Scattering approach to fidelity decay in closed systems and parametric level correlations

This paper is based on recent work which provided an exact analytical description of scattering fidelity experiments with a microwave cavity under the variation of an antenna coupling [K\"ober et al., Phys. Rev. E 82, 036207 (2010)]. It is shown that this description can also be used to predict the decay of the fidelity amplitude for arbitrary Hermitian perturbations of a closed system. Two applications are presented: First, the known result for global perturbations is re-derived, and second, the exact analytical expression for the perturbation due to a moving S-wave scatterer is worked out. The latter is compared to measured data from microwave experiments, which have been reported some time ago. Finally, we generalize an important relation between fidelity decay and parametric level correlations to arbitrary perturbations.Comment: 20 pages, 2 figures, research article, (v2: stylistic changes, ref. added

A trivial observation on time reversal in random matrix theory

It is commonly thought that a state-dependent quantity, after being averaged over a classical ensemble of random Hamiltonians, will always become independent of the state. We point out that this is in general incorrect: if the ensemble of Hamiltonians is time reversal invariant, and the quantity involves the state in higher than bilinear order, then we show that the quantity is only a constant over the orbits of the invariance group on the Hilbert space. Examples include fidelity and decoherence in appropriate models.Comment: 7 pages 3 figure

Monomial integrals on the classical groups

This paper presents a powerfull method to integrate general monomials on the classical groups with respect to their invariant (Haar) measure. The method has first been applied to the orthogonal group in [J. Math. Phys. 43, 3342 (2002)], and is here used to obtain similar integration formulas for the unitary and the unitary symplectic group. The integration formulas turn out to be of similar form. They are all recursive, where the recursion parameter is the number of column (row) vectors from which the elements in the monomial are taken. This is an important difference to other integration methods. The integration formulas are easily implemented in a computer algebra environment, which allows to obtain analytical expressions very efficiently. Those expressions contain the matrix dimension as a free parameter.Comment: 16 page

Fidelity amplitude of the scattering matrix in microwave cavities

The concept of fidelity decay is discussed from the point of view of the scattering matrix, and the scattering fidelity is introduced as the parametric cross-correlation of a given S-matrix element, taken in the time domain, normalized by the corresponding autocorrelation function. We show that for chaotic systems, this quantity represents the usual fidelity amplitude, if appropriate ensemble and/or energy averages are taken. We present a microwave experiment where the scattering fidelity is measured for an ensemble of chaotic systems. The results are in excellent agreement with random matrix theory for the standard fidelity amplitude. The only parameter, namely the perturbation strength could be determined independently from level dynamics of the system, thus providing a parameter free agreement between theory and experiment

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

The multilevel trigger system of the DIRAC experiment

The multilevel trigger system of the DIRAC experiment at CERN is presented. It includes a fast first level trigger as well as various trigger processors to select events with a pair of pions having a low relative momentum typical of the physical process under study. One of these processors employs the drift chamber data, another one is based on a neural network algorithm and the others use various hit-map detector correlations. Two versions of the trigger system used at different stages of the experiment are described. The complete system reduces the event rate by a factor of 1000, with efficiency $\geq$95% of detecting the events in the relative momentum range of interest.Comment: 21 pages, 11 figure

A random matrix theory of decoherence

Random matrix theory is used to represent generic loss of coherence of a fixed central system coupled to a quantum-chaotic environment, represented by a random matrix ensemble, via random interactions. We study the average density matrix arising from the ensemble induced, in contrast to previous studies where the average values of purity, concurrence, and entropy were considered; we further discuss when one or the other approach is relevant. The two approaches agree in the limit of large environments. Analytic results for the average density matrix and its purity are presented in linear response approximation. The two-qubit system is analysed, mainly numerically, in more detail.Comment: 20 pages, 2 figure

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

Learning domain-invariant classifiers for infant cry sounds

The issue of domain shift remains a problematic phenomenon in most real-world datasets and clinical audio is no exception. In this work, we study the nature of domain shift in a clinical database of infant cry sounds acquired across different geographies. We find that though the pitches of infant cries are similarly distributed regardless of the place of birth, other characteristics introduce peculiar biases into the data. We explore methodologies for mitigating the impact of domain shift in a model for identifying neurological injury from cry sounds. We adapt unsupervised domain adaptation methods from computer vision which learn an audio representation that is domain-invariant to hospitals and is task discriminative. We also propose a new approach, target noise injection (TNI), for unsupervised domain adaptation which requires neither labels nor training data from the target domain. Our best-performing model significantly improves target accuracy by 7.2%, without negatively affecting the source domain