论文标题
有限晶格的离散Wigner-Weyl微积分
Discrete Wigner-Weyl calculus for the finite lattice
论文作者
论文摘要
我们开发了Felix Buot对晶格模型构建Wigner-Weyl演算的方法。我们将这种方法应用于具有有限数量的晶格单元的紧密结合模型。为简单起见，我们将自己限制在矩形晶格的情况下。我们从运算符符号的原始Buot定义开始。纠正了该定义，以维持代数结构的自隔离。但是，当晶格尺寸趋于无穷大时，简单操作员的布特符号似乎没有规则的限制。因此，使用更密集的辅助晶格，我们修改了操作员的布特符号，以构建我们的新离散Weyl符号。后者服从从连续理论继承的几种有用的身份。此外，无限大的晶格的极限变得常规。我们使用拟议的操作员的Weyl符号为晶格模型制定了Keldysh技术。在该技术中，得出了二维非平衡和非均匀系统的电导率的简单表达。在较小的温度和较大的系统区域，这种表达在热平衡的极限中平滑接近拓扑。
We develop the approach of Felix Buot to construction of Wigner-Weyl calculus for the lattice models. We apply this approach to the tight-binding models with finite number of lattice cells. For simplicity we restrict ourselves to the case of rectangular lattice. We start from the original Buot definition of the symbol of operator. This definition is corrected in order to maintain self-consistency of the algebraic constructions. It appears, however, that the Buot symbol for simple operators does not have a regular limit when the lattice size tends to infinity. Therefore, using a more dense auxiliary lattice we modify the Buot symbol of operator in order to build our new discrete Weyl symbol. The latter obeys several useful identities inherited from the continuum theory. Besides, the limit of infinitely large lattice becomes regular. We formulate Keldysh technique for the lattice models using the proposed Weyl symbols of operators. Within this technique the simple expression for the electric conductivity of a two dimensional non - equilibrium and non - homogeneous system is derived. This expression smoothly approaches the topological one in the limit of thermal equilibrium at small temperature and large system area.
