In the spectrum of systems showing chaos-assisted tunneling, three-state crossings are formed when a chaotic singlet intersects a tunnel doublet. We study the dissipative quantum dynamics in the vicinity of such crossings. A harmonically driven double well coupled to a bath serves as a model. Markov and rotating-wave approximations are introduced with respect to the Floquet spectrum of the time-dependent central system. The resulting master equation is integrated numerically. We find various types of transient tunneling, determined by the relation of the level width to the inherent energy scales of the crossing. The decay of coherent tunneling can be significantly retarded or accelerated. Modifications of the quantum asymptotic state by the crossing are also studied. The comparison with a simple three-state model shows that in contrast to the undamped case, the participation of states outside the crossing cannot be neglected in the presence of dissipation. 42.50.Lc, 03.65.Sq Typeset using REVT E X
We study the interplay between coherent transport by tunneling and diffusive transport through classically chaotic phase-space regions, as it is reflected in the Floquet spectrum of the periodically driven quartic double well. The tunnel splittings in the semiclassical regime are determined with high numerical accuracy, and the association of the corresponding doublet states to either chaotic or regular regions of the classical phase space is quantified in terms of the overlap of the Husimi distribution with the chaotic layer along the separatrix. We find a strong correlation between both quantities. They show an increase by orders of magnitude as chaotic diffusion between the wells starts to dominate the classical dynamics. We discuss semiclassical explanations for this correlation. 05.45.+b, 03.65.Sq, 73.40.Gk
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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