We present a numerical analysis of the particle creation for a quantum fieldin the presence of time dependent boundary conditions. Having in mind recentexperiments involving superconducting circuits, we consider their descriptionin terms of a scalar field in a one dimensional cavity satisfying generalizedboundary conditions that involve a time-dependent linear combination of thefield and its spatial and time derivatives. We evaluate numerically theBogoliubov transformation between {\it in} and {\it out}-states and find thatthe rate of particle production strongly depends on whether the spectrum of theunperturbed cavity is equidistant or not, and also on the amplitude of thetemporal oscillations of the boundary conditions. We provide analyticjustifications for the different regimes found numerically.
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机译：我们提出了在存在时间依赖的边界条件的情况下为量子场创建粒子的数值分析。考虑到最近涉及超导电路的实验，我们考虑用满足广义边界条件的一维腔中的标量场的描述来描述它们，该条件涉及场的时间依赖线性组合及其空间和时间导数。我们对{\ it in}和{\ it out}状态之间的Bogoliubov变换进行了数值评估，发现粒子产生的速率强烈取决于未扰动腔的频谱是否等距，还取决于粒子的时间振荡幅度。边界条件。我们提供了在数值上发现的不同制度的分析论证。
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