The effect of anharmonicity (coupling) in the field theory generally results in dissipation of plane waves. It has been appreciated that anharmonicity and ensuing dissipation of plane waves can be accompanied by the emergence of the gapped momentum state. Here, we show that the same effect can lead to a gapped energy state and a dispersion relation where the frequency (energy) gap emerges explicitly. We discuss several notable properties of gapped energy and momentum states and connections between them.

中文翻译：

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耗散和能隙

场论中的非谐（耦合）效应通常会导致平面波的耗散。已经认识到，平面波的非谐性和随之而来的耗散可以伴随有间隙动量状态的出现。在这里，我们表明相同的效果可以导致有间隙的能量状态和频率（能量）间隙明确出现的色散关系。我们讨论了间隙能量和动量状态的几个显着特性以及它们之间的联系。