Instituto de Ciencia de Materiales de Madrid
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Driven tunneling: Chaos and decoherence

Peter Hänggi, Sigmund Kohler, and Thomas Dittrich
Lecture Notes in Physics 547, 125 (2000)

Chaotic tunneling in a driven double-well system is investigated in absence as well as in the presence of dissipation. As the constitutive mechanism of chaos-assisted tunneling, we focus on the dynamics in the vicinity of three-level crossings in the quasienergy spectrum. They are formed when a tunnel doublet, located on a pair of symmetry-related tori in the classical phase space, approaches a chaotic singlet in energy. The coherent quantum dynamics near the crossing, in particular the enhanced tunneling that involves the chaotic singlet state as a "step stone", is described satisfactorily by a three-state model. It fails, however, for the corresponding dissipative dynamics, because incoherent transitions due to the interaction with the environment indirectly couple the three states in the crossing to the remaining quasienergy states. We model dissipation by coupling the double well, the driving included, to a heat bath. The time dependence of the central system, with a quasienergy spectrum containing exponentially small tunnel splittings, requires special considerations when applying the Born-Markov and rotating-wave approximations to derive a master equation for the density operator. We discuss the effect of decoherence on the now transient chaos-assisted tunneling: While decoherence is accelerated practically independent of temperature near the center of the crossing, it can be stabilzed with increasing temperature at a chaotic-state induced exact crossing of the ground-state quasienergies. Moreover the asymptotic amount of coherence left within the vicinity of the crossing is enhanced if the temperature is below the splitting of the avoided crossing; but becomes diminished when temperature raises above the splitting (chaos-induced coherence or incoherence, respectively). The asymptotic state of the driven dissipative quantum dynamics partially resembles the, possibly strange, attractor of the corresponding damped driven classical dynamics, but also exhibits characteristic quantum effects.

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last modified: 15.3.2024 by Sigmund Kohler