We investigate the dynamic Casimir effect (DCE) of a ( 1 + 1 )-dimensional free massless scalar field in a finite or semi-infinite cavity for which the boundary condition (BC) instantaneously changes from the Neumann to the Dirichlet BC or reversely. While this setup is motivated by the gravitational phenomena, such as the formation of strong naked singularities or wormholes, and the topology change of spacetimes or strings in quantum gravity, the analysis is quite general. For the Neumann-to-Dirichlet cases, we find two components of diverging flux emanate from the point where the BC changes. We carefully compare this result with that of Ishibashi and Hosoya (2002) obtained in the context of a quantum version of cosmic censorship hypothesis, and show that one of the diverging components was overlooked by them and is actually nonrenormalizable, suggesting to bring non-negligible backreaction or semiclassical instability. On the other hand, for the Dirichlet-to-Neumann cases, we reveal for the first time that only one component of diverging flux emanates, which is the same kind as that overlooked in the Neumann-to-Dirichlet cases. This result suggests not only the robustness of the appearance of diverging flux in instantaneous limits of DCE but also that the type of divergence sensitively depends on the combination of initial and final BCs.
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机译：我们研究了一个有限或半无限腔中（1 +1）维自由无质量标量场的动态卡西米尔效应（DCE），其边界条件（BC）瞬间从Neumann变为Dirichlet BC或反向变化。虽然这种设置是受重力现象（例如，强烈的裸奇点或虫洞的形成以及时空或量子引力的弦的拓扑结构变化）的影响，但分析还是很笼统的。对于Neumann-to-Dirichlet情况，我们发现从BC的变化点发散的两个通量分量。我们将这一结果与Ishibashi和Hosoya（2002）的结果进行了仔细比较，Ishibashi and Hosoya（2002）是在宇宙审查假说的量子版本的背景下获得的，表明这些差异成分之一被它们忽略了，并且实际上是不可归一化的，这表明带来的不可忽略性背反应或半经典不稳定。另一方面，对于Dirichlet-to-Neumann案例，我们首次揭示了发散通量中只有一个分量散发，这与Neumann-to-Dirichlet案例中忽略的分量相同。该结果不仅表明在DCE的瞬时极限中出现发散通量的鲁棒性，而且发散的类型敏感地取决于初始和最终BC的组合。
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