We study a concrete model of a confined particle in form of a Schrödinger operator with a compactly supported smooth potential coupled to a bosonic field at positive temperature. We show, that the model exhibits thermal ionization for any positive temperature, provided the coupling is sufficiently small. Mathematically, one has to rule out that zero is an eigenvalue of the self-adjoint generator of time evolution—the Liouvillian. This will be done by using positive commutator methods with dilations in the space of scattering functions. Our proof relies on a spatial cutoff in the coupling but does otherwise not require any unnatural restrictions.

中文翻译：

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短程电势的热电离

我们研究了薛定谔算子形式的受限粒子的具体模型，该算子具有紧密支撑的光滑势，耦合到正温度下的玻色子场。我们表明，该模型在任何正温度下都表现出热电离，前提是耦合足够小。在数学上，我们必须排除零是时间演化的自伴随生成元——刘维良的特征值。这将通过在散射函数空间中使用具有膨胀的正换向器方法来完成。我们的证明依赖于耦合中的空间截止，但不需要任何不自然的限制。