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Fidelity Decay in Chaotical and Random Systems

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Kohler H.

Acta Physica Polonica A

2011

vol. 120

issue 6A

A-119-A-126

Fidelity is the overlap of wave functions with the same initial state propagated in time by slightly different Hamiltonians. Its behavior depends crucially on the choice of the initial wave function state. We review two cases: first, the initial state is random. In this case a simple analytic relation with parametric spectral correlations can be established. The latter quantity is completely determined by the spectral data and can therefore be measured, without knowledge about the wave function. Second, the initial state is an eigenstate of the unperturbed system. In this case fidelity is identical to the survival probability. We find unexpected features like revival and non-ergodicity. In this case fluctuations around the mean are large and the full fidelity distribution becomes a non-trivial function. The full fidelity distribution can be calculated in the long time limit and for small perturbations.

Asymmetry Induced Localization

100%

Kohler H.

Acta Physica Polonica A

2013

vol. 124

issue 6

1053-1059

We consider a two-level system, which couples via non-commuting operators to two independent oscillator baths. When the coupling is symmetric, the renormalized hopping matrix element is finite even for infinitely strong coupling strength. The two-level system is in a delocalized phase. For finite coupling strength a localization transition occurs for a critical asymmetry angle, which separates the localized from the delocalized phase. Using the method of flow equations we are able to monitor real time dynamics.

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2 Acta Physica Polonica A

1 2013

1 2011

2 Kohler H.

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Fidelity Decay in Chaotical and Random Systems

Asymmetry Induced Localization