Surface growth governed by the Kardar-Parisi-Zhang (KPZ) equation in dimensions higher than two undergoes a roughening transition from smooth to rough phases with increasing the nonlinearity. It is also known that the KPZ equation can be mapped onto quantum mechanics of attractive bosons with a contact interaction, where the roughening transition corresponds to a binding transition of two bosons with increasing the attraction. Such critical bosons in three dimensions actually exhibit the Efimov effect, where a three-boson coupling turns out to be relevant under the renormalization group so as to break the scale invariance down to a discrete one. On the basis of these facts linking the two distinct subjects in physics, we predict that the KPZ roughening transition in three dimensions shows either the discrete scale invariance or no intrinsic scale invariance.

中文翻译：

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Karfid-Parisi-Zhang粗化过渡处的Efimov效应

由Kardar-Parisi-Zhang（KPZ）方程控制的尺寸大于2的表面生长会经历从平滑相到粗糙相的粗糙过渡，并增加了非线性。还已知KPZ方程可以通过接触相互作用映射到有吸引力的玻色子的量子力学上，其中粗糙化转变对应于两个玻色子随着吸引力的结合转变。这种在三维上的临界玻色子实际上表现出Efimov效应，在重归一化组中三玻色子耦合被证明是相关的，从而将尺度不变性分解为离散的。基于将物理学中两个不同学科联系在一起的这些事实，