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Under a strong $ac$ drive the zero-frequency linear response dissipativeresistivity $\rho_{d}(j=0)$ of a homogeneous state is allowed to becomenegative. We show that such a state is absolutely unstable. The onlytime-independent state of a system with a $\rho_{d}(j=0)<0$ is characterized bya current which almost everywhere has a magnitude $j_{0}$ fixed by thecondition that the nonlinear dissipative resistivity $\rho_{d}(j_{0}^{2})=0$.As a result, the dissipative component of the $dc$ electric field vanishes. Thetotal current may be varied by rearranging the current pattern appropriatelywith the dissipative component of the $dc$-electric field remaining zero. Thisresult, together with the calculation of Durst \emph{et. al.}, indicating theexistence of regimes of applied $ac$ microwave field and $dc$ magnetic fieldwhere $\rho_{d}(j=0)<0$, explains the zero-resistance state observed by Mani\emph{et. al.} and Zudov \emph{et. al.}.Comment: Published versio

Dynamical Symmetry Breaking as the Origin of the Zero-dc-Resistance State in an ac-Driven System