Skyrmions in Condensed Matter by Jung Hoon Han

Author:Jung Hoon Han
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

(4.9)

The crucial assumption here is that time dependence arises solely from that of the vortex coordinates . With this ansatz, the first-order time derivative of the phase angle becomes , and the kinetic energy of the phase field in terms of the vortex velocity becomes

(4.10)

The integral gives the well-known logarithmic divergence (bounded by the linear dimension of the container L and the atomic spacing a), which carries over to the effective mass of a single vortex,

(4.11)

Starting from the Gross–Pitaevskii Lagrangian, we were able to work our way to deducing the kinetic energy of the vortex , and providing an estimate of the effective mass. On the other hand, the approach failed to produce the desired Berry phase in the action, which is linear in the vortex velocity , and ultimately leads to the transverse Magnus force. In the next section, we outline a different track of thoughts that directly aims to unearth the Berry phase dynamics of the vortex.

Download

Copyright Disclaimer:
This site does not store any files on its server. We only index and link to content provided by other sites. Please contact the content providers to delete copyright contents if any and email us, we'll remove relevant links or contents immediately.