PACS. 05.45 -Theory and models of chaotic systems. PACS. 33.80B -Level crossing and optical pumping.PACS. 74.50 -Proximity effects, tunnelling phenomena, and Josephson effect.Abstract. -We study the quantal dynamics of a harmonically driven quartic double well in the presence of dissipation. A master equation for the reduced density operator is derived in the Floquet representation. In the classical limit, this system corresponds to a Duffing oscillator with Ohmic damping. We present numerical results for the transient time evolution and for the stationary sate. The influence of the weak dissipation on interference effects in the context of driven tunnelling is discussed on the basis of these 'results. We find that the coherent suppression of tunnelling can be stabilized by reservoir-induced noise for a suitably chosen temperature.

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