论文标题
异常效应方程的路径积分衍生
A path integral derivation of the equations of anomalous Hall effect
论文作者
论文摘要
A path integral (Lagrangian formalism) is used to derive the effective equations of motion of the anomalous Hall effect with Berry's phase on the basis of the adiabatic condition $|E_{n\pm1}-E_{n}|\gg 2π\hbar/T$, where $T$ is the typical time scale of the slower system and $E_{n}$ is the energy level of the fast system. 在传统的定义中，具有$ t \ rightArrow {\ rm大} $和固定能量特征值的绝热状况，除了启动的规定换向器外，Bjorken-Johnson-low处方均未定义较慢的变量的换向关系。另一方面，在一个单数极限$ | e_ {n \ pm1} -e_ {n} | \ rightArrow \ rightArrow \ infty $带有特定的$ e_ {n} $保持固定的固定的固定的较慢变量的任何动作$ x_ {k {k} $都可以予以治疗，以供无效的动态系统效果，并效果出现，并效果出现，并效果出现，并符合供应和遗产。在基于规范的换向关系的出生 - 上海痴呆症近似中，如果一个人使用辅助变量$ x_ {k}^{（n）} = x__ {k} = x_ {k}+{k}+{\ cal a}^（n）}^{k k} _ { a}^{（n）} _ {k} $在没有电磁矢量电位$ ea_ {k}（x）$的情况下，因此没有nernst效果。结果表明，与Berry的连接相关的量规对称性以及电磁矢量电位$ EA_ {K}（X）$在规范的Hamiltonian形式主义中是不兼容的。具有NERNST效果的非经典动力系统的出现是量子原理变形以结合两个不兼容的仪表对称性的结果。
A path integral (Lagrangian formalism) is used to derive the effective equations of motion of the anomalous Hall effect with Berry's phase on the basis of the adiabatic condition $|E_{n\pm1}-E_{n}|\gg 2π\hbar/T$, where $T$ is the typical time scale of the slower system and $E_{n}$ is the energy level of the fast system. In the conventional definition of the adiabatic condition with $T\rightarrow {\rm large}$ and fixed energy eigenvalues, no commutation relations are defined for slower variables by the Bjorken-Johnson-Low prescription except for the starting canonical commutators. On the other hand, in a singular limit $|E_{n\pm1}-E_{n}|\rightarrow \infty$ with specific $E_{n}$ kept fixed for which any motions of the slower variables $X_{k}$ can be treated to be adiabatic, the non-canonical dynamical system with deformed commutators and the Nernst effect appear. In the Born-Oppenheimer approximation based on the canonical commutation relations, the equations of motion of the anomalous Hall effect is obtained if one uses an auxiliary variable $X_{k}^{(n)}=X_{k}+{\cal A}^{(n)}_{k}$ with Berry's connection ${\cal A}^{(n)}_{k}$ in the absence of the electromagnetic vector potential $eA_{k}(X)$ and thus without the Nernst effect. It is shown that the gauge symmetries associated with Berry's connection and the electromagnetic vector potential $eA_{k}(X)$ are incompatible in the canonical Hamiltonian formalism. The appearance of the non-canonical dynamical system with the Nernst effect is a consequence of the deformation of the quantum principle to incorporate the two incompatible gauge symmetries.
