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We analyze theoretically the role of the exciton-phonon interactions inphenomena related to the Josephson effect between two spatially separatedexciton and exciton-polariton condensates. We consider the role of thedephasing introduced by phonons in such phenomena as Josephson tunneling,self-trapping and spontaneous polarization separation. In the regime of cwpumping we find a remarkable bistability effect arising from exciton- excitoninteractions as well as regimes of self- sustained regular and chaoticoscillations.

Phonon-mediated Josephson oscillations in excitonic and polaritonic condensates