论文标题
一些类似狄拉克的伪差异操作员的差距开口
Gap opening in the spectrum of some Dirac-like pseudo-differential operators
论文作者
论文摘要
在本文中，我们研究了一类二维周期性汉密尔顿人的光谱差距的开放，其中包括那些建模多层石墨烯。 hamiltonian的动力学部分由$σ\ cdot f（-i \ nabla）$给出，其中$σ$表示Pauli矩阵，$ f $是一个足够的常规矢量值函数，在Infinity和Infinity上成长为0。它的频谱是整个真实线。我们证明，根据$ f $的不同，在某些类别的周期性矩阵值值潜在电位中出现差距，我们研究了该差距如何取决于不同的参数。
In this paper, we study the opening of a spectral gap for a class of 2-dimensional periodic Hamiltonians which include those modelling multilayer graphene. The kinetic part of the Hamiltonian is given by $σ\cdot F(-i\nabla)$, where $σ$ denotes the Pauli matrices and $F$ is a sufficiently regular vector-valued function which equals 0 at the origin and grows at infinity. Its spectrum is the whole real line. We prove that a gap appears for perturbations in a certain class of periodic matrix-valued potentials depending on $F$, and we study how this gap depends on different parameters.
