Scattering fidelity in chaotic microwave billiards
In this work microwave experiments are used to study the time dependent stability of quantum systems against perturbations. For flat microwave cavities the corresponding wave equation is equivalent to the Schrödinger equation, therefore measurements with so called microwave billiards are suitable fo...
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|Summary:||In this work microwave experiments are used to study the time dependent stability of quantum systems against perturbations. For flat microwave cavities the corresponding wave equation is equivalent to the Schrödinger equation, therefore measurements with so called microwave billiards are suitable for studying quantum-mechanical questions experimentally. To quantify the stability of quantum time evolution against perturbations Peres introduced the overlap of the time-evolution of the same initial state under an unperturbed and a perturbed Hamiltonian. This quantity is known as fidelity or Loschmidt echo; it can be determined in microwave billiards using the concept of scattering fidelity, which for chaotic systems and weak coupling of the measuring antenna approaches the ordinary fidelity. In the first part of this work a study of the fidelity decay in classically chaotic microwave billiard for a local, pistonlike boundary perturbation is presented. Experimentally a predicted nonmonotonic crossover from the Fermi golden rule to the escape-rate regime of the Loschmidt echo decay with increasing local boundary perturbation is verified. In particular, pronounced oscillations of the decay rate as a function of the piston position have been observed in the experiments which quantitatively agree with corresponding theoretical results based on a refined semiclassical approach for local boundary perturbations. In the second part of this work the scattering fidelity decay in a microwave billiard is studied for a perturbation, where the coupling to the outside is varied. The resulting quantity, coupling fidelity, is experimentally studied first for an attached wave guide with variable opening of a slit. Thereby the effect on the fidelity due to the change of boundary condition was larger than the effect of the change of coupling. Thus instead of using a channel for the coupling an antenna was introduced and three different terminations attached. Terminations of reflexion on open and closed end and total absorption were compared. Quantitative agreement is found with the theory, which is obtained from a modified Verbaarschot, Weidenmüller, Zirnbauer (VWZ) approach.|