and the gradient of the condensate phase. Since the current is not constant, the phase cannot vary uniformly in space, and thus a random current configuration gives rise to a spatially fluctuating phase. We note that in this work the term ’fluctuations’ will be used for random spatial inhomogeneities. The correlation length, over which the phase typically varies by $2\pi$, is given by ${\mathcal{L}_{\phi}}\approx \sqrt{2}\pi \, {\mathcal{L}_{\mathrm{n}}}/ \alpha$. This scale can be obtained by a generalized Imry-Ma argument [@Janot.2013]: a condensate current flowing out of (or into) a region of diameter ${\mathcal{L}_{\phi}}$ is generated by an effective source (or sink) determined through an area average of multiple random sources and sinks. In contrast to an equilibrium condensate ($\alpha \to 0$ with ${\mathcal{L}_{\phi}}\to \infty$), the phase fluctuations occurring in the case ${\mathcal{L}_{\phi}}< \infty$ destroy the quasi-long-range order of the condensate. As a consequence of these phase fluctuations, the superfluid stiffness vanishes in the thermodynamic limit even for weak disorder, and a superfluid behavior is only present below a finite length scale, namely the superfluid depletion length ${\mathcal{L}_{s}}\approx \sqrt{2} \pi \, {\mathcal{L}_{\mathrm{n}}}/ \alpha^2$. [@Janot.2013]

### Finite condensate size

From the analysis above we conclude that in a disordered environment a condensate of 