Random matrix description of decaying quantum systems

This contribution describes a statistical model for decaying quantum systems (e.g. photo-dissociation or -ionization). It takes the interference between direct and indirect decay processes explicitely into account. The resulting expressions for the partial decay amplitudes and the corresponding cross sections may be considered a many-channel many-resonance generalization of Fano's original work on resonance lineshapes [Phys. Rev 124, 1866 (1961)]. A statistical (random matrix) model is then introduced. It allows to describe chaotic scattering systems with tunable couplings to the decay channels. We focus on the autocorrelation function of the total (photo) cross section, and we find that it depends on the same combination of parameters, as the Fano-parameter distribution. These combinations are statistical variants of the one-channel Fano parameter. It is thus possible to study Fano interference (i.e. the interference between direct and indirect decay paths) on the basis of the autocorrelation function, and thereby in the regime of overlapping resonances. It allows us, to study the Fano interference in the limit of strongly overlapping resonances, where we find a persisting effect on the level of the weak localization correction.Comment: 16 pages, 2 figure

Scattering fidelity in elastodynamics

The recent introduction of the concept of scattering fidelity, causes us to revisit the experiment by Lobkis and Weaver [Phys. Rev. Lett. 90, 254302 (2003)]. There, the ``distortion'' of the coda of an acoustic signal is measured under temperature changes. This quantity is in fact the negative logarithm of scattering fidelity. We re-analyse their experimental data for two samples, and we find good agreement with random matrix predictions for the standard fidelity. Usually, one may expect such an agreement for chaotic systems only. While the first sample, may indeed be assumed chaotic, for the second sample, a perfect cuboid, such an agreement is more surprising. For the first sample, the random matrix analysis yields a perturbation strength compatible with semiclassical predictions. For the cuboid the measured perturbation strength is much larger than expected, but with the fitted values for this strength, the experimental data are well reproduced.Comment: 4 page

The decay of photoexcited quantum systems: a description within the statistical scattering model

The decay of photoexcited quantum systems (examples are photodissociation of molecules and autoionization of atoms) can be viewed as a half-collision process (an incoming photon excites the system which subsequently decays by dissociation or autoionization). For this reason, the standard statistical approach to quantum scattering, originally developed to describe nuclear compound reactions, is not directly applicable. Using an alternative approach, correlations and fluctuations of observables characterizing this process were first derived in [Fyodorov YV and Alhassid Y 1998 Phys. Rev. A 58, R3375]. Here we show how the results cited above, and more recent results incorporating direct decay processes, can be obtained from the standard statistical scattering approach by introducing one additional channel.Comment: 7 pages, 2 figure

Natron glass production and supply in the late antique and early medieval Near East: The effect of the Byzantine-Islamic transition

Palestine and Egypt supplied the Mediterranean and Europe with virtually all of its glass for most of the first millennium CE. While the Muslim conquest in the 7th century saw major political and economic adjustment, immediate changes to material culture appear to have been minimal. This paper examines the impact of the Byzantine-Islamic transition on the natron glass industry of Palestine from the 7th to 12th century. A series of 133 well-contextualised glass vessels from selected excavations in modern day Israel have been analysed for major, minor and trace elements using LA-ICP-MS. These glasses are assigned to previously established primary production groups, allowing the elucidation of the chronology of key changes in glass production in the region. Results indicate a relatively abrupt compositional change in the late 7th - early 8th centuries, covering the reforming reigns of al-Malik and al-Walid, which marks the end of “Byzantine” glass production and the establishment of the furnaces at Bet Eli'ezer. At about this time there was an influx of glass of an Egyptian composition. Production of Bet Eli'ezer type glass appears to have been limited to a short time span, less than 50 years, after which natron glass production in Palestine ceased. Plant ash glass is first encountered in the late 8th-early 9th century, probably as a result of reduced local natron glass production creating the conditions in which plant ash glass technology was adopted. Egypt continued to produce natron glass for up to a century after its demise in Palestine. It is reasoned that the change and then collapse in natron glass production in Palestine may well have been as a consequence of a reduction in the quantities of available natron. This affected Palestine first, and Egypt up to 100 years later, which suggests that the factors causing the reduction in natron supply originated at the source and were long term and gradual, not short term events

