<p>Gapless phase modes in non-equilibrium condensates fall within the Kardar-Parisi-Zhang (KPZ) universality class, but key single-component symmetries do not clearly generalise to the multicomponent case. We discuss the phase diagram of coupled KPZ equations describing the low-energy theory of a <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="42005_2025_2233_Article_IEq1.gif" Format="GIF" Height="16" Rendition="HTML" Resolution="72" Type="Linedraw" Width="18" /> </InlineMediaObject> <EquationSource Format="TEX">\({{\mathbb{Z}}}_{2}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mrow> <mi mathvariant="double-struck">Z</mi> </mrow> <mrow> <mn>2</mn> </mrow> </msub> </math></EquationSource> </InlineEquation> degenerate driven-dissipative condensate with global <i>U</i>(1)&#xa0;×&#xa0;<i>U</i>(1) symmetry. In the homogeneous condensate regime, a dynamical renormalisation group (RG) analysis in one dimension reveals that coupled stochastic complex Ginsburg-Landau equations exhibit an emergent stationary distribution, enforcing the KPZ dynamical exponent <i>z</i>&#xa0;=&#xa0;3/2 and roughness exponent <i>χ</i>&#xa0;=&#xa0;1/2 for both components. In specific parameter regimes relevant to polaritons, the RG fixed point offers a transformation to decoupled KPZ equations. By tuning the intercomponent coupling, the system offers non-KPZ regimes, including a fragmentation transition, and a non-thermal spacetime vortex phase driven by the KPZ non-linear terms. Our findings have broad implications for experiments and understanding multicomponent KPZ systems in the long-wavelength limit.</p>

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Multicomponent Kardar-Parisi-Zhang universality in degenerate coupled condensates

  • Harvey Weinberger,
  • Paolo Comaron,
  • Marzena H. Szymańska

摘要

Gapless phase modes in non-equilibrium condensates fall within the Kardar-Parisi-Zhang (KPZ) universality class, but key single-component symmetries do not clearly generalise to the multicomponent case. We discuss the phase diagram of coupled KPZ equations describing the low-energy theory of a \({{\mathbb{Z}}}_{2}\) Z 2 degenerate driven-dissipative condensate with global U(1) × U(1) symmetry. In the homogeneous condensate regime, a dynamical renormalisation group (RG) analysis in one dimension reveals that coupled stochastic complex Ginsburg-Landau equations exhibit an emergent stationary distribution, enforcing the KPZ dynamical exponent z = 3/2 and roughness exponent χ = 1/2 for both components. In specific parameter regimes relevant to polaritons, the RG fixed point offers a transformation to decoupled KPZ equations. By tuning the intercomponent coupling, the system offers non-KPZ regimes, including a fragmentation transition, and a non-thermal spacetime vortex phase driven by the KPZ non-linear terms. Our findings have broad implications for experiments and understanding multicomponent KPZ systems in the long-wavelength limit.