupled to a bosonic dissipative environment by using the exact master equations derived in this paper. Two examples involving four-level systems with or without external control fields are investigated. Our results show that non-Markovian master equations are capable of exhibiting quantum interference phenomena in a temporal domain that has not fully explored before. In particular, we show that the environmental memory is instrumental in the onset of non-Markovian quantum interference pattern in differen…
Engineering non-Markovianity from spectral shaping of bosonic and fermionic baths
Fudan University（复旦大学）；University of Science and Technology of China（中国科学技术大学）；Hefei National Laboratory（合肥国家实验室）；University of California San Diego（加利福尼亚大学圣迭戈分校）
