Vortex-Phonon Interaction in the Kosterlitz-Thouless Theory

Abstract

The "canonical" variables of the Kosterlitz-Thouless theory--fields ${\Phi }_0(\mathbf{r})$ and $\varphi (\mathbf{r})$, generally believed to stand for vortices and phonons (or their XY equivalents, like spin waves, etc.) turn out to be neither vortices and phonons, nor, strictly speaking, {\it canonical} variables. The latter fact explains paradoxes of (i) absence of interaction between ${\Phi }_0$ and $\varphi$, and (ii) non-physical contribution of small vortex pairs to long-range phase correlations. We resolve the paradoxes by explicitly relating ${\Phi }_0$ and $\varphi$ to canonical vortex-pair and phonon variables.

4 pages, RevTex

References in corpus (1)

• Vortex--Phonon Interaction

Cited by in corpus (2)

• Theory of decay of superfluid turbulence in the low-temperature limit
• Vacuum tunneling of vortices in two-dimensional ${}^4$He superfluid films