English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

A path integral (Lagrangian formalism) is used to derive the effectiveequations of motion of the anomalous Hall effect with Berry's phase on thebasis of the adiabatic condition $|E_{n\pm1}-E_{n}|\gg 2\pi\hbar/T$, where $T$is the typical time scale of the slower system and $E_{n}$ is the energy levelof the fast system.  In the conventional definition of the adiabatic condition with $T\rightarrow{\rm large}$ and fixed energy eigenvalues, no commutation relations are definedfor slower variables by the Bjorken-Johnson-Low prescription except for thestarting canonical commutators. On the other hand, in a singular limit$|E_{n\pm1}-E_{n}|\rightarrow \infty$ with specific $E_{n}$ kept fixed forwhich any motions of the slower variables $X_{k}$ can be treated to beadiabatic, the non-canonical dynamical system with deformed commutators and theNernst effect appear. In the Born-Oppenheimer approximation based on thecanonical commutation relations, the equations of motion of the anomalous Halleffect is obtained if one uses an auxiliary variable $X_{k}^{(n)}=X_{k}+{\calA}^{(n)}_{k}$ with Berry's connection ${\cal A}^{(n)}_{k}$ in the absence ofthe electromagnetic vector potential $eA_{k}(X)$ and thus without the Nernsteffect. It is shown that the gauge symmetries associated with Berry'sconnection and the electromagnetic vector potential $eA_{k}(X)$ areincompatible in the canonical Hamiltonian formalism. The appearance of thenon-canonical dynamical system with the Nernst effect is a consequence of thedeformation of the quantum principle to incorporate the two incompatible gaugesymmetries.

A path integral derivation of the equations of anomalous Hall effect