Nakayama Yu, Nishida Yusuke
Department of Physics, Rikkyo University, Toshima, Tokyo 171-8501, Japan.
Department of Physics, Tokyo Institute of Technology, Ookayama, Meguro, Tokyo 152-8551, Japan.
Phys Rev E. 2021 Jan;103(1-1):012117. doi: 10.1103/PhysRevE.103.012117.
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.
在高于二维的维度中，由 Kardar-Parisi-Zhang（KPZ）方程控制的表面生长随着非线性的增加会经历从光滑相到粗糙相的粗化转变。还已知 KPZ 方程可以映射到具有接触相互作用的吸引玻色子的量子力学上，其中粗化转变对应于随着吸引力增加两个玻色子的束缚转变。三维中的这种临界玻色子实际上表现出埃菲莫夫效应，即在重整化群下，三玻色子耦合变得相关，从而将尺度不变性打破为离散的尺度不变性。基于这些将物理学中两个不同主题联系起来的事实，我们预测三维中的 KPZ 粗化转变要么表现出离散尺度不变性，要么不具有内在尺度不变性。
