标题： 有限温度下圆锥空间中带有圆形边缘的费米电荷和电流密度 显示英文标题

标题： Finite temperature fermionic charge and current densities in conical space with a circular edge

摘要： 我们研究了在二维圆锥空间中，磁通量穿过的情况下，有限温度和边缘效应对于局域于该空间的具有质量的旋量场的电荷和电流密度的影响。 场算符通过袋子边界条件以及边界的法向量项前符号相反的条件被限制在一个与圆锥顶点同心的圆形边界上。 在二维空间中存在两种非等价的Clifford代数表示，分析分别针对实现这些表示的场进行。 圆形边界将圆锥空间分为两部分，称为内部（I-）区域和外部（E-）区域。 径向电流密度为零。 在一般化学势情况下，电荷和环向电流密度期望值中的边缘诱导贡献在两个区域中被明确分离。 它们是磁通量的周期函数，并且在磁通量和化学势符号同时改变时为奇函数。 在E-区域，所有旋量模式都是正则的，总电荷和电流密度是磁通量的连续函数。 在I-区域，相应的期望值在磁通量与通量量子之比为半整数时是不连续的。 2D费米子模型，在没有磁场的情况下对称于宇称和时间反演变换，结合了实现Clifford代数非等价表示的两个旋量场。 讨论了不同边界条件组合下单独场的总电荷和电流密度。 讨论了由二维狄拉克模型描述的石墨锥体中电子子系统的应用。 显示英文摘要

摘要： We study the finite temperature and edge induced effects on the charge and current densities for a massive spinor field localized on a 2D conical space threaded by a magnetic flux. The field operator is constrained on a circular boundary, concentric with the cone apex, by the bag boundary condition and by the condition with the opposite sign in front of the term containing the normal to the edge. In two-dimensional spaces there exist two inequivalent representations of the Clifford algebra and the analysis is presented for both the fields realizing those representations. The circular boundary divides the conical space into two parts, referred as interior (I-) and exterior (E-) regions. The radial current density vanishes. The edge induced contributions in the expectation values of the charge and azimuthal current densities are explicitly separated in the both regions for the general case of the chemical potential. They are periodic functions of the magnetic flux and odd functions under the simultaneous change of the signs of magnetic flux and chemical potential. In the E-region all the spinorial modes are regular and the total charge and current densities are continuous functions of the magnetic flux. In the I-region the corresponding expectation values are discontinuous at half-integer values of the ratio of the magnetic flux to the flux quantum. 2D fermionic models, symmetric under the parity and time-reversal transformations (in the absence of magnetic fields) combine two spinor fields realizing the inequivalent representations of the Clifford algebra. The total charge and current densities in those models are discussed for different combinations of the boundary conditions for separate fields. Applications are discussed for electronic subsystem in graphitic cones described by the 2D Dirac model.