Universität zu Köln

Sieberer, L. M., Wachtel, G., Altman, E. and Diehl, S. (2016). Lattice duality for the compact Kardar-Parisi-Zhang equation. Phys. Rev. B, 94 (10). COLLEGE PK: AMER PHYSICAL SOC. ISSN 2469-9969

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Abstract

A comprehensive theory of the Kosterlitz-Thouless transition in two-dimensional superfluids in thermal equilibrium can be developed within a dual representation which maps vortices in the superfluid to charges in a Coulomb gas. In this framework, the dissociation of vortex-antivortex pairs at the critical temperature corresponds to the formation of a plasma of free charges. The physics of vortex unbinding in driven-dissipative systems such as fluids of light, on the other hand, is much less understood. Here, we make a crucial step to fill this gap by deriving a transformation that maps the compact Kardar-Parisi-Zhang (KPZ) equation, which describes the dynamics of the phase of a driven-dissipative condensate, to a dual electrodynamic theory. The latter is formulated in terms of modified Maxwell equations for the electromagnetic fields and a diffusion equation for the charges representing vortices in the KPZ equation. This mapping utilizes an adaption of the Villain approximation to a generalized Martin-Siggia-Rose functional integral representation of the compact KPZ equation on a lattice.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Sieberer, L. M. UNSPECIFIED UNSPECIFIED UNSPECIFIED Wachtel, G. UNSPECIFIED UNSPECIFIED UNSPECIFIED Altman, E. UNSPECIFIED UNSPECIFIED UNSPECIFIED Diehl, S. UNSPECIFIED UNSPECIFIED UNSPECIFIED
URN:	urn:nbn:de:hbz:38-262020
DOI:	10.1103/PhysRevB.94.104521
Journal or Publication Title:	Phys. Rev. B
Volume:	94
Number:	10
Date:	2016
Publisher:	AMER PHYSICAL SOC
Place of Publication:	COLLEGE PK
ISSN:	2469-9969
Language:	English
Faculty:	Unspecified
Divisions:	Unspecified
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language GINZBURG-LANDAU EQUATION; BACTERIAL COLONIES; GROWING INTERFACES; VORTEX DYNAMICS; SYSTEMS; CHARGE; MEDIA; FILMS; FIELD Multiple languages Materials Science, Multidisciplinary; Physics, Applied; Physics, Condensed Matter Multiple languages
Refereed:	Yes
URI:	http://kups.ub.uni-koeln.de/id/eprint/26202