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We consider effects of a long-wavelength disorder potential on the ZeroConductance State (ZCS) of the microwave-irradiated 2D electron gas. Assuming auniform Hall conductivity, we construct a Lyapunov functional and derivestability conditions on the domain structure of the photo-generated fields. Wesolve the resulting equations for a general one-dimensional and certaintwo-dimensional disorder potentials, and find non-zero conductances,photo-voltages, and circulating dissipative currents. In contrast, weak whitenoise disorder does not destroy the ZCS, but induces mesoscopic currentfluctuations.Comment: 4 pages, 2 colour figure

Steady States of a Microwave-Irradiated Quantum-Hall Gas