准晶的线性零模谱
Linear zero mode spectra for quasicrystals
摘要：
一个逆的是众所周知的事实，即超平面局部零模式的晶体棒关节框架产生的线或线的零模式（RUM）的频谱。这些连接激励定义的线性零模式谱，为非周期性的酒吧联合框架$G$，这是基于相对密集的线性本地化的弯曲。对于平面中的Delone框架，极限谱${\bf L}_{lim}(G, a)$以这种方式被定义为用于环境空间的参考基$a$的倒易空间的子集。还定义了一个更小的谱，即滑移谱${\bf L}_{slip}(G, a)$。在与规则的多重网格相关联的准晶双金属框架的情况下，在de Bruijn和Beenker的意义上，这些光谱重合，并根据$G$的几何形状确定。
英文摘要：
A converse is given to the well-known fact that a hyperplane localised zero mode of a crystallographic bar-joint framework gives rise to a line or lines in the zero mode (RUM) spectrum. These connections motivate definitions of linear zero mode spectra, for an aperiodic bar-joint framework $G$, that are based on relatively dense sets of linearly localised flexes. For a Delone framework in the plane the limit spectrum ${\bf L}_{lim}(G, a)$ is defined in this way, as a subset of the reciprocal space for a reference basis $a$ of the ambient space. A smaller spectrum, the slippage spectrum ${\bf L}_{slip}(G, a)$, is also defined. In the case of the quasicrystal parallelogram frameworks associated with regular multi-grids, in the sense of de Bruijn and Beenker, these spectra coincide and are determined in terms of the geometry of $G$.
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