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Asymptotic dynamics of a Hadamard walk of two non-interacting quantum particles on a dynamically percolated finite line or a circle is investigated. We construct a basis of the attractor space of the corresponding random-unitary dynamics and prove the completeness of our solution. In comparison to the one-particle case, the structure of the attractor space is much more complex, resulting in intriguing asymptotic dynamics. General results are illustrated on two examples. First, for circles of length not divisible by 4 the boundary conditions reduces the number of attractors considerably, allowing for fully analytic solution. Second, we investigate line of length 4 and determine the asymptotic cycle of reduced coin states and position distributions, focusing on the correlations between the two particles. Our results show that a random unitary evolution, which is a combination of quantum dynamics and a classical stochasticity, leads to correlations between initially uncorrelated particles. This is not possible for purely unitary evolution of non-interacting quantum particles. The shared dynamically percolated graph can thus be considered as a weak form of interaction.

We report on the noise performance characteristics of magnetic sensors using both magnetic tunnel junction (MTJ) and giant magnetoresistance (GMR) elements. Each sensor studied has a notably different noise and detectivity. Of the sensors we measured, those based on GMR multilayers have the lowest noise and detectivity. However, the GMR sensor also has a significantly smaller linear range. To make a direct comparison between sensors we scale the linear operating ranges of each sensor to be the same. This is the phenomenological equivalent of modifying the flux concentration. Upon scaling the low frequency detectivity of the TMR sensors becomes essentially equal to that of the GMR sensor. Using the scaling approach we are able to place the detectivity in the context of other key parameters, namely size and power consumption. Lastly, we use this technique to examine the upper limit for magnetoresistive sensor performance based on a notional MTJ sensor using present record setting TMR values., Comment: Accepted to Applied Physics Letters, 6 pages, 7 figures

The radiative corrections to double-Dalitz ($P\to\bar{\ell}\ell\bar{\ell'}\ell'$) decays are revisited and completed up to next-to-leading order in QED, finding mild differences with respect to previous studies. These might be relevant for extracting information about the mesons transition form factors, which play an important role in determining the hadronic light-by-light contribution to the anomalous magnetic moment of the muon., Comment: Contribution to the MESON 2018 proceedings

This work refers to the new formula for the superpotential Uikl in conservation laws in general relativity satisfying the integral and differential conservation laws within the Schwarzschild metric. The new superpotential is composed of two terms. The first term is based on Mollers concept and its a function of the metric gik and its first derivative only. The second term is the antisymmetric tensor density of weight plus one and it consists of higher derivatives of the metric gik. Although the new superpotential consists of higher derivatives of the metric gik it might bring a new evaluation of the conservative quantities in general relativity, Comment: 6 pages, 1 table

The MesonNet International Workshop was held in the Laboratori Nazionali di Frascati from September the 29th to October the 1st, 2014, being the concluding meeting of the MesonNet research network within EU HadronPhysics3 project. MesonNet is a research network focused on light meson physics gathering experimentalist and theoreticians from Europe and abroad. An overview of the research projects related to the scope of the network is presented in these mini-proceedings., Comment: 93 pages, 12 figures, MesonNet 2014 International Workshop, 29/9 - 1/10 Frascati LNF INFN

The dispersive approach based only on very general principles, unitarity, analyticity and crossing symmetry, combined with chiral counting enables to construct fully relativistic model-independent representations of the eta and K three-pion decays valid up to and including two-loop corrections. Here we demonstrate the procedure on the eta->3pi^0 decay. We perform possible matchings of our dispersive approach with the two-loop ChPT result and briefly discuss corresponding predictions of the Dalitz plot slope parameter alpha., Comment: To appear in the proceedings of "6th International Workshop on Chiral Dynamics", CD09, July 2009, Bern, Switzerland. 6 pages. PoS style

We analyze the asymptotic dynamics of quantum systems resulting from large numbers of iterations of random unitary operations. Although, in general, these quantum operations cannot be diagonalized it is shown that their resulting asymptotic dynamics is described by a diagonalizable superoperator. We prove that this asymptotic dynamics takes place in a typically low dimensional attractor space which is independent of the probability distribution of the unitary operations applied. This vector space is spanned by all eigenvectors of the unitary operations involved which are associated with eigenvalues of unit modulus. Implications for possible asymptotic dynamics of iterated random unitary operations are presented and exemplified in an example involving random controlled-not operations acting on two qubits.

