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.
We study the conservative as well as the dissipative quanta] dynamics in a harmonically driven, quartic double-well potential. In the deep quanta] regime, we find coherent modifications of tunneling, including its complete suppression. In the semiclassical regime of the conservative system, the dynamics is dominated by the interplay of tunneling and chaotic diffusion. A strong correlation exists between the tunnel splittings and the overlaps of the associated doublet states with the chaotic layer. With weak dissipation, remnants of coherent behaviour occur as transients, such as the tunneling between symmetry-related pairs of limit cycles. The coherent suppression of tunneling observed in the conservative case is stabilized by weak incoherence.The quanta] stationary states are broadened anisotropica]ly due to quantum noise, as compared to the corresponding classical attractors.
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