abstract

In this paper, synchronising two coupled ratchet Josephson junctions subjected to a quasiperiodic field is achieved. In the limit of weak perturbation of irrational frequencies equal to the square root of the transcendental number \(\pi \) and for small damping parameters, phase locking occurs as the coupling between both junctions is increased. It turns out that the transition from non-synchronous to synchronous chaotic state does not involve attractors appearing and disappearing. The undertaken symmetry analysis of the system demonstrates the suppression of the massive phase fluctuations as the coupling rises, allowing chaos synchronisation between both junctions to take place. The calculations also reveal the persistence of the synchronous state for high coupling strengths, taking into consideration the symmetry particularity of the external drive and potential.

abstract

We study the radiative lepton–flavor violating \(l_1\rightarrow l_2\gamma \) decays in the two Higgs doublet model with localized new Higgs doublet in the Randall Sundrum background. We estimate the contributions of the KK modes of new Higgs bosons and left (right) handed charged lepton doublets (singlets) on the branching ratios of the decays considered. We observe that there is an enhancement in the branching ratios with the addition of new Higgs boson and lepton KK modes.

abstract

The form factors of the semileptonic \(B_c \rightarrow D^{0}l\nu \) transition with \(l=e, \tau \) are calculated in the framework of the three point QCD sum rules. In this case, the two gluon condensate contributions as the important correction on the non-perturbative part of the correlation function, are taken into account. The heavy quark effective theory limits of the form factors are also computed. The branching fractions of these decays are also evaluated and compared with the predictions of the other non-perturbative approaches.

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In the present paper, that is the second part devoted to the construction of an electroweak model based on a nonlinear realization of the gauge group SU(2) \(\otimes \) U(1), we study the tree-level vertex functional with all the sources necessary for the functional formulation of the relevant symmetries (Local Functional Equation, Slavnov–Taylor identity, Landau Gauge Equation) and for the symmetric removal of the divergences. The Weak Power Counting criterion is proven in the presence of the novel sources. The local invariant solutions of the functional equations are constructed in order to represent the counterterms for the one-loop subtractions. The bleaching technique is fully extended to the fermion sector. The neutral sector of the vector mesons is analyzed in detail in order to identify the physical fields for the photon and the \(Z\) boson. The identities necessary for the decoupling of the unphysical modes are fully analyzed. These latter results are crucially bound to the Landau gauge used throughout the paper.

abstract

The regularized signum-Gordon potential has a smooth minimum and is linear in the modulus of the field value for higher amplitudes. The \(Q\)-ball solutions in this model are investigated. Their existence for charges large enough is demonstrated. In three dimensions numerical solutions are presented and the absolute stability of large \(Q\)-balls is proved. It is also shown, that the solutions of the regularized model approach uniformly the solution of the unregularized signum-Gordon model. From the stability of \(Q\)-balls in the regularized model follows the stability of the solutions in the original theory.

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The recent experimental estimate for \(\tau \) lepton mass comes significantly near to a theoretical value proposed by us in 1992. We recall our argumentation supporting this proposal.

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We update our 2006–2007 results for FCNC processes in the Littlest Higgs model with T-parity (LHT). The removal of the logarithmic UV cutoff dependence in our previous results through a new contribution to the \(Z^0\)-penguin diagrams identified by Goto et al. and del Aguila et al. , while making the deviations from the SM expectations in the quark sector less spectacular, still allows for sizable new physics effects in \(K\to \pi \nu \bar \nu \) and \(K_L\to \pi ^0 \ell ^+\ell ^-\) decays and in the CP-asymmetry \(S_{\psi \phi }\) with the latter unaffected by the new contribution. We extend our analysis by a study of the fine-tuning required to fit the data on \(\varepsilon _K\) and by the inclusion of the decay \(K_L\to \mu ^+\mu ^-\). A number of correlations can distinguish this model from the custodially protected Randall–Sundrum model analysed recently. We also reconsider lepton flavour violating decays, including now a discussion of fine-tuning. While the \(\ell _i\to \ell _j\gamma \) decays are unaffected by the removal of the logarithmic cutoff dependence, the branching ratios for decays with three leptons in the final state, like \(\mu \to 3 e\) are lowered by almost an order of magnitude. In spite of this, the pattern of lepton flavour violation in the LHT model can still be distinguished from the one in supersymmetric models.

abstract

A simple and general prescription for evaluating unambiguously the sign of the grand canonical trace of quasi-particle statistical density operators (the so-called sign ambiguity in taking the square root of determinants) is given. Sign ambiguities of this kind appear in the evaluation of the grand canonical partition function projected to good quantum numbers (angular momentum, parity and particle number) in the Hartree–Fock–Bogoliubov approximation at finite temperature, since traces are usually expressed as the square root of determinants. A comparison is made with the numerical continuity method.

abstract

In this research we have studied the effect of ground state quadrupole and hexadecapole deformation of \(^{35}\)Cl on the calculation of the interacting potential and the heavy ion fusion cross-section of \(^{35}\)Cl+\(^{92}\)Zr system. The results that are obtained based on the Double Folding method show that the height of fusion barrier strongly depends on the orientation between two interacting nuclei. Also the calculated cross-sections are in a better agreement with the experimental data in comparison to those calculated assuming that the interacting nuclei are spherical in their ground state.

abstract

The information flow with time lag is investigated to fulfill the efficient functioning of communication in networks. As one crucial factor to determine the processing ability of nodes, the information flow with potential time lag is modeled by co-processing diffusion which couples the continuous time processing and the discrete diffusing dynamics. Exact results on master equation and stationary state are achieved to disclose the formation and control of congestion which results from the time lag. Besides, some statistical properties are obtained to provide well understanding on the co-processing diffusion, e.g., memorylessness of the information flow. Moreover, numerical simulations suggest that many scale-free network systems undergo a special convention from free diffusion state to congestion due to the variety of processing ability.

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The appearance of the Big Bounce (BB) in the evolution of the Universe is analyzed in the setting of loop quantum cosmology (LQC). Making use of an idea of a minimum length turns classical Big Bang into BB. We argue why the spectrum of the kinematical area operator of loop quantum gravity cannot be used for the determination of this length. We find that the fundamental length, at the present stage of development of LQC, is a free parameter of this model.