The branching ratio of the \eta->3\pi decay is an important source of information on the value of the quark mass ratio 1/R=(m_d-m_u)/(m_s-\hat m). Furthermore, isospin breaking effects in the decays K->3\pi provide information on the pion scattering lengths. The cusp effect in the K->3\pi decays is presently being analyzed by the NA48 and KTeV experiments. From the theoretical point of view, these processes have been studied by different methods. We propose a unified and relativistic treatment relying on very general principles, unitarity, analyticity and crossing symmetry, combined with chiral counting, in order to construct model-independent representations of the corresponding amplitudes that are valid at two loops. A general description of the procedure is given and is illustrated in the case of the \eta decay amplitude in the leading order in the isospin breaking., Comment: Talk given at "International Workshop on Effective Field Theories: from the pion to the upsilon", February 2009, Valencia, Spain. 8 pages. PoS style

We investigate the asymptotic dynamics of quantum networks under repeated applications of random unitary operations. It is shown that in the asymptotic limit of large numbers of iterations this dynamics is generally governed by a typically low dimensional attractor space. This space is determined completely by the unitary operations involved and it is independent of the probabilities with which these unitary operations are applied. Based on this general feature analytical results are presented for the asymptotic dynamics of arbitrarily large cyclic qubit networks whose nodes are coupled by randomly applied controlled-NOT operations., Comment: 4 pages, 2 figures

We generalise the reconstruction theorem of Stern, Sazdjian, and Fuchs based on the dispersion relations to the case of the (2 -> 2) scattering of all the pseudoscalar octet mesons (pi, K, eta). We formulate it in a general way and include also a discussion of the assumptions of the theorem. It is used to obtain the amplitudes of all such processes in the isospin limit to the one-loop order (and can be straightforwardly extended to two loops) independently on the particular power-counting scheme of the chiral perturbation theory in question. The results in this general form are presented., Comment: 25 pages, 1 figure; added one appendix and correction of typos

We discuss various aspects of resummed chiral perturbation theory, which was developed recently in order to consistently include the possibility of large vacuum fluctuations of the ss-pairs and the scenario with smaller value of the chiral condensate for N_f=3. The subtleties of this approach are illustrated using a concrete example of observables connected with pi-eta scattering. This process seems to be a suitable theoretical laboratory for this purpose due to its sensitivity to the values of the O(p^4) LEC's, namely to the values of the fluctuation parameters L4 and L6. We discuss several issues in detail, namely the choice of `good' observables and properties of their bare expansions, the `safe' reparametrization in terms of physical observables, the implementation of exact perturbative unitarity and exact renormalization scale independence, the role of higher order remainders and their estimates. We make a detailed comparison with standard chiral perturbation theory and use generalized ChPT as well as resonance chiral theory to estimate the higher order remainders., Comment: Version submitted to EPJ C

The recently developed 'Resummed' ChPT is illustrated on the case of pseudoscalar meson decay constants. We try to get an estimate of the eta decay constant, which is not well known from experiments, while using several ways including the Generalized ChPT Lagrangian to gather information beyond Standard next-to-leading order. We compare the results to published ChPT predictions, our own Standard ChPT calculations and available phenomenological estimates., Comment: Presented by M.K. at Hadron Structure'07, Modra, Slovakia, 3-7.9.2007

A six-qubit quantum network consisting of conditional unitary gates is presented which is capable of implementing a large class of covariant two-qubit quantum operations. Optimal covariant NOT operations for one and two-qubit systems are special cases contained in this class. The design of this quantum network exploits basic algebraic properties which also shed new light onto these covariant quantum processes.

