condensate is totally dominated by gain and loss. In this work, we will focus on single-mode steady-state solutions and therefor make the ansatz $\Psi(\vec{x},t) = \Psi(\vec{x}) \exp( - {\mathrm{i}}\omega t)$, where $\hbar \omega$ is the condensate energy. However, in experimental realizations more than one condensate mode can exist. For any further details we refer to Appendix \[sec:theory\_detailsmodel\].

Disorder Effects
----------------

### Infinite condensate size

Before we discuss a finite size polariton BEC we would like to consider a homogeneously excited condensate ($\xi_P \to \infty$), such that the reservoir function [Eq. ]{} is a constant in space. We will i) review disorder effects on an equilibrium condensate [@Nattermann.2008; @Falco.2009], and ii) describe differences to a polariton BEC (driven dissipative condensate) [@Janot.2013].

*Equilibrium condensate i):* The disorder potential attempts to pin the condensate into its minima, whereby the energy costs for density deformations (kinetic term in [Eq. ]{}) have to be compensated. The balance of pinning and kinetic energy determines the density Larkin length ${\mathcal{L}_{\mathrm{n}}}\approx \sqrt{\pi} \: \hbar^2 / m \: \xi_V V_0$ [@ImryMa.1975; @Nattermann.2008; @Falco.2009]. On the other hand, for a sufficiently large interaction energy $n_0U$ the disorder gets screened. [@Falco.2009] The ratio of healing to Larkin length, $\xi/{\mathcal{L}_{\mathrm{n}}}\sim \kappa$, describes 