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 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

Channel cross-correlations in transport through complex media

Measuring transmission between four antennas in microwave cavities, we investigate directly the channel cross-correlations $C$ of the cross sections $\sigma^{ab}$ from antenna at $\vec{r}_a$ to antenna $\vec{r}_b$. Specifically we look for the $C_\Sigma$ and $C_\Lambda$, where the only difference is that $C_\Lambda$ has none of the four channels in common, whereas $C_\Sigma$ has exactly one channel in common. We find experimentally that these two channel cross-correlations are anti-phased as a function of the channel coupling strength, as predicted by theory. This anti-correlation is essential to give the correct values for the universal conductance fluctuations. To obtain a good agreement between experiment and predictions from random matrix theory the effect of absorption had to be included.Comment: 6 pages, 5 figure

Fidelity decay for local perturbations: microwave evidence for oscillating decay exponents

We study fidelity decay in classically chaotic microwave billiards for a local, piston-like boundary perturbation. We experimentally verify a predicted non-monotonic cross-over from the Fermi Golden Rule to the escape-rate regime of the Loschmidt echo decay with increasing local boundary perturbation. In particular, we observe pronounced oscillations of the decay rate as a function of the piston position which quantitatively agree with corresponding theoretical results based on a refined semiclassical approach for local boundary perturbations

Précipitation de carbonate, datation U/Th et varations isotopiques de l'Uranium d'une plateforme de travertin holocène à Bad Langelsalza - Bassin de Thuringe, Allemagne

International audienceTravertine and calcareous tufa deposits, are important archives for Quaternary continental climate and archaeology. Here we present a comprehensive study on Holocene travertine deposition in the Thuringia basin based on a detailed survey of U-series measurements and dating that demonstrates rapid accumulation of carbonate during the early Holocene until 8000 years (up to 8 mm yr-1) followed by significant change in tra-vertine accumulation that ended around 5800 years BP at the investigated site. We further demonstrate that systematic changes of the U-isotopic composition through time occur in agreement with major changes in travertine accumulation and texture, which are likely to reflect changes of spring water U-isotopic composition rather than U-series system opening or contamination with non-carbonate particles.Les travertins et les tufs calcaires constituent des archives importantes pour les études sur le climat continental quaternaire et l’Archéologie. Nous présentons l’étude de la formation d’un travertin holocène du bassin de Thuringe, basée sur un exposé détaillé des données uranium-thorium et des âges U-Th obtenus, qui démontrent une accumulation rapide du carbonate pendant le début de l’Holocène jusque vers 8000 ans (jusqu’à 8 mm par an) suivie par un changement significatif dans le rythme d’accumulation du travertin qui s’achève vers 5800 ans BP sur le site étudié. Nous démontrons ensuite que les changements systématiques dans la composition isotopique de l’uranium au cours du temps sont en accord avec les variations majeures de texture et d’accumulation du travertin et reflètent les changements de composition isotopique de l’uranium des eaux de source plutôt qu’une ouverture du système des séries de l’uranium voire une contamination par des particules non carbonatées

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 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