The structure of all completely positive quantum operations is investigated which transform pure two-qubit input states of a given degree of entanglement in a covariant way. Special cases thereof are quantum NOT operations which transform entangled pure two-qubit input states of a given degree of entanglement into orthogonal states in an optimal way. Based on our general analysis all covariant optimal two-qubit quantum NOT operations are determined. In particular, it is demonstrated that only in the case of maximally entangled input states these quantum NOT operations can be performed perfectly., Comment: 14 pages, 2 figures

We investigate the problem of copying pure two-qubit states of a given degree of entanglement in an optimal way. Completely positive covariant quantum operations are constructed which maximize the fidelity of the output states with respect to two separable copies. These optimal copying processes hint at the intricate relationship between fundamental laws of quantum theory and entanglement., Comment: 13 pages, 7 figures

Calculations of eta->pi^0 pi^0 gamma gamma decay in Generalized chiral perturbation theory are presented. Tree level and next-to-leading corrections are involved. Sensitivity to the violation of the standard counting is discussed., Comment: 5 pages, 3 figures, Talk presented at Int. Conf. "Advanced Studies Institute - Symmetries and Spin" (SPIN-Praha-2003),July 12 - 19, 2003, Prague, Czech Republic, to be published in proceedings

Calculations of eta->pi^0 pi^0 gamma gamma decay in generalized chiral perturbation theory are presented. Tree level and some of next-to-leading corrections are involved. Sensitivity to the deviations from the standard chiral perturbation theory is discussed., Comment: 7 pages, 6 figures, Talk presented at Int. Conf. Hadron Structure '02, Herlany, Slovakia, September 22-27, 2002

We calculate the amplitude of pi-eta scattering in generalized chiral perturbation theory at the order O(p^4) and present preliminary results of the numerical analysis of the S-wave scattering length, which seems to be particularly sensitive to the deviations from the standard case., Comment: 7 pages, 2 figures, Talk presented at Int. Conf. Hadron Structure '02, Herlany, Slovakia, September 22-27, 2002. Typos and one reference corrected

A calculation of the Dalitz decay in next-to-leading order in chiral perturbation theory of two flavour case extended by virtual photons is presented. The whole kinematic sector is covered and realistic experimental situation is discussed., Comment: 8 pages, 5 figures; presented at Int. Conf. Hadron Structure '02, September 2002, Slovakia

Two solutions of the coupled Einstein-Maxwell field equations are found by means of the Horsky-Mitskievitch generating conjecture. The vacuum limit of those obtained classes of spacetimes is the seed gamma-metric and each of the generated solutions is connected with one Killing vector of the seed spacetime. Some of the limiting cases of our solutions are identified with already known metrics, the relations among various limits are illustrated through a limiting diagram. We also verify our calculation through the Ernst potentials. The existence of circular geodesics is briefly discussed in the Appendix., Comment: 20 pages, LaTeX2e, 8 eps-figures. to be published in Czech. J. Phys

The method based on the Horsky-Mitskievitch conjecture is applied to the Levi-Civita vacuum metric. It is shown, that every Killing vector is connected with a particular class of Einstein-Maxwell fields and each of those classes is found explicitly. Some of obtained classes are quite new. Radial geodesic motion in constructed space-times is discussed and graphically illustrated in the Appendix., Comment: 18 pages, 4 figures, to be published in Czechoslovak Journal of Physics

The point-splitting regularization technique for composite operators is discussed in connection with anomaly calculation. We present a pedagogical and self-contained review of the topic with an emphasis on the technical details. We also develop simple algebraic tools to handle the path ordered exponential insertions used within the covariant and non-covariant version of the point-splitting method. The method is then applied to the calculation of the chiral, vector, trace, translation and Lorentz anomalies within diverse versions of the point-splitting regularization and a connection between the results is described. As an alternative to the standard approach we use the idea of deformed point-split transformation and corresponding Ward-Takahashi identities rather than an application of the equation of motion, which seems to save the complexity of the calculations., Comment: 42 pages, LATEX 2.09, a4wide