用最大熵方法确定量子观测量的全统计量
Determination of the full statistics of quantum observables using the maximum entropy method
摘要：
描述非平衡态多粒子量子系统的数值方法，如运动方程方法，通常不能计算观测量的全部统计量，而只能计算其矩，如均值、方差和高阶矩。在这里，我们采用最大熵的方法来数值构造无偏统计量的基础上的知识的时刻。我们验证了所提出的方法的可行性，通过数值模拟的一个简单的生-死模型的量子点微腔激光器，其中全光子和载流子的统计数据可用于比较。我们表明，不仅构造的统计，而且计算的熵和拉格朗日乘子，这出现在这里作为副产品，提供了有价值的洞察所考虑的系统的物理。例如，熵揭示了与常识相反，微腔激光器在阈值以上的光子统计更好地由高斯分布而不是泊松分布来描述。我们的方法是通用的，可以应用到物理学和相关领域中出现的许多其他系统。
英文摘要：
Numerical methods for the description of nonequilibrium many-particle quantum systems such as equation of motion techniques often cannot compute the full statistics of observables but only moments of it, such as mean, variance and higher-order moments. We employ here the maximum entropy method to numerically construct unbiased statistics based on the knowledge of moments. We verify the feasibility of the proposed method by numerical simulation of a simple birth-death model for quantum-dot-microcavity lasers, where the full photon and carrier statistics are available for comparison. We show that not only the constructed statistics but also the computed entropy and the Lagrange multipliers, which appear here as a byproduct, provide valuable insight into the physics of the considered system. For example, the entropy reveals that, in contrast to common wisdom, the photon statistics of the microcavity laser above threshold is better described by a Gaussian distribution than by a Poisson distribution. Our approach is general and can be applied to many other systems emerging in physics and related fields.
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