2016
DOI: 10.1103/physrevb.94.104521
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Lattice duality for the compact Kardar-Parisi-Zhang equation

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… Show more

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Cited by 30 publications
(44 citation statements)
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“…It was found in numerical simulations [24] that at low density, vortex-antivortex pairs proliferate, where at higher density they bind together, resembling the equilibrium case. A renormalization group study on the other hand found qualitative differences at large scales [25,26], due to a modification of the vortex-antivortex interactions out of equilibrium. Some experimental indications for a transition between exponential and algebraic decay of correlation functions have been obtained [27,28].…”
Section: Introductionmentioning
confidence: 99%
“…It was found in numerical simulations [24] that at low density, vortex-antivortex pairs proliferate, where at higher density they bind together, resembling the equilibrium case. A renormalization group study on the other hand found qualitative differences at large scales [25,26], due to a modification of the vortex-antivortex interactions out of equilibrium. Some experimental indications for a transition between exponential and algebraic decay of correlation functions have been obtained [27,28].…”
Section: Introductionmentioning
confidence: 99%
“…Due to this non-linear term, the vortex interaction is exponentially screened at large distances -thus, the ordered phase ceases to exist. This finding is particularly relevant, since the cKPZ equation is the long-wavelength description of a vast variety of systems, ranging from "polar active smectics" or "moving stripes" [11], to driven-dissipative condensates such as exciton-polaritons [3,[8][9][10][12][13][14][15][16][17][18][19], synchronization in arrays of limit-cycle oscillators [20], and limit-cycle phases that emerge from a Hopf bifurcation [21][22][23][24][25] such phases have attracted a lot of attention recently and could be coined dissipative time crystals [26].…”
mentioning
confidence: 99%
“…It is an interesting open question how the logarithmic dependence of the vortex field (3) in the SA regime affects the interaction at asymptotic distances. Electrodynamic duality and vortex interaction.-The vortex interaction can be calculated explicitly within a dual electrodynamic formalism [3,15]. This calculation treats the non-linearity in Eq.…”
mentioning
confidence: 99%
“…In the immiscible phase, the different components occupy different spatial regions. Due to the fact that all the couplings in the system are local, one naturally expects that the two-component DOC system reduces to two independent single-component ones with the properties revealed in previous investigations [17][18][19][20][22][23][24].…”
Section: Long Wavelength Properties Of the Two-component Doc In The Mmentioning
confidence: 94%
“…They can be realized, for instance, in exciton-polariton systems [1][2][3][4][5][6][7][8][9]. On the one hand, recent theoretical investigations [17][18][19][20][21][22][23][24] on singlecomponent DOCs have revealed a new class of nonequilibrium phenomena, that are related to a variant of the famous Kardar-Parisi-Zhang (KPZ) equation [25] in nonequilibrium statistical physics. On the other hand, investigations on multi-component Bose-Einstein condensates (BECs), realized mainly in ultracold atom experiments, have shown that the inter-component couplings generally give rise to very rich physics [26, and the references therein].…”
Section: Introductionmentioning
confidence: 99%