Non-stationary resonance dynamics of weakly coupled pendula

In this paper we fill the gap in understanding the non-stationary resonance dynamics of the weakly coupled pendula model, having significant applications in numerous fields of physics such as super- conducting Josephson junctions, Bose-Einstein condensates, DNA, etc.. While common knowledge of the problem is based on two alternative limiting asymptotics, namely the quasi-linear approach and the approximation of independent pendula, we present a unified description in the framework of new concept of Limiting Phase Trajectories (LPT), without any restriction on the amplitudes of oscillation. As a result the conditions of intense energy exchange between the pendula and transition to energy localization are revealed in all possible diapason of initial conditions. By doing so, the roots and the domain of chaotic behavior are clarified as they are associated with this transition while simultaneously approaching the pendulum separatrix. The analytical findings are corrobo- rated by numerical simulations. By considering the simplest case of two weakly coupled pendula, we pave the ground for new opening possibilities of significant extensions in both fundamental and applied directions.Comment: 7 pages, 7 figure

Decays of open charmed mesons in the extended Linear Sigma Model

We enlarge the so-called extended linear Sigma model (eLSM) by including the charm quark according to the global $U(4)_r\times U(4)_l$ chiral symmetry. In the eLSM, besides scalar and pseudoscalar mesons, also vector and axial-vector mesons are present. Almost all the parameters of the model were fixed in a previous study of mesons below 2 GeV. In the extension to the four-flavor case, only three additional parameters (all of them related to the bare mass of the charm quark) appear. We compute the (OZI-dominant) strong decays of open charmed mesons. The results are compatible with the experimental data, although the theoretical uncertainties are still large.Comment: 3 pages, 1 table, prepared for proceedings of the 13th International Workshop on Meson Production, Properties and Interaction, 29th May - 3rd June 2014, Cracow, POLAN

Phenomenology of charmed mesons in the extended Linear Sigma Model

We study the so-called extended linear sigma model for the case of four quark flavors. This model is based on global chiral symmetry and dilatation invariance and includes, besides scalar and pseudoscalar mesons, vector and axial-vector mesons. Most of the parameters of the model have been determined in previous work by fitting properties of mesons with three quark flavors. Only three new parameters, all related to the current charm quark mass, appear when introducing charmed mesons. Surprisingly, within the accuracy expected from our approach, the masses of open charmed mesons turn out to be in quantitative agreement with experimental data. On the other hand, with the exception of $J/\psi$, the masses of charmonia are underpredicted by about 10\%. It is remarkable that our approach correctly predicts (within errors) the mass splitting between spin-0 and spin-1 negative-parity open charm states. This indicates that, although the charm quark mass breaks chiral symmetry quite strongly explicitly, this symmetry still seems to have some influence on the properties of charmed mesons.Comment: 19 pages, 1 figure, 3 table

The solution of the quantum A1A_1 T-system for arbitrary boundary

We solve the quantum version of the $A_1$ $T$-system by use of quantum networks. The system is interpreted as a particular set of mutations of a suitable (infinite-rank) quantum cluster algebra, and Laurent positivity follows from our solution. As an application we re-derive the corresponding quantum network solution to the quantum $A_1$ $Q$-system and generalize it to the fully non-commutative case. We give the relation between the quantum $T$-system and the quantum lattice Liouville equation, which is the quantized $Y$-system.Comment: 24 pages, 18 figure

Helicons in Weyl semimetals

Helicons are transverse electromagnetic waves propagating in three-dimensional (3D) electron systems subject to a static magnetic field. We present a theory of helicons propagating through a 3D Weyl semimetal. Our approach relies on the evaluation of the optical conductivity tensor from semiclassical Boltzmann transport theory, with the inclusion of certain Berry curvature corrections that have been neglected in the earlier literature (such as the one due to the orbital magnetic moment). We demonstrate that the axion term characterizing the electromagnetic response of Weyl semimetals dramatically alters the helicon dispersion with respect to that in nontopological metals. We also discuss axion-related anomalies that appear in the plasmon dispersion relation.Comment: 5 pages, 1 figur

Discrete integrable systems, positivity, and continued fraction rearrangements

In this review article, we present a unified approach to solving discrete, integrable, possibly non-commutative, dynamical systems, including the $Q$- and $T$-systems based on $A_r$. The initial data of the systems are seen as cluster variables in a suitable cluster algebra, and may evolve by local mutations. We show that the solutions are always expressed as Laurent polynomials of the initial data with non-negative integer coefficients. This is done by reformulating the mutations of initial data as local rearrangements of continued fractions generating some particular solutions, that preserve manifest positivity. We also show how these techniques apply as well to non-commutative settings.Comment: 24 pages, 2 figure