正P、Q和双相空间表示中的多时间相关性
Multi-time correlations in the positive-P, Q, and doubled phase-space representations
摘要：
对量子力学相空间表象中的多时间关联的计算，得到了一些物理上直观的结果。它们将时间相关的随机样本与多时间可观测量联系起来，并依赖于无导数算子恒等式的存在。特别是，表达式的时间有序正常有序的观测值的正P分布，取代海森堡算子与裸露的时间依赖的随机变量，确认扩展早期的结果为Glauber Sudarshan P.类似的表达式被发现的反正常有序的情况下，双相空间Q表示，以及双相空间S-有序表示之间的转换规则。后者被证明是很容易利用，以进一步计算反正常和混合有序的多时间观测值的正P，维格纳，双维格纳表示。哪些混合阶观测值是顺从的，哪些不是，并明确吻合给出了四阶。总的来说，相空间表示中的量子多时间观测量理论得到了扩展，允许对许多情况进行非微扰处理。的准确性，可用性和可扩展性的结果，以大型系统证明使用随机模拟的非常规光子封锁系统和相关的玻色-哈伯德链。此外，一个强大的，但简单的算法相空间样本的随机方程的积分。
英文摘要：
A number of physically intuitive results for the calculation of multi-time correlations in phase-space representations of quantum mechanics are obtained. They relate time-dependent stochastic samples to multi-time observables, and rely on the presence of derivative-free operator identities. In particular, expressions for time-ordered normal-ordered observables in the positive-P distribution are derived which replace Heisenberg operators with the bare time-dependent stochastic variables, confirming extension of earlier such results for the Glauber-Sudarshan P. Analogous expressions are found for the anti-normal-ordered case of the doubled phase-space Q representation, along with conversion rules among doubled phase-space s-ordered representations. The latter are then shown to be readily exploited to further calculate anti-normal and mixed-ordered multi-time observables in the positive-P, Wigner, and doubled-Wigner representations. Which mixed-order observables are amenable and which are not is indicated, and explicit tallies are given up to 4th order. Overall, the theory of quantum multi-time observables in phase-space representations is extended, allowing non-perturbative treatment of many cases. The accuracy, usability, and scalability of the results to large systems is demonstrated using stochastic simulations of the unconventional photon blockade system and a related Bose-Hubbard chain. In addition, a robust but simple algorithm for integration of stochastic equations for phase-space samples is provided.
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