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

A random matrix approach to decoherence

In order to analyze the effect of chaos or order on the rate of decoherence in a subsystem, we aim to distinguish effects of the two types of dynamics by choosing initial states as random product states from two factor spaces representing two subsystems. We introduce a random matrix model that permits to vary the coupling strength between the subsystems. The case of strong coupling is analyzed in detail, and we find no significant differences except for very low-dimensional spaces.Comment: 11 pages, 5 eps-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

Generic spectral properties of right triangle billiards

This article presents a new method to calculate eigenvalues of right triangle billiards. Its efficiency is comparable to the boundary integral method and more recently developed variants. Its simplicity and explicitness however allow new insight into the statistical properties of the spectra. We analyse numerically the correlations in level sequences at high level numbers (>10^5) for several examples of right triangle billiards. We find that the strength of the correlations is closely related to the genus of the invariant surface of the classical billiard flow. Surprisingly, the genus plays and important role on the quantum level also. Based on this observation a mechanism is discussed, which may explain the particular quantum-classical correspondence in right triangle billiards. Though this class of systems is rather small, it contains examples for integrable, pseudo integrable, and non integrable (ergodic, mixing) dynamics, so that the results might be relevant in a more general context.Comment: 18 pages, 8 eps-figures, revised: stylistic changes, improved presentatio

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)

Simulation of static and random errors on Grover's search algorithm implemented in a Ising nuclear spin chain quantum computer with few qubits

We consider Grover's search algorithm on a model quantum computer implemented on a chain of four or five nuclear spins with first and second neighbour Ising interactions. Noise is introduced into the system in terms of random fluctuations of the external fields. By averaging over many repetitions of the algorithm, the output state becomes effectively a mixed state. We study its overlap with the nominal output state of the algorithm, which is called fidelity. We find either an exponential or a Gaussian decay for the fidelity as a function of the strength of the noise, depending on the type of noise (static or random) and whether error supression is applied (the 2pi k-method) or not.Comment: 18 pages, 8 figures, extensive revision with new figure

Fidelity and level correlations in the transition from regularity to chaos

Mean fidelity amplitude and parametric energy--energy correlations are calculated exactly for a regular system, which is subject to a chaotic random perturbation. It turns out that in this particular case under the average both quantities are identical. The result is compared with the susceptibility of chaotic systems against random perturbations. Regular systems are more susceptible against random perturbations than chaotic ones.Comment: 7 pages, 1 figur

Stability of quantum motion and correlation decay

We derive a simple and general relation between the fidelity of quantum motion, characterizing the stability of quantum dynamics with respect to arbitrary static perturbation of the unitary evolution propagator, and the integrated time auto-correlation function of the generator of perturbation. Surprisingly, this relation predicts the slower decay of fidelity the faster decay of correlations is. In particular, for non-ergodic and non-mixing dynamics, where asymptotic decay of correlations is absent, a qualitatively different and faster decay of fidelity is predicted on a time scale 1/delta as opposed to mixing dynamics where the fidelity is found to decay exponentially on a time-scale 1/delta^2, where delta is a strength of perturbation. A detailed discussion of a semi-classical regime of small effective values of Planck constant is given where classical correlation functions can be used to predict quantum fidelity decay. Note that the correct and intuitively expected classical stability behavior is recovered in the classical limit hbar->0, as the two limits delta->0 and hbar->0 do not commute. In addition we also discuss non-trivial dependence on the number of degrees of freedom. All the theoretical results are clearly demonstrated numerically on a celebrated example of a quantized kicked top.Comment: 32 pages, 10 EPS figures and 2 color PS figures. Higher resolution color figures can be obtained from authors; minor changes, to appear in J.Phys.A (March 2002

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