绝热粒子数的时间依赖性
On the Time Dependence of Adiabatic Particle Number
摘要：
我们认为量子场论系统的依赖于时间的扰动，并讨论的问题，定义一个依赖于时间的粒子数不仅在渐近的早期和晚期的时间，而且在扰动。对于这样一个非平衡过程，这并不是一个定义明确的概念，因为中间时刻的粒子数取决于粒子和反粒子定义的参考态的基础选择，尽管最终的后期粒子数与这个基础选择无关。基的选择与绝热膨胀的特定截断有关。绝热膨胀是发散的，我们表明，如果这种发散的膨胀截断在其最佳顺序，一个普遍的时间依赖性，得到确认丁格尔和贝瑞的一般结果。这个最佳截断粒子数提供了一个清晰的图片的量子干涉效应的扰动与非平凡的时间子结构。我们用几种绝热粒子数的等价定义来说明这些结果：Bogoliubov，Riccati，谱函数和薛定谔图像方法。在每一种方法中，粒子数都可以用与时间相关的振荡器的Ermakov-Milne方程的精确解和绝热解之间的微小偏差来表示。
英文摘要：
We consider quantum field theoretic systems subject to a time-dependent perturbation, and discuss the question of defining a time dependent particle number not just at asymptotic early and late times, but also during the perturbation. Naively, this is not a well-defined notion for such a non-equilibrium process, as the particle number at intermediate times depends on a basis choice of reference states with respect to which particles and anti-particles are defined, even though the final late-time particle number is independent of this basis choice. The basis choice is associated with a particular truncation of the adiabatic expansion. The adiabatic expansion is divergent, and we show that if this divergent expansion is truncated at its optimal order, a universal time dependence is obtained, confirming a general result of Dingle and Berry. This optimally truncated particle number provides a clear picture of quantum interference effects for perturbations with non-trivial temporal sub-structure. We illustrate these results using several equivalent definitions of adiabatic particle number: the Bogoliubov, Riccati, Spectral Function and Schrodinger picture approaches. In each approach, the particle number may be expressed in terms of the tiny deviations between the exact and adiabatic solutions of the Ermakov-Milne equation for the associated time-dependent oscillators.
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