Instituto de Ciencia de Materiales de Madrid
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The interplay of chaos and dissipation in driven quantum systems

Sigmund Kohler
Dissertation (Universität Augsburg, 1999)

Bistable quantum systems show in parameter regimes with mixed regular/chaotic dynamics a characteristic phenomenon: chaotic tunneling - coherent transport between regular islands which are separated by a chaotic layer. In this process, quantum mechanical states which are localized in chaotic regions of phase space, serve as a bridge between regular regions. The fact that chaotic states are typically delocalized, results in enhanced transport - for the present case in larger tunneling rates. As the associated spectral feature, one finds crossings of chaotic singlets with regular (tunnel) doublets. The influence of dissipation and the related decoherence on this tunnel phenomenon is studied in this work. The harmonically driven double well potential served as a model. It turned out that chaotic tunneling is accompanyed by enhanced decoherence and that the dynamics involves by far more than two levels. In the long term limit it results in a steady flow between all states whose mean energy is below the barrier. While the influence of the driving has been treated exactly within a Floquet formalism, it was for an efficient description of the dissipative effects neccessary to restrict ourselves to weak dissipation. The applicability of the approximations known from literature, namely Born-Markov and rotating-wave approximation, has been investigated and a modified approach based on the Floquet theorem has been derived. Its quality has been studied by means of an exactly solvable model, the parameterically driven harmonic oscillator. For this model system we derived analytical solutions of the different master equations.

[ICMM-CSIC] [Condensed Matter Theory]
last modified: 23.11.2017 by Sigmund Kohler