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中国物理学会期刊

基于Keldysh场论的均匀耦合BCS模型的非平衡动力学

Nonequilibrium dynamics of a homogeneously coupled BCS model based on Keldysh field theory

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  • 量子配对体系在参数骤变后可形成不同于热平衡态的预热动力学相。本文利用Keldysh非平衡场论研究均匀耦合BCS系统淬火后的非平衡动力学,通过闭合路径积分和复辅助配对场构造有效作用量,在鞍点近似下导出自洽能隙方程,并利用Dyson方程推导出在平均场下描述配对动力学的类Bloch方程组,即动量模式占据数和配对振幅的实时演化方程。对具有双峰均匀能谱分布的体系在淬火后的动力学过程进行数值模拟,以序参量模长在预热化时间窗内的平均值和标准差判定动力学相。结果表明,体系可进入序参量衰减至零的动力学退相干相(相I)、趋于非零值的非热稳态相(相II)以及保持持续振荡的动力学振荡相(相III);振荡相还可按复序参量轨迹是否经过原点分为两类,其中经过原点的情形伴随约为π的相位跳变。数值相边界与Lax矢量解析结果一致。本文进一步建立了理论配对场与腔输出光场正交分量的对应关系,可由实验信号的幅度、相位和频谱特征识别动力学相,从而形成连接费米子微观演化、宏观动力学相和实验可观测量的统一场论描述。

     

    Quantum pairing systems subjected to a sudden parameter quench can exhibit long-lived prethermal dynamical phases that are distinct from thermal equilibrium states. We investigate the post-quench nonequilibrium dynamics of a Bardeen-Cooper-Schrieffer (BCS) model with homogeneous pairing interactions using Keldysh nonequilibrium field theory. Starting from the closed-time-path functional integral, we introduce a complex auxiliary pairing field to decouple the four-fermion interaction and derive the effective action. Within the saddle-point approximation, the stationarity condition yields the self-consistent time-dependent gap equation. Using the Dyson equation in Keldysh–Nambu space, we further obtain a closed set of Bloch-type mean-field equations for the real-time evolution of momentum-mode occupations and anomalous pairing amplitudes. For a single-particle spectrum consisting of two subbands with homogeneous density of states, the dynamical phases are identified from the long-time average and standard deviation of the order-parameter magnitude over a prethermal time window after the transient regime. Three prethermal phases are found: phase I, in which the macroscopic order parameter decays to zero through dephasing among different energy modes; phase II, in which it approaches a nonzero nonthermal plateau; and phase III, characterized by persistent collective oscillations. The oscillatory phase is further divided according to the trajectory of the complex order parameter. In phase IIIa, the trajectory does not cross the origin and the order-parameter magnitude remains finite, whereas in phase IIIb it periodically passes through the origin, producing zero crossings accompanied by phase jumps close to \pi. The numerical phase boundaries agree with the analytical Lax-vector results in the Anderson-pseudospin representation. We also establish the correspondence between the theoretical pairing field and experimentally measurable cavity-output quadratures. The amplitude, phase, and spectrum of the output signal provide operational signatures for distinguishing the dynamical phases. At the mean-field level, the same self-consistent dynamical structure applies to weakly interacting two-component Fermi gases in the BCS regime, while quantitative applications to the BCS-BEC crossover and the unitary regime require the inclusion of fluctuations and collision effects. These results provide a unified framework connecting microscopic fermionic evolution, macroscopic dynamical phases, and experimental observables.

     

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