A glass workshop in ‘Aqir, Israel and a new type of compositional contamination

Materials associated with a secondary workshop of early Byzantine date (4th-5th centuries) were unearthed in excavations by the Israel Antiquities Authority in ‘Aqir, central Israel. Fragments of furnace structure, production debris and glass vessels have been analysed by scanning electron microscopy with energy dispersive X-ray analysis (SEM-EDS) and thin-section petrography. The results suggest that the workshop melted raw glass chunks of similar composition to the primary glass made at Apollonia, Israel, to produce secondary glass products. Some glass vessels associated with the furnace are of different composition, and some of these may represent material brought in as cullet for recycling. The furnace was built with ceramic bricks comprising alluvial-type clay with inclusions of quartz sand, probably added as temper. It was fired by potash-rich fuel to approximately 1100°C. Lime mortar was used either to cement the gaps between mudbricks or to line the furnace as a parting layer, and it has introduced a previously unrecognised type of contamination in glass of the period, mainly of Fe2O3 and CaO. The contamination may be identified in glass vessel assemblages elsewhere but is not ubiquitous. As its origin relates to the furnace structure, its occurrence may depend upon chronology or geography and further work is needed to resolve this issue

Glass production at Jalame, Israel: Process, composition and relationship to Roman glass in Europe

Following an initial micro-XRF assay, 42 samples of glass from the twentieth-century excavations of the fourth-century CE production site at Jalame, Israel, were selected and analysed by EPMA, with subsets for trace elements by LA-ICP-MS (n=29 samples) and for Hf isotopes by MC-ICP-MS (n=6). Comparison of major elements for ten samples originally measured in Brill (1988) was good, although the earlier SiO2 values are slightly high. Analyses of furnace debris and contaminated glass imply that glass furnaces were made of, or lined with a lime-rich material, leading to contamination by CaO, rather than Al2O3. This confirms that higher alumina contents measured for Jalame glass relative to Roman Mn-decolourised glass of first-third century Europe are significant and it is suggested that the source of the earlier Roman glass lies further North on the eastern Mediterranean coast. A wide range of trace elements are shown to have entered the glass with the addition of manganese, so caution should be exercised when interpreting trace element and isotopic data on glass with significant amounts of Mn, although the effects on REE and some of the lithophiles most often used in provenancing appear minor or insignificant in Jalame glass with MnO below 1.3 wt%. For example, the hafnium isotope composition of the Jalame material does not appear to have been significantly affected and falls within the previously determined Levantine range, distinguishable from Egyptian glass. Associated trace elements indicate that two Mn sources were exploited and this raises the possibility of further investigation of Mn sources in early glass production. The wide range of added manganese suggests problems in obtaining a homogeneous batch and it is suggested that (a) a single initially inhomogeneous furnace load melted to a range of colours, which were subsequently colour-sorted as chunks, and/or (b) the recycling of poorly fused manganese-decolourised glass into later manganese-free batches resulted in the observed variation. The cobalt pigment used was the high-nickel late antique type and allows the introduction of this source to be pushed back from the sixth to the fourth century CE. The use of antimony in glassmaking ceased at around the same time, and it is speculated that these changes were related

Functionalization of PET track-etched membranes by UV-induced graft (co)polymerization for detection of heavy metal ions in water

Nowadays, water quality monitoring is an essential task since environmental contamination and human exposure to heavy metals increased. Sensors that are able to detect ever lower concentrations of heavy metal ions with greater accuracy and speed are needed to effectively monitor water quality and prevent poisoning. This article shows studies of the modification of flexible track-etched membranes as the basis for the sensor with various polymers and their influence on the accuracy of detection of copper, cadmium, and lead ions in water. We report the UV-induced graft (co)polymerization of acrylic acid (AA) and 4-vinylpyridine (4-VPy) on poly(ethylene terephthalate) track-etched membrane (PET TeMs) and use them after platinum layer sputtering in square wave anodic stripping voltammetry (SW-ASV) for detection of Cu2+, Cd2+, and Pb2+. Optimal conditions leading to functionalization of the surface and retention of the pore structure were found. Modified membranes were characterized by SEM, FTIR, X-ray photoelectron spectroscopy (XPS) and colorimetric analysis. The dependence of the modification method on the sensitivity of the sensor was shown. Membrane modified with polyacrylic acid (PET TeMs-g-PAA), poly(4-vinylpyridine) (PET TeMs-g-P4VPy), and their copolymer (PET TeMs-g-P4VPy/PAA) with average grafting yield of 3% have been found to be sensitive to μg/L concentration of copper, lead, and cadmium ions. Limits of detection (LOD) for sensors based on PET TeMs-g-PAA are 2.22, 1.05, and 2.53 μg/L for Cu2+, Pb2+, and Cd2+, respectively. LODs for sensors based on PET TeMs-g-P4VPy are 5.23 μg/L (Cu2+), 1.78 μg/L (Pb2+), and 3.64 μg/L (Cd2+) μg/L. PET TeMs-g-P4VPy/PAA electrodes are found to be sensitive with LODs of 0.74 μg/L(Cu2+), 1.13 μg/L (Pb2+), and 2.07 μg/L(Cd2+). Thus, it was shown that the modification of membranes by copolymers with carboxylic and amino groups leads to more accurate detection of heavy metal ions, associated with the formation of more stable complexes. © 2019 by the authors.Ministry of Education and Science of the Republic of KazakhstanMinistry of Education and Science of the Republic of KazakhstanFunding: The research was funded by the Ministry of Energy of the Republic of Kazakhstan (technological program, #74 on 02.04.2018).Acknowledgments: The research was funded by the Ministry of Energy of the Republic of Kazakhstan (technological program, #74 on 02.04.2018)

Fano interference and cross-section fluctuations in molecular photodissociation

We derive an expression for the total photodissociation cross section of a molecule incorporating both indirect processes that proceed through excited resonances, and direct processes. We show that this cross section exhibits generalized Beutler-Fano line shapes in the limit of isolated resonances. Assuming that the closed system can be modeled by random matrix theory, we derive the statistical properties of the photodissociation cross section and find that they are significantly affected by the direct processes. We identify a unique signature of the direct processes in the cross-section distribution in the limit of isolated resonances.Comment: 4 pages, 4 figure

Signatures of the correlation hole in total and partial cross sections

In a complex scattering system with few open channels, say a quantum dot with leads, the correlation properties of the poles of the scattering matrix are most directly related to the internal dynamics of the system. We may ask how to extract these properties from an analysis of cross sections. In general this is very difficult, if we leave the domain of isolated resonances. We propose to consider the cross correlation function of two different elastic or total cross sections. For these we can show numerically and to some extent also analytically a significant dependence on the correlations between the scattering poles. The difference between uncorrelated and strongly correlated poles is clearly visible, even for strongly overlapping resonances.Comment: 25 pages, 13 Postscript figures, typos corrected and references adde

Generalized Entanglement as a Natural Framework for Exploring Quantum Chaos

We demonstrate that generalized entanglement [Barnum {\em et al.}, Phys. Rev. A {\bf 68}, 032308 (2003)] provides a natural and reliable indicator of quantum chaotic behavior. Since generalized entanglement depends directly on a choice of preferred observables, exploring how generalized entanglement increases under dynamical evolution is possible without invoking an auxiliary coupled system or decomposing the system into arbitrary subsystems. We find that, in the chaotic regime, the long-time saturation value of generalized entanglement agrees with random matrix theory predictions. For our system, we provide physical intuition into generalized entanglement within a single system by invoking the notion of extent of a state. The latter, in turn, is related to other signatures of quantum chaos.Comment: clarified and expanded version accepted by Europhys